Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#17438 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C22×D4 |
| commutator | C4 | C23×C8×C19 |
| Frattini, cosocle | C42 | C24×C19 |
| socle | C22×C19 | C22×C22⋊C4 |
| prime radical | C2×C19×H(5,𝔽2) | C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C4×#41×C19 ◁ G | |
1290 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,24,23,25,26,27)(28,29)(30,34)(31,33)(32,36)(35,39)(37,41)(38,40)(42,43);(29,33)(31,39)(34,40)(35,36)(38,43)(41,42);(28,30)(29,34)(31,38)(32,37)(33,40)(35,42)(36,41)(39,43);(30,37)(34,41)(38,43)(40,42)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10426);