Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C82×C11 · Schur multiplier (H2) = C22×C8 |
| direct product | C8×C11×C4⋊C8 |
| unambiguous semidirect product | C4⋊(C82×C11) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C8×C11 | C22 |
| commutator | C2 | C2×C82×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| socle, prime radical | C23×C11 | C2×C42 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C8×C11 ◁ G | |
550 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7,8)(21,22,23,24,25,26,27,28,29,30,31);(10,12)(13,14,15,17,16,18,19,20);(9,10,11,12)1760 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1247);