Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11×C16 · Schur multiplier (H2) = C27 |
| direct product | C22×C11×C22⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C8×C11 | C22 |
| commutator | C2 | C23×C11×C16 |
| Frattini, cosocle | C2×C8 | C24×C11 |
| socle | C24×C11 | C2×C8 |
| prime radical | C25×C11 | C8 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C8×C11 ◁ G | |
1470 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2)(25,26,27,28,29,30,31,32,33,34,35);(3,4);(5,6)(7,8)(9,10,11,14,12,15,17,20,13,16,18,21,19,22,23,24);(6,8)1760 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26318);