Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#8402 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #120 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| socle | C22×C19 | #379 |
| prime radical | C19×#537 | C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C42×C19 ◁ G | |
716 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2432 |
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)(21,24,25,26)(28,29,32,36,33,30,37,35)(31,34,39,43,40,38,41,42);(20,21)(22,26)(23,25)(24,27)(28,30)(29,33)(31,38)(32,35)(34,40)(36,37)(39,42)(41,43);(28,31,33,40)(29,34,30,38)(32,41,37,39)(35,43,36,42)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 1390);