Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #327 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C19 · Schur multiplier (H2) = C4 |
| direct product | C19×#7198 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C19 | C22⋊C4 |
| commutator | C2×C4 | C4×C8×C19 |
| Frattini, cosocle | C2×C4×C8 | C22×C19 |
| socle | C22×C19 | #336 |
| prime radical | C23×C19 | #97 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
192 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 2 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)(22,28,29,25)(23,27)(24,26)(30,34,35,32)(31,33)(36,37,40,45,41,46,55,63,42,47,56,64,39,44,53,61)(38,48,50,65,49,59,66,62,51,60,54,67,52,43,57,58);(20,22,23,30,24,29,31,35)(21,25,27,32,26,28,33,34)(36,38)(37,43)(39,52)(40,54)(41,49)(42,51)(44,60)(45,62)(46,48)(47,59)(50,56)(53,66)(55,57)(58,64)(61,65)(63,67)1444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 186);