Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11234 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#11245 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #391 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C2×C11 | #1441 |
| prime radical | C24×C11 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
624 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)(14,22)(15,19,27,34)(16,28)(17,21)(18,24)(20,29)(23,37,39,35)(25,36)(26,41,42,33)(30,38,32,43)(31,40);(12,14,16,24,17,25,29,40)(13,18,20,22,21,31,28,36)(15,23,26,38,27,39,42,43)(19,32,33,37,34,30,41,35);(12,15,16,26,17,27,29,42)(13,19,20,33,21,34,28,41)(14,23,24,38,25,39,40,43)(18,30,22,35,31,32,36,37)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4233);