Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D4×D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C29 |
| direct product | C2×Q8×C11×D8 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| prime radical | C22×C11×D8 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C4×Q8×C11 ◁ G | |
2286 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 29 points:
(1,2)(19,20,21,22,23,24,25,26,27,28,29);(3,4,5,6)(7,10,9,8);(3,7,5,9)(4,8,6,10);(11,12,13,14,15,16,17,18);(12,18)(13,17)(14,16)770 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54339);