Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#10318 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C19 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C42×C19 ◁ G | |
602 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(25,29)(26,27)(30,31)(32,33,37,41)(34,42,45,46)(35,40,36,39)(38,44,47,43);(21,23)(25,30)(26,27)(29,31)(32,34,37,45)(33,38,41,47)(35,44,36,43)(39,46,40,42);(24,25,28,31)(26,30,27,29)(34,43)(35,36)(38,42)(39,40)(44,45)(46,47)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3306);