Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9307 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#9314 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #386 |
| commutator | C42 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C2×#41×C19 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
406 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)(20,21,24,27,25,28,23,33)(22,29,32,34,30,35,31,26)(36,37)(38,47,50,58)(39,51)(40,45)(41,55)(42,46)(43,49,59,54)(44,52)(48,63,66,57)(53,60)(56,61)(62,64,67,65);(20,22,25,30)(21,26)(23,31,24,32)(27,29)(28,34)(33,35)(36,38,40,54,42,50,41,49)(37,43,45,58,46,59,55,47)(39,48,52,65,53,66,56,64)(44,57,60,67,61,63,51,62);(22,30)(26,34)(29,35)(31,32)(36,39)(37,44)(38,48)(40,52)(41,56)(42,53)(43,57)(45,60)(46,61)(47,62)(49,64)(50,66)(51,55)(54,65)(58,67)(59,63)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 2302);