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×#18088 |
| 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)(12,13,18,23)(14,24,15,20)(16,22,17,21)(19,26,27,25)(28,29,33,36,34,30,32,38)(31,35,40,42,41,37,39,43);(12,14,18,15)(13,19,23,27)(16,25,17,26)(20,21,24,22)(28,30,34,29)(31,37,41,35)(32,36,33,38)(39,42,40,43);(12,15,18,14)(13,20,23,24)(16,25,17,26)(19,21,27,22)(28,31,33,40,34,41,32,39)(29,35,36,42,30,37,38,43);(12,16,18,17)(13,21,23,22)(14,25,15,26)(19,24,27,20)(28,32,34,33)(29,36,30,38)(31,39,41,40)(35,42,37,43)770 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11076);