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×#11278 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #387 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C2×C11 | #1442 |
| 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)(12,13,17,23,18,21,16,22)(14,24,26,39,27,19,33,35)(15,28,31,38,30,20,32,37)(25,34,42,43,41,40,29,36);(12,14)(13,19)(15,29,30,42)(16,26)(17,33)(18,27)(20,36,28,43)(21,24)(22,35)(23,39)(25,31,41,32)(34,37,40,38);(12,15)(13,20,21,28)(14,25)(16,32)(17,31)(18,30)(19,34,24,40)(22,38,23,37)(26,42)(27,41)(29,33)(35,43,39,36)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4266);