Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24292 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#25194 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3013 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ G | |
980 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)(24,25,30,34,31,36,29,35)(26,37,39,32,27,41,40,48)(28,43,44,33,46,50,45,51)(38,47,54,55,42,49,53,52);(20,21)(22,23)(24,26,30,39,31,27,29,40)(25,32,34,41,36,48,35,37)(28,42,44,53,46,38,45,54)(33,49,50,52,51,47,43,55);(21,23)(24,27,31,26)(25,32,36,48)(28,42,46,38)(29,40,30,39)(33,47,51,49)(34,37,35,41)(43,55,50,52)(44,54,45,53);(24,28)(25,33)(26,38)(27,42)(29,45)(30,44)(31,46)(32,47)(34,50)(35,43)(36,51)(37,52)(39,54)(40,53)(41,55)(48,49)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 18182);