Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11247 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#11247 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #387 |
| 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 | |
620 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)(14,24)(15,28,31,38)(16,22)(17,21)(18,23)(19,26)(20,30,39,33)(25,34,41,43)(27,35)(29,37,40,42)(32,36);(12,14,16,26,18,27,17,32)(13,19,21,24,23,36,22,35)(15,29,30,25,31,40,33,41)(20,37,38,43,39,42,28,34);(12,15,16,30,18,31,17,33)(13,20,21,38,23,39,22,28)(14,25,26,40,27,41,32,29)(19,34,24,37,36,43,35,42)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4235);