Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C43×C19 · Schur multiplier (H2) = C22×C42 |
| direct product | C19×#10701 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C2×D4 |
| commutator | C4 | C43×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C23×C19 | C2×C22⋊C4 |
| prime radical | C24×C19 | C2×D4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ C22×C42×C19 ◁ G | |
998 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23)(28,29)(30,36)(31,39)(32,35)(33,38)(34,40)(37,42)(41,43);(28,30)(29,33,35,41)(31,38)(32,37)(34,36,39,42)(40,43);(24,25,26,27)(30,37)(33,41)(36,42)(38,43)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3689);