Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33501 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C19 | C24 |
| commutator | C22 | C23×C8×C19 |
| Frattini, cosocle | C2×C8 | C24×C19 |
| socle | C22×C19 | C23×C8 |
| prime radical | C23×C19 | C22×C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C19 ◁ G | |
444 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 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)(23,26)(24,27)(25,30)(29,34)(31,33)(32,35)(36,37,39,44,40,45,49,57,41,43,50,55,51,56,61,65)(38,42,47,53,48,54,60,64,46,52,58,62,59,63,66,67);(20,22,24,30)(21,25,27,28)(23,31,32,29)(26,34,35,33)(36,38)(37,42)(39,47)(40,48)(41,46)(43,52)(44,53)(45,54)(49,60)(50,58)(51,59)(55,62)(56,63)(57,64)(61,66)(65,67);(20,23,24,32)(21,26,27,35)(22,29,30,31)(25,33,28,34)(37,43)(38,46)(44,55)(45,56)(47,58)(48,59)(57,65)(60,66);(21,27)(25,28)(26,35)(33,34)(38,46)(42,52)(47,58)(48,59)(53,62)(54,63)(60,66)(64,67)1444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26489);