Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C23 |
| direct product | C59×#33270 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C59 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C43×C59 ◁ G | |
654 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 15104 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2)(3,8)(4,6)(5,7)(9,10)(11,13)(12,14)(15,16)(17,18,21,24)(19,25,26,32)(20,29,27,23)(22,30,31,28)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91);(1,3,5,4)(2,6,7,8)(9,11,12,15)(10,13,14,16)(19,26)(22,31)(25,32)(28,30);(17,19,27,30,21,26,20,28)(18,22,29,32,24,31,23,25);(1,4,5,3)(2,6,7,8)(10,14)(13,16)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 26258);