Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24292 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C24 |
| direct product | C59×#26504 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| prime radical | C22×D8×C59 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C22×C4×C59 ◁ G | |
720 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 4 generators on 83 points:
(1,2,4,5)(3,7,8,6)(9,10,16,19)(11,20,23,13)(12,14,24,15)(17,18,21,22)(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)(6,7)(9,11,14,22,16,23,15,18)(10,17,12,20,19,21,24,13);(9,12,14,19,16,24,15,10)(11,21,22,13,23,17,18,20);(1,3,4,8)(2,6,5,7)(9,13,15,21,16,20,14,17)(10,18,24,23,19,22,12,11)2360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 19492);