Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#13456 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C23×C19 | AGL(1,ℤ/8) |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
318 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)(20,21,24,26)(22,27,23,25)(28,29,31,36)(30,40,42,34)(32,35,45,51)(33,38,46,39)(37,53,52,47)(41,49,44,54)(43,58,57,50)(48,56,55,59);(20,22,24,23)(21,25,26,27)(28,30,31,42)(29,34,36,40)(32,43,45,57)(33,41,46,44)(35,50,51,58)(37,48,52,55)(38,54,39,49)(47,56,53,59);(20,23,24,22)(21,25,26,27)(29,35)(30,41)(32,47)(33,46)(34,48)(36,51)(37,39)(38,52)(40,55)(42,44)(43,57)(45,53)(49,58)(50,54)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6444);