Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8674 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C2×C4 |
| direct product | C19×#8697 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #380 |
| commutator | C42 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C19×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
384 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)(20,21,24,27,25,23,22,26)(28,29,33,36,34,31,32,42)(30,37,40,38,41,43,39,35);(20,22,25,24)(21,26,23,27)(28,30,33,40,34,41,32,39)(29,35,42,43,31,38,36,37);(20,23)(21,25)(22,27)(24,26)(28,31)(29,34)(30,38)(32,42)(33,36)(35,41)(37,40)(39,43)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 1685);