Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#12869 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C2×D8 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C22×C19 | C2×#102 |
| prime radical | C24×C19 | SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C23×C4×C19 ◁ C23×C8×C19 ◁ G | |
404 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,25)(23,24)(26,27)(28,29,32,37,34,38,33,48)(30,39,41,55,42,56,49,53)(31,43,45,54,47,58,46,36)(35,44,50,57,52,59,51,40);(21,24)(25,27);(20,22,23,26)(21,25,24,27)(28,30)(29,35)(31,44)(32,41)(33,49)(34,42)(36,53)(37,50)(38,52)(39,43)(40,46)(45,57)(47,59)(48,51)(54,55)(56,58)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5857);