Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C59 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×C59×#1393 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C59 | #99 |
| commutator | C2×C4 | C2×C42×C59 |
| Frattini, cosocle | C22×D4 | C23×C59 |
| prime radical | C23×D4×C59 | C22 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C24×C59 ◁ C23×D4×C59 ◁ G | |
1154 conjugacy classes of subgroups.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 3 generators on 73 points:
(1,2)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73);(7,8)(9,12,14,11)(10,13);(3,4,5,6)(8,11,13,12)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 5568);