Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17405 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25×C4 |
| direct product | C19×#21751 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C24 | C24×C19 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×Q8×C19 ◁ G | |
1294 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,26)(23,25)(24,27)(28,29)(30,34)(31,41,43,35)(32,36)(33,37)(38,52,54,46)(39,47)(40,48)(42,55,57,49)(44,50)(45,51)(53,59,56,58);(20,22)(21,24)(23,27)(25,26)(28,30,33,40)(29,34,37,48)(31,38,43,54)(32,44,45,39)(35,46,41,52)(36,50,51,47)(42,56,57,53)(49,59,55,58);(22,27)(24,26)(28,31)(29,35)(30,38)(32,42)(33,43)(34,46)(36,49)(37,41)(39,53)(40,54)(44,56)(45,57)(47,58)(48,52)(50,59)(51,55);(21,25)(24,26)(28,32,33,45)(29,36,37,51)(30,39,40,44)(31,42,43,57)(34,47,48,50)(35,49,41,55)(38,53,54,56)(46,58,52,59)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14739);