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×#9280 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #386 |
| commutator | C42 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C23×C19 | #121 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
382 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)(21,25,27,30)(22,28,29,31)(36,37)(38,46)(39,50,52,43)(40,53)(41,45)(42,48)(44,55)(47,60,63,67)(49,61)(51,58,54,59)(56,62,66,64)(57,65);(20,21,23,30,24,27,32,25)(22,26,31,34,29,35,28,33)(36,38,40,48,41,49,55,65)(37,42,44,46,45,57,53,61)(39,47,54,64,52,63,51,62)(43,56,59,60,50,66,58,67);(20,22)(21,26)(23,31)(24,29)(25,33)(27,35)(28,32)(30,34)(36,39,41,52)(37,43,45,50)(38,47,49,63)(40,54,55,51)(42,56,57,66)(44,59,53,58)(46,60,61,67)(48,64,65,62)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 2268);