Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17597 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#17629 |
| 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×#3506 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C4×D4×C19 ◁ G | |
1010 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)(21,27,29,42)(22,32)(24,38)(28,41,45,44)(30,43,31,39)(33,48)(34,35)(46,51,47,50);(20,21)(22,27)(23,28)(24,39)(25,30)(26,31)(29,40)(32,43)(33,41)(34,44)(35,50)(36,46)(37,47)(38,42)(45,49)(48,51);(20,22,26,24)(21,27,31,39)(23,34,37,48)(25,32,40,38)(28,44,47,51)(29,42,30,43)(33,36,35,49)(41,46,50,45);(20,23,26,37)(21,28,31,47)(22,33,24,35)(25,36,40,49)(27,41,39,50)(29,45,30,46)(32,48,38,34)(42,44,43,51)931 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10617);