Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9914 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C59 · Schur multiplier (H2) = C23 |
| direct product | C59×#10568 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C59 | #120 |
| commutator, Frattini, cosocle | C23×C4 | C23×C59 |
| prime radical | C24×C59 | C2×D4 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C23×C4×C59 ◁ G | |
560 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 3 generators on 83 points:
(1,2,5,7)(3,8,4,6)(9,10,12,15)(11,16,13,14)(17,18)(19,21)(20,22)(23,24)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83);(1,3,5,4)(2,6,7,8)(9,11,12,13)(10,14,15,16)(17,19)(18,21)(20,23)(22,24);(1,4,5,3)(2,6,7,8)(10,14)(11,13)(15,16)(21,24)2360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 3556);