Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#13370 |
| 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 | |
358 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)(20,21,23,25)(22,26,27,24)(28,29)(30,39)(31,45)(32,37)(33,50)(34,38)(35,41)(36,48)(40,55)(42,52)(43,59)(44,57)(46,54)(47,53)(49,56)(51,58);(20,22,23,27)(21,24,25,26)(28,29)(30,40)(31,36)(32,50)(33,37)(34,38)(35,42)(39,55)(41,52)(43,51)(44,54)(45,48)(46,57)(47,56)(49,53)(58,59);(28,30,34,44)(29,35,38,51)(31,46,49,55)(32,43,33,42)(36,52,53,59)(37,54,50,40)(39,56,57,45)(41,47,58,48)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6358);