Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D4×D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#18069 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C22×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C42 | C24×C11 |
| socle | C22×C11 | C2×C4×D4 |
| prime radical | C11×#466 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C4×C11×M16 ◁ G | |
600 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,21)(15,19)(16,24)(17,20)(18,22)(23,26)(25,27)(28,29,33,36,32,35,41,43)(30,37,39,40,38,34,42,31);(12,14)(13,18)(15,22)(16,25)(17,23)(19,26)(20,27)(21,24)(28,30)(29,34)(31,36)(32,38)(33,39)(35,37)(40,43)(41,42);(28,31,33,37,32,40,41,34)(29,30,36,39,35,38,43,42);(12,15,17,16)(13,19,20,24)(14,22,23,25)(18,26,27,21)(30,38)(31,40)(34,37)(39,42)770 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11057);