Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11×C16 · Schur multiplier (H2) = C22 |
| direct product | C11×C16×SD16 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C11×C16 | D4 |
| commutator | C4 | C22×C11×C16 |
| Frattini, cosocle | C4×C8 | C23×C11 |
| socle | C22×C11 | C8×D4 |
| prime radical | C2×D4×C11 | C2×C8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11×C16 ◁ C4×C11×C16 ◁ G | |
238 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27);(28,29,30,31,32,33,34,35);(29,31)(30,34)(33,35)1232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 5036);