Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#23889 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ G | |
1648 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)(26,36)(27,41)(28,35)(29,34)(30,39)(31,43)(32,42)(33,46)(37,52)(38,47)(40,49)(44,51)(45,48)(50,54)(53,55);(24,26,29,40)(25,30,34,48)(27,38,43,53)(28,45,46,39)(31,50,41,52)(32,47,51,55)(33,49,35,36)(37,42,54,44);(21,23)(24,27)(25,31)(26,37)(28,42)(29,43)(30,47)(32,33)(34,41)(35,51)(36,50)(38,45)(39,53)(40,54)(44,46)(48,55)(49,52);(24,27)(25,32)(26,38)(28,44)(29,43)(30,47)(31,33)(34,51)(35,41)(36,52)(37,45)(39,54)(40,53)(42,46)(48,55)(49,50)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16877);