Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13329 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C22×D8×C19 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
578 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
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)(22,23)(28,29,33,38)(30,39,42,57)(31,35,46,53)(32,47,45,37)(34,49,51,40)(36,54,52,44)(41,58,48,55)(43,56,59,50);(21,23)(24,25)(26,27)(28,30,33,42)(29,34,38,51)(31,43,46,59)(32,48,45,41)(35,39,53,57)(36,55,52,58)(37,56,47,50)(40,54,49,44);(25,27)(29,35)(31,44)(32,45)(34,39)(36,37)(38,53)(40,43)(41,48)(46,54)(47,52)(49,59)(50,58)(51,57)(55,56)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6317);