Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C59 · Schur multiplier (H2) = C22×C4 |
| direct product | C59×#9860 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | #127 |
| commutator | C42 | C22×C4×C59 |
| Frattini, cosocle | C2×C42 | C23×C59 |
| socle | C22×C59 | #390 |
| prime radical | C59×#3147 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C2×C42×C59 ◁ G | |
498 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 3 generators on 83 points:
(1,2)(3,7)(4,8)(5,6)(9,10,12,14,13,17,20,16)(11,18,21,15,19,22,24,23)(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);(1,3,7,2,5,8,4,6)(10,14,17,16)(11,19)(15,18,23,22)(21,24);(2,6)(3,8)(9,11,20,24,13,19,12,21)(10,15,14,22,17,23,16,18)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 2848);