Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C59 · Schur multiplier (H2) = C24 |
| direct product | C59×#21629 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | C22×D4 |
| commutator | C2×C4 | C23×C4×C59 |
| Frattini, cosocle | C22×C4 | C24×C59 |
| socle | C22×C59 | C2×C4×D4 |
| prime radical | C2×#41×C59 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C2×#97×C59 ◁ G | |
730 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 4 generators on 83 points:
(1,2)(3,8)(4,6)(5,7)(9,10,13,17,14,11,18,16)(12,15,21,23,20,19,24,22)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83);(1,3,5,4)(2,6,7,8)(12,20)(15,19)(21,24)(22,23);(9,11)(10,14)(12,19)(13,16)(15,20)(17,18)(21,22)(23,24);(1,4,5,3)(2,6,7,8)(9,12,13,21,14,20,18,24)(10,15,17,23,11,19,16,22)3776 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 14617);