Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#24458 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×C19×#577 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ G | |
1328 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)(20,21,22,23)(24,25)(26,31)(27,39)(28,30)(29,34)(32,40)(33,43)(35,46)(36,51)(37,44)(38,47)(41,48)(42,49)(45,50)(52,54)(53,55);(25,30)(26,35)(28,43)(32,39)(33,34)(36,50)(37,38)(40,41)(44,46)(48,49)(51,54)(52,53);(21,23)(24,26,29,38)(25,31,34,47)(27,36,42,52)(28,37,43,35)(30,44,33,46)(32,45,48,55)(39,51,49,54)(40,50,41,53);(24,27)(25,32)(26,36)(28,41)(29,42)(30,39)(31,45)(33,49)(34,48)(35,50)(37,53)(38,52)(40,43)(44,51)(46,54)(47,55)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17446);