Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13442 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#13442 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2054 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C2×C19×#509 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
398 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)(21,28)(22,34)(23,39)(24,25)(26,40)(30,43)(31,33)(32,41)(35,44)(36,50)(37,42)(38,48)(45,49)(47,51);(20,21)(22,35)(23,30)(24,31)(25,41)(26,43)(27,33)(28,39)(29,36)(32,40)(34,45)(37,51)(38,47)(42,46)(44,50)(48,49);(20,22,23,36,40,50,24,34,27,38,25,42,26,37,39,48)(21,29,28,35,43,49,41,51,33,46,31,47,32,45,30,44)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6430);