Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C59 · Schur multiplier (H2) = C23×C4 |
| direct product | C59×#21662 |
| 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 | C59×#532 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C2×#97×C59 ◁ G | |
738 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)(3,6)(4,5)(7,8)(9,10,14,18,15,20,13,19)(11,21,12,17,23,24,22,16)(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);(2,5)(6,8)(9,11,14,12,15,23,13,22)(10,16,19,24,20,17,18,21);(1,3,4,7)(2,6,5,8)(9,11,13,22,15,23,14,12)(10,17,18,24,20,16,19,21);(9,12,14,23,15,22,13,11)(10,17,18,24,20,16,19,21)3776 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 14650);