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×#13030 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1879 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C19×#3414 | 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)(20,21,24,29,25,31,41,45,26,32,23,30,40,49,38,27)(22,33,35,46,36,48,42,47,37,44,34,51,43,50,39,28);(21,27,32,45)(23,38)(24,41)(25,40)(28,44,47,33)(29,31,30,49)(34,39)(35,42)(36,43)(46,48,51,50);(20,22)(21,28)(23,39)(24,42)(25,43)(26,37)(27,44)(29,48)(30,50)(31,51)(32,47)(33,45)(34,38)(35,41)(36,40)(46,49)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6018);