Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C59 · Schur multiplier (H2) = C2×C42 |
| direct product | C59×#23351 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C59 | C24 |
| commutator | C23 | C23×C4×C59 |
| Frattini, cosocle | C22×C4 | C24×C59 |
| socle | C23×C59 | C23×C4 |
| prime radical | C22×D4×C59 | C2×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C59 ◁ G | |
696 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 4 generators on 91 points:
(2,5)(3,7)(9,10)(11,15)(12,14)(13,16)(17,18,22,26,21,23,20,25)(19,27,29,32,28,24,30,31)(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);(1,2)(3,8)(4,5)(6,7)(11,16)(13,15)(18,23)(19,28)(25,26)(29,30);(2,5)(6,8)(9,11,12,16)(10,13,14,15)(17,19,21,28)(18,24,23,27)(20,30,22,29)(25,32,26,31);(1,3,4,7)(2,6,5,8)(10,14)(13,15)(17,20,21,22)(18,25,23,26)(19,29,28,30)(24,31,27,32)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 16339);