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×#11118 |
| 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 | |
852 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)(12,13,17,21,18,22,16,32)(14,23,27,34,26,35,25,19)(15,20,30,37,31,39,29,38)(24,40,42,33,41,36,28,43);(12,14,16,25,18,26,17,27)(13,19,21,23,22,34,32,35)(15,28,29,41,31,42,30,24)(20,36,37,43,39,40,38,33);(12,15)(13,20)(14,24)(16,29)(17,30)(18,31)(19,33)(21,37)(22,39)(23,36)(25,28)(26,41)(27,42)(32,38)(34,43)(35,40)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4106);