Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#17327 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C19 | C24 |
| commutator | C22 | C22×C42×C19 |
| Frattini, cosocle | C42 | C24×C19 |
| socle | C22×C19 | C22×C42 |
| prime radical | C24×C19 | C42 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C42×C19 ◁ G | |
836 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)(20,21,23,27,25,26,24,22)(28,29,31,35,32,34,38,41)(30,33,37,40,36,39,42,43);(20,22,24,26,25,27,23,21)(28,30)(29,33)(31,37)(32,36)(34,39)(35,40)(38,42)(41,43);(29,34)(33,39)(35,41)(40,43);(21,26)(22,27)(29,34)(30,36)(35,41)(37,42)1900 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10315);