Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12503 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C4 |
| direct product | C19×#12522 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C19 | #493 |
| commutator, Frattini, cosocle | C4×C8 | C23×C19 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C42×C19 ◁ C82×C19 ◁ G | |
238 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 4864 |
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)(22,28,31,35)(23,32,29,26)(25,33,34,30)(36,37)(38,46)(39,42)(40,53)(41,54)(43,49)(44,47)(45,52)(48,58)(50,65)(51,66)(55,63)(56,62)(57,67)(59,61)(60,64);(20,22,29,33,24,31,23,30)(21,25,32,35,27,34,26,28)(37,42)(43,55)(44,56)(45,54)(46,58)(53,66)(57,59)(60,65);(36,38,47,61,41,50,51,63,39,48,62,67,52,64,40,49)(37,43,53,60,45,57,56,58,42,55,66,65,54,59,44,46)1330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5510);