Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8465 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#8475 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #379 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C19×#3500 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
932 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)(30,38)(31,42,44,35)(32,45)(33,37)(34,40)(36,48)(39,54,56,59)(41,52)(43,51,47,53)(46,50)(49,55,58,57);(21,24)(22,26)(28,30)(29,34)(31,39)(32,46)(33,41)(35,49)(36,52)(37,50)(38,45)(40,48)(42,58)(43,57)(44,56)(47,55)(51,54)(53,59);(21,24)(22,26)(28,31)(29,35)(30,39)(32,47)(33,44)(34,49)(36,53)(37,42)(38,54)(40,57)(41,56)(43,48)(45,51)(46,55)(50,58)(52,59)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 1463);