Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#17789 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C22×D4 |
| commutator | C4 | C23×C8×C19 |
| Frattini, cosocle | C42 | C24×C19 |
| socle | C22×C19 | C22×C4⋊C4 |
| prime radical | C2×#41×C19 | C2×C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C4×#41×C19 ◁ G | |
734 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2432 |
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)(29,33)(31,34)(35,39)(36,40)(38,41)(42,43);(28,29,34,40,32,36,31,33)(30,35,41,43,37,42,38,39);(28,30)(29,35)(31,38)(32,37)(33,39)(34,41)(36,42)(40,43);(30,37)(35,42)(38,41)(39,43)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10777);