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×#11360 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #387 |
| 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 | |
576 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)(14,23)(15,28,32,38)(16,33)(17,21)(18,22)(19,25)(20,31,39,30)(24,40,42,34)(26,36)(27,35)(29,43,41,37);(12,14)(13,19,22,36)(15,29)(16,25)(17,26)(18,27)(20,37,39,43)(21,23,33,35)(24,30)(28,40,38,34)(31,42)(32,41);(12,15)(13,20,22,39)(14,24)(16,30)(17,31)(18,32)(19,34,36,40)(21,28,33,38)(23,37,35,43)(25,41)(26,29)(27,42)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4348);