Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#24798 |
| 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 | |
846 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)(26,31,39,47)(27,40,43,49)(28,34,41,33)(30,38,45,37)(32,48,50,42)(36,51,54,44)(46,53,55,52);(24,26,28,37,29,39,41,38)(25,30,33,31,35,45,34,47)(27,36,42,52,43,54,48,53)(32,44,40,46,50,51,49,55);(21,23)(24,26)(25,31)(27,36)(28,37)(29,39)(30,34)(32,46)(33,45)(35,47)(38,41)(40,51)(42,52)(43,54)(44,49)(48,53)(50,55);(24,27,41,48,29,43,28,42)(25,32,34,49,35,50,33,40)(26,36,38,53,39,54,37,52)(30,44,47,55,45,51,31,46)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17786);