Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C59 · Schur multiplier (H2) = C24 |
| direct product | C59×#11237 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | #124 |
| commutator | C22×C4 | C22×C4×C59 |
| Frattini, cosocle | C23×C4 | C23×C59 |
| socle | C22×C59 | #400 |
| prime radical | C24×C59 | C2×Q8 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C23×C4×C59 ◁ G | |
622 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 3 generators on 95 points:
(2,3)(5,6,10,14,11,15,9,25)(7,16,19,28,20,27,18,12)(8,21,23,30,24,36,22,13)(17,26,33,31,34,29,32,35)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(1,2,4,3)(5,7,9,18,11,20,10,19)(6,12,14,16,15,28,25,27)(8,17,22,32,24,34,23,33)(13,29,21,35,30,26,36,31);(1,3,4,2)(5,8,9,22,11,24,10,23)(6,13,14,21,15,30,25,36)(7,17,18,32,20,34,19,33)(12,26,16,31,28,29,27,35)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 4225);