A003802
Order of universal Chevalley group A_4(q), q = prime power.
Original entry on oeis.org
9999360, 237783237120, 258492255436800, 56653740000000000, 187035198320488089600, 4638226007491010887680, 78660280796419613491200, 9760263542825295931200000, 539322992420959314658621440, 78898131096541739561779200000
Offset: 1
- J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. xvi.
- H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 131.
-
f[m_, n_] := m^(n (n + 1)/2) Product[m^k - 1, {k, 2, n + 1}]; f[#, 4] & /@ Select[Range[2, 16], PrimePowerQ] (* Michael De Vlieger, Sep 18 2015 *)
A003804
Order of universal Chevalley group A_6(q), q = prime power.
Original entry on oeis.org
163849992929280, 67034222101339041669120, 72736898347485916060188672000, 3376566710423156250000000000000000, 35832085525362833262818017603275320524800, 21903309038581548352789123727634573903790080, 6274437692242927471137606015213542491815936000
Offset: 1
- J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. xvi.
- H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 131.
-
f[m_, n_] := m^(n (n + 1)/2) Product[m^k - 1, {k, 2, n + 1}]; f[#, 6] & /@ Select[Range[2, 10], PrimePowerQ] (* Michael De Vlieger, Sep 18 2015 *)
A220791
Number of nonsingular n X n matrices over GF(13).
Original entry on oeis.org
1, 12, 26208, 9726417792, 610296923230525440, 6471875909051511775903457280, 11598637276362103019770723830073032376320, 3512938445418644176053176560741858449740612202579886080
Offset: 0
-
[1] cat [&*[(13^n - 13^k): k in [0..n-1]]: n in [1..8]];
-
Table[Product[13^n - 13^k, {k, 0, n-1}], {n, 0, 8}]
A003803
Order of universal Chevalley group A_5 (q), q = prime power.
Original entry on oeis.org
20158709760, 42064805779476480, 1083930404878024704000, 2766118855500000000000000, 369826556020831611935738265600, 39841906041871272087686291128320, 2468438315722201136962330755072000
Offset: 1
- J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. xvi.
- H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 131.
-
f[m_, n_] := m^(n (n + 1)/2) Product[m^k - 1, {k, 2, n + 1}]; f[#, 5] & /@ Select[Range[2, 10], PrimePowerQ] (* Michael De Vlieger, Sep 18 2015 *)
A003805
Order of universal Chevalley group A_7 (q), q = prime power.
Original entry on oeis.org
5348063769211699200, 961721214905722855895197286400, 78099458182389588115529148326215680000, 103044374585338670859375000000000000000000000, 170115000551935077294273059250893063598899496222720000, 770654129255561941216424578913668563609374922170066534400
Offset: 1
- J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. xvi.
- H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 131.
-
f[m_, n_] := m^(n (n + 1)/2) Product[m^k - 1, {k, 2, n + 1}]; f[#, 7] & /@ Select[Range[2, 8], PrimePowerQ] (* Michael De Vlieger, Sep 18 2015 *)
A003806
Order of universal Chevalley group A_8 (q), q = prime power.
Original entry on oeis.org
699612310033197642547200, 124190524600592082795473760093457612800, 1341733356588640095264385107865053233298800640000, 78616578542037111790447631835937500000000000000000000000, 39573939034651534226739680064959446854442420750012276098670264320000
Offset: 1
- J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. xvi.
- H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 131.
-
f[m_, n_] := m^(n (n + 1)/2) Product[m^k - 1, {k, 2, n + 1}]; f[#, 8] & /@ Select[Range[2, 7], PrimePowerQ] (* Michael De Vlieger, Sep 18 2015 *)