Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2032 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#11090 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #393 |
| commutator | C24 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C2×C11 | #1439 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
852 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)(12,13,16,21,17,20,30,35)(14,18,24,33,23,32,39,42)(15,25,28,36,27,19,29,34)(22,37,38,43,26,31,40,41);(12,14)(13,18)(15,26,27,22)(16,24)(17,23)(19,31,25,37)(20,32)(21,33)(28,40,29,38)(30,39)(34,41,36,43)(35,42);(12,15)(13,19)(14,22)(16,29)(17,27)(18,31)(20,25)(21,36)(23,26)(24,40)(28,30)(32,37)(33,43)(34,35)(38,39)(41,42)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4078);