Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9331 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#9331 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #386 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| prime radical | C19×#525 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
438 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 67 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,25,29,33)(23,30,31,26)(24,27)(28,32)(34,35)(36,37)(38,47)(39,51,54,61)(40,55)(41,45)(42,46)(43,49)(44,53,60,52)(48,63,65,57)(50,58)(56,59)(62,64,67,66);(20,22)(21,25,27,33)(23,28)(24,29)(26,32,30,35)(31,34)(36,38,40,49,42,50,41,56)(37,43,45,47,46,59,55,58)(39,48,53,66,54,65,52,64)(44,57,61,62,60,63,51,67);(20,23)(21,26)(22,28)(24,31)(25,32)(27,30)(29,34)(33,35)(36,39)(37,44)(38,48)(40,53)(41,52)(42,54)(43,57)(45,61)(46,60)(47,62)(49,66)(50,65)(51,55)(56,64)(58,67)(59,63)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 2319);