Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#20829 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C22×D4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C22×C19 | C22×C4⋊C4 |
| prime radical | C24×C19 | C2×Q8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C19×#117 ◁ G | |
718 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 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)(28,29,33,37,34,38,32,48)(30,35,42,51,40,50,41,57)(31,43,46,53,47,59,45,36)(39,54,56,52,44,58,55,49);(21,24)(25,27)(28,30)(29,35)(31,44)(32,41)(33,42)(34,40)(36,52)(37,51)(38,50)(39,47)(43,58)(45,56)(46,55)(48,57)(49,53)(54,59);(28,31,32,45,34,47,33,46)(29,36,37,43,38,53,48,59)(30,39,41,55,40,44,42,56)(35,49,51,54,50,52,57,58);(20,22,23,26)(21,25,24,27)(30,40)(35,50)(39,44)(41,42)(49,52)(51,57)(54,58)(55,56)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13817);