Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13030 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13032 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1879 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C2×C19×#509 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
476 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)(20,21,26,32,34,37,25,30,28,33,43,36,27,22,24,31)(23,38,40,29,46,47,39,35,42,51,44,49,41,50,45,48);(20,22,34,33,28,37,27,21)(23,35,41,49,42,48,46,29)(24,31,26,36,25,30,43,32)(38,40,47,45,51,44,50,39);(20,23)(21,29)(22,35)(24,40)(25,44)(26,45)(27,46)(28,42)(30,50)(31,47)(32,38)(33,49)(34,41)(36,51)(37,48)(39,43)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6020);