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×#18086 |
| 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 | C23×C11 | C4×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C11×#431 ◁ G | |
572 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)(12,13,17,20,18,14,16,22)(15,19,24,26,25,21,23,27)(28,29,33,36,32,35,41,43)(30,37,39,40,38,34,42,31);(12,14,18,13)(15,21,25,19)(16,20,17,22)(23,26,24,27)(28,30)(29,34)(31,36)(32,38)(33,39)(35,37)(40,43)(41,42);(12,15,16,23,18,25,17,24)(13,19,22,27,14,21,20,26)(28,31,33,37,32,40,41,34)(29,30,36,39,35,38,43,42);(13,14)(19,21)(20,22)(26,27)(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, 11074);