Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#18435 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#1600 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
922 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,26)(22,30)(23,34)(27,39)(28,37)(29,35)(31,43)(33,47)(36,46)(38,42)(40,50)(41,49)(44,45)(48,51);(20,21,24,29)(22,27,31,40)(23,35,34,26)(25,28,32,41)(30,42,43,51)(33,48,45,38)(36,49,46,37)(39,44,50,47);(22,31)(23,36)(26,37)(27,40)(30,43)(33,47)(34,46)(35,49)(38,50)(39,48)(42,51)(44,45);(20,22,32,43)(21,27,41,51)(23,33,46,47)(24,31,25,30)(26,38,49,50)(28,42,29,40)(34,45,36,44)(35,48,37,39)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11423);