Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C11 · Schur multiplier (H2) = C22×C4 |
| direct product | C11×#8184 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C8×C11 | D4 |
| commutator | C4 | C2×C4×C8×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| socle | C22×C11 | C4×C22⋊C4 |
| prime radical | C2×C11×#41 | C2×C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C8×C11 ◁ C2×C4×C8×C11 ◁ G | |
530 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)(20,21,24,28,25,29,23,26)(22,27,31,34,32,35,30,33);(12,13,14,16,15,17,18,19)(21,26,29,28)(27,33,35,34);(20,22,24,31,25,32,23,30)(21,27,28,34,29,35,26,33)1232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1172);