Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13336 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
586 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(24,25)(26,37)(27,31)(28,44)(29,47)(30,36)(32,39)(33,41)(34,45)(35,43)(38,50)(40,49)(42,51)(46,54)(48,53)(52,55);(20,21)(22,23)(25,31)(26,38)(27,41)(28,45)(29,43)(32,50)(33,35)(34,47)(36,44)(37,54)(39,55)(40,48)(49,51)(52,53);(21,23)(24,26)(25,32)(27,42)(28,46)(29,48)(30,40)(31,49)(33,50)(34,53)(35,54)(36,52)(37,44)(38,43)(39,45)(41,55)(47,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6324);