Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23400 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#23401 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3449 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1954 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)(26,34)(27,31)(28,40)(29,33)(30,36)(32,43)(35,51)(37,49)(38,47)(39,50)(41,45)(42,48)(44,54)(46,53)(52,55);(24,26,29,37)(25,30,33,45)(27,35,38,52)(28,41,43,36)(31,46,47,44)(32,49,40,34)(39,54,42,53)(48,55,50,51);(21,23)(24,27)(25,31)(26,35)(28,42)(29,38)(30,44)(32,50)(33,47)(34,51)(36,54)(37,52)(39,43)(40,48)(41,53)(45,46)(49,55);(27,38)(31,47)(35,52)(39,42)(44,46)(48,50)(51,55)(53,54)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16389);