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×#19858 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#459 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C42×C11 ◁ G | |
580 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,18)(14,16)(19,26)(20,24)(21,25)(22,27)(28,29)(30,34)(31,38)(32,40)(33,36)(35,37)(39,42)(41,43);(12,13,17,20)(14,18,16,24)(15,22,23,26)(19,25,27,21)(28,30,33,32)(29,34,36,40)(31,37,39,41)(35,42,43,38);(12,14,17,16)(13,18,20,24)(15,21,23,25)(19,26,27,22)(28,31)(29,35)(30,37)(32,41)(33,39)(34,42)(36,43)(38,40);(12,15,17,23)(13,19,20,27)(14,21,16,25)(18,26,24,22)(28,30,33,32)(29,34,36,40)(31,37,39,41)(35,42,43,38)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 12846);