Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9279 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#9286 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #386 |
| commutator | C42 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C23×C19 | #123 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
374 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 2432 |
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)(21,25,27,30)(22,28,29,31)(36,37,41,45,42,46,40,56)(38,47,51,58,50,62,49,43)(39,52,54,60,55,44,53,59)(48,61,65,57,64,67,63,66);(20,21,23,30,24,27,32,25)(22,26,31,34,29,35,28,33)(36,38,42,50)(37,43)(39,48,55,64)(40,49,41,51)(44,57)(45,47)(46,58)(52,66)(53,63,54,65)(56,62)(59,67)(60,61);(20,22)(21,26)(23,31)(24,29)(25,33)(27,35)(28,32)(30,34)(36,39,42,55)(37,44,46,52)(38,48,50,64)(40,54,41,53)(43,57,58,66)(45,60,56,59)(47,61,62,67)(49,65,51,63)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 2274);