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×#13320 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C2×C19×#472 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ C2×C19×#131 ◁ G | |
540 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)(25,31)(26,36)(27,39)(28,29)(32,48)(33,40)(34,46)(35,47)(37,41)(38,44)(42,43)(45,50)(49,52)(51,54);(20,21)(22,23)(24,25,30,35)(26,32,38,51)(27,40,43,46)(28,34,29,33)(31,42,47,39)(36,52,44,50)(37,54,41,48)(45,53,49,55);(21,23)(24,26)(25,32)(27,41)(28,44)(29,36)(30,38)(31,45)(33,52)(34,50)(35,51)(37,43)(39,55)(40,48)(42,53)(46,54)(47,49)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6308);