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×#18087 |
| 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 ◁ C11×#431 ◁ G | |
606 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)(14,19)(15,21)(16,20)(17,22)(18,23)(24,27)(25,26)(28,29,33,36,34,30,32,37)(31,35,40,42,41,38,39,43);(12,14)(13,18)(15,23)(16,25)(17,24)(19,20)(21,27)(22,26)(28,30)(29,34)(31,38)(32,36)(33,37)(35,41)(39,42)(40,43);(12,14)(13,19)(15,25)(16,23)(17,24)(18,20)(21,26)(22,27)(28,31,33,40,34,41,32,39)(29,35,36,42,30,38,37,43);(12,15,17,16)(13,20,22,21)(14,23,24,25)(18,19,26,27)(28,32,34,33)(29,36,30,37)(31,39,41,40)(35,42,38,43)770 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11075);