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×#13036 |
| 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)(20,21,26,31,33,36,25,30,28,32,44,45,27,22,24,35)(23,37,40,29,46,47,38,34,42,50,43,49,41,51,39,48);(20,22,33,32,28,36,27,21)(23,34,41,49,42,48,46,29)(24,35,26,45,25,30,44,31)(37,40,47,39,50,43,51,38);(20,23)(21,29)(22,34)(24,43)(25,40)(26,38)(27,46)(28,42)(30,47)(31,50)(32,49)(33,41)(35,51)(36,48)(37,45)(39,44)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6024);