Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33836 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#3285 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C4×D4×C19 ◁ C8×D4×C19 ◁ G | |
664 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 2432 |
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)(25,30)(26,34)(27,38)(28,41)(31,48)(32,52)(33,47)(35,51)(36,49)(37,44)(39,43)(42,45)(46,50)(53,54);(24,25,29,33)(26,35,37,48)(27,39,42,52)(28,43,41,32)(30,45,47,38)(31,49,51,36)(34,54,44,46)(40,53,55,50);(21,23);(24,26,29,37)(25,31,33,51)(27,40,42,55)(28,44,41,34)(30,46,47,54)(32,53,43,50)(35,52,48,39)(36,45,49,38)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26824);