Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17367 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#20730 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C24×C19 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C19×#117 ◁ G | |
1166 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)(28,29,32,37,33,36,45,50)(30,34,40,48,39,47,55,58)(31,41,42,51,43,35,44,49)(38,52,54,59,53,46,56,57);(21,24)(25,27)(28,30)(29,34)(31,38)(32,40)(33,39)(35,46)(36,47)(37,48)(41,52)(42,54)(43,53)(44,56)(45,55)(49,57)(50,58)(51,59);(28,31,33,43)(29,35,36,41)(30,38,39,53)(32,44,45,42)(34,46,47,52)(37,51,50,49)(40,56,55,54)(48,59,58,57);(20,22,23,26)(21,25,24,27)(30,39)(34,47)(38,53)(40,55)(46,52)(48,58)(54,56)(57,59)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13718);