Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17603 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#17604 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3494 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C19×#117 ◁ G | |
1004 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)(21,26,28,39)(23,34)(27,38,42,49)(29,40,30,35)(32,46)(36,48)(41,47,43,50)(44,51);(20,21)(22,27)(23,35)(24,29)(25,30)(26,36)(28,37)(31,41)(32,47)(33,43)(34,39)(38,44)(40,48)(42,45)(46,49)(50,51);(20,22,24,33)(21,27,29,43)(23,32,34,46)(25,31,37,45)(26,38,40,50)(28,42,30,41)(35,47,39,49)(36,44,48,51);(22,31)(27,41)(32,44)(33,45)(38,47)(42,43)(46,51)(49,50)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10592);