Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9415 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#9416 |
| 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 | |
380 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)(22,29,30,33)(23,26,31,32)(24,27)(25,28)(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);(20,22,24,32,25,30,34,26)(21,23,27,33,28,31,35,29)(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)(22,27)(24,33)(25,31)(28,32)(29,34)(30,35)(36,39,42,54)(37,44,46,60)(38,48,50,65)(40,53,41,52)(43,57,59,63)(45,61,55,51)(47,62,58,67)(49,66,56,64)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 2404);