Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13309 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#13466 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #469 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C2×C19 | #2065 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×C4×C19 ◁ C2×C4×C8×C19 ◁ G | |
314 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,28,33)(22,34)(23,40)(24,31,45,51)(25,30,26,48)(27,35,47,32)(29,42)(36,44)(37,50)(38,41)(39,49)(43,46);(20,22,24,36,27,38,25,46,28,39,45,40,47,29,26,37)(21,23,30,34,32,43,31,42,33,44,48,49,35,50,51,41);(20,23)(21,29)(22,35)(24,42)(25,34)(26,49)(27,50)(28,44)(30,36)(31,37)(32,39)(33,38)(40,48)(41,45)(43,47)(46,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6454);