Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C43×C19 · Schur multiplier (H2) = C22×C42 |
| direct product | C19×#10711 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C19 | C22⋊C4 |
| commutator | C22 | C43×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C22×C19 | C4×C22⋊C4 |
| prime radical | C24×C19 | C22×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C19 ◁ C23×C8×C19 ◁ G | |
842 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(24,25)(26,34,36,30)(27,31)(28,33)(29,32)(35,46,48,41)(37,47,50,42)(38,44)(39,43)(40,45)(49,54,55,52)(51,53);(20,21,22,23)(24,26)(25,30)(27,35)(28,37)(29,36)(31,41)(32,34)(33,42)(38,49)(39,48)(40,50)(43,46)(44,52)(45,47)(51,55)(53,54);(24,27,28,38,29,39,40,51)(25,31,33,44,32,43,45,53)(26,35,37,49,36,48,50,55)(30,41,42,52,34,46,47,54)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3699);