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×#33842 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#3283 | 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)(24,25,30,27)(26,34,37,53)(28,41,45,52)(29,40,43,33)(31,48,38,36)(32,47,39,44)(35,54,46,50)(42,51,55,49);(24,26,30,37)(25,31,27,38)(28,42,45,55)(29,46,43,35)(32,50,39,54)(33,51,40,49)(34,52,53,41)(36,47,48,44);(21,23)(24,27,30,25)(26,31,37,38)(28,39,45,32)(29,40,43,33)(34,48,53,36)(35,49,46,51)(41,44,52,47)(42,50,55,54);(24,28)(25,32)(26,35)(27,39)(29,47)(30,45)(31,49)(33,52)(34,53)(36,48)(37,46)(38,51)(40,41)(43,44)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26830);