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×#11361 |
| 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 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
592 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)(12,13,17,21,18,23,16,22)(14,24,27,35,28,39,26,19)(15,29,31,20,33,37,32,38)(25,41,30,40,43,34,42,36);(12,14)(13,19,23,35)(15,30)(16,26)(17,27)(18,28)(20,36,38,40)(21,24,22,39)(25,32)(29,34,37,41)(31,43)(33,42);(12,15)(13,20,23,38)(14,25)(16,31)(17,32)(18,33)(19,34,35,41)(21,29,22,37)(24,40,39,36)(26,30)(27,42)(28,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4349);