Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18346 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18352 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#2635 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
996 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,26)(22,30)(23,34)(27,40)(28,38)(29,35)(31,46)(32,48)(33,45)(36,50)(39,41)(42,51)(43,47)(44,49);(20,21,24,29)(22,31,33,27)(23,35,34,26)(25,28,37,42)(30,43,45,41)(32,39,49,47)(36,51,50,38)(40,48,46,44);(23,36)(26,38)(32,44)(34,50)(35,51)(39,40)(46,47)(48,49);(20,22,24,33)(21,27,29,31)(23,32,34,49)(25,30,37,45)(26,39,35,47)(28,41,42,43)(36,44,50,48)(38,40,51,46)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11340);