Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24292 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#24800 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ G | |
842 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23)(24,25,29,35)(26,31,39,48)(27,40,43,51)(28,34,44,33)(30,38,46,37)(32,49,52,42)(36,53,41,45)(47,55,50,54);(24,26,28,37,29,39,44,38)(25,30,33,31,35,46,34,48)(27,36,42,54,43,41,49,55)(32,45,40,47,52,53,51,50);(21,23)(24,26)(25,31)(27,41)(28,37)(29,39)(30,34)(32,50)(33,46)(35,48)(36,43)(38,44)(40,45)(42,55)(47,52)(49,54)(51,53);(24,27,28,42,29,43,44,49)(25,32,33,40,35,52,34,51)(26,36,37,54,39,41,38,55)(30,45,31,47,46,53,48,50)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17788);