Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C24 |
| direct product | C59×#26501 |
| 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 | |
724 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)(9,10,15,19)(11,13,22,24)(12,23,18,14)(16,21,20,17)(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)(9,11,14,17,15,22,23,21)(10,16,18,13,19,20,12,24);(9,12,14,10,15,18,23,19)(11,20,17,24,22,16,21,13);(1,3,4,8)(2,6,5,7)(9,13,23,16,15,24,14,20)(10,17,12,11,19,21,18,22)2714 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 19489);