Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19755 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#19825 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#1619 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C42×C11 ◁ G | |
642 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,17)(15,23)(18,24)(19,20)(21,27)(25,26)(28,29)(30,34)(31,38)(32,40)(33,36)(35,37)(39,42)(41,43);(12,13,16,20)(14,18,22,26)(15,19,23,17)(21,25,27,24)(28,30,33,32)(29,34,36,40)(31,37,39,41)(35,42,43,38);(12,14,16,22)(13,18,20,26)(15,21,23,27)(17,24,19,25)(28,31,33,39)(29,35,36,43)(30,37,32,41)(34,42,40,38);(13,19)(15,23)(17,20)(18,25)(21,27)(24,26)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 12813);