Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#13412 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
430 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,22)(24,25)(26,31)(27,32)(28,45)(29,46)(30,35)(33,42)(34,43)(36,54)(37,50)(38,55)(39,48)(40,52)(41,49)(44,53)(47,51);(20,21)(22,23)(24,26,30,40)(25,31,35,52)(27,41,44,38)(28,36,42,37)(29,47,43,39)(32,49,53,55)(33,50,45,54)(34,48,46,51);(20,22,23,21)(25,32)(26,36)(27,42)(28,44)(29,43)(31,48)(33,34)(35,53)(37,40)(38,47)(39,41)(45,46)(50,54)(51,52)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6400);