Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13313 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#13440 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #466 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C22×D8×C19 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
398 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
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)(20,21)(22,23)(24,25,30,36)(26,37,41,48)(27,31,28,44)(29,46,43,35)(32,38,50,39)(33,45,34,42)(40,47,53,51)(49,55,52,54);(25,31)(26,38)(27,42)(28,45)(29,43)(33,35)(34,46)(36,44)(37,51)(39,41)(40,55)(47,48)(49,52)(53,54);(21,23)(24,26,27,38,43,53,45,55,30,41,28,39,29,40,42,54)(25,32,33,48,46,52,44,51,36,50,34,37,35,49,31,47)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6428);