Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2008 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#11094 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #392 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C2×C11 | #1439 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
868 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,21,18,22,16,31)(14,19,26,34,25,35,24,40)(15,27,30,20,29,37,32,36)(23,38,39,33,28,42,41,43);(12,14)(13,19)(15,28,29,23)(16,24)(17,26)(18,25)(20,33,36,43)(21,34)(22,35)(27,38,37,42)(30,41,32,39)(31,40);(12,15)(13,20)(14,23)(16,32)(17,30)(18,29)(19,33)(21,37)(22,36)(24,41)(25,28)(26,39)(27,31)(34,42)(35,43)(38,40)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4082);