Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13337 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C2×C19×#509 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
554 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)(25,32)(26,38)(27,43)(28,46)(29,30)(33,50)(34,37)(35,44)(36,47)(40,48)(41,45)(42,54)(49,51)(53,55);(20,21)(22,23)(24,25,31,37)(26,39,42,52)(27,44,28,47)(29,36,30,35)(32,46,34,43)(33,41,50,40)(38,51,54,55)(45,53,48,49);(21,23)(24,26)(25,33)(27,45)(28,48)(29,41)(30,40)(31,42)(32,49)(34,53)(35,52)(36,39)(37,50)(38,46)(43,54)(44,55)(47,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6325);