Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3585 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C11 · Schur multiplier (H2) = C210 |
| direct product | C11×#60093 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | C23×D4 |
| commutator | C4 | C24×C4×C11 |
| Frattini, cosocle | C2×C4 | C25×C11 |
| socle | C2×C11 | C23×C22⋊C4 |
| prime radical | C2×C11×#585 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C11×#41 ◁ G | |
4852 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 5 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,22,18,21,16,30)(14,23,25,19,26,34,31,33)(15,20,29,36,27,35,28,40)(24,37,39,32,38,43,41,42);(12,14)(13,19)(15,24)(16,31)(17,25)(18,26)(20,32)(21,33)(22,34)(23,30)(27,38)(28,41)(29,39)(35,42)(36,43)(37,40);(12,15)(13,20)(14,24)(16,28)(17,29)(18,27)(19,32)(21,35)(22,36)(23,37)(25,39)(26,38)(30,40)(31,41)(33,42)(34,43);(15,27)(20,35)(24,38)(28,29)(32,42)(36,40)(37,43)(39,41);(13,21)(19,33)(20,35)(22,30)(23,34)(32,42)(36,40)(37,43)902 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53081);