Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13033 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13033 |
| 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 | |
498 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)(20,21,24,29,25,30,39,47,26,31,23,37,40,49,41,28)(22,32,34,45,35,48,42,46,36,44,33,50,43,51,38,27);(20,22)(21,27,31,46)(23,38)(24,42)(25,43)(26,36)(28,44,47,32)(29,48,37,51)(30,50,49,45)(33,41)(34,39)(35,40);(21,28)(23,39)(24,41)(25,40)(27,44)(29,49)(30,37)(31,47)(32,46)(33,42)(34,38)(35,43)(45,48)(50,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6021);