Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11000 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#11356 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #390 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C2×C11 | #1445 |
| prime radical | C24×C11 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
580 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)(15,26,28,19)(16,29)(17,21)(18,24)(20,31)(23,37,39,43)(25,36)(27,35,42,40)(30,33)(32,41,34,38);(12,14,16,30,17,25,31,24)(13,18,29,22,21,33,20,36)(15,23,27,41,28,39,42,38)(19,34,40,43,26,32,35,37);(12,15,16,27,17,28,31,42)(13,19,29,40,21,26,20,35)(14,23,30,41,25,39,24,38)(18,32,22,37,33,34,36,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4344);