Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9369 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#9372 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #386 |
| commutator | C42 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C19×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
390 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)(20,21,26,29,24,23,25,28)(22,30,32,34,33,27,31,35)(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);(20,22,25,32,24,33,26,31)(21,27,29,34,23,30,28,35)(36,38)(37,43,46,58)(39,48)(40,49)(41,51)(42,50)(44,57,52,66)(45,47,56,62)(53,63)(54,65)(55,64)(59,67,60,61);(20,23,24,21)(22,30,33,27)(25,28,26,29)(31,34,32,35)(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)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 2360);