Finite Group DatabasebetaFinite Group Databasebeta| order | 2156 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C49 · Schur multiplier (H2) = C2 |
| direct product | C2×D11×C49 |
| unambiguous semidirect product | C11⋊(C22×C49) |
| unambiguous semidirect product | (C2×C11)⋊(C2×C49) |
| Fitting | C2×C11×C49 ⋊ C2 |
| derived, Sylow | C11 ⋊ C22×C49 |
| Hall | C11×C49 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C49 | D11 |
| commutator, hypocenter | C11 | C22×C49 |
| Frattini | C7 | C2×C7×D11 |
| Fitting | C2×C11×C49 | C2 |
| socle | C2×C7×C11 | C2×C7 |
| prime radical | C2×C7×D11 | C7 |
| cosocle | C7×C11 | C22×C7 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C2×C49 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1078 |
686 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C49×D121, D112×C49, C2×C49×C11⋊D11, … |
| maximal normal subgroup of | C2×C11×D11×C49, C2×C13×D11×C49, C2×C17×D11×C49 |
| maximal quotient of | C2×C49×D121, D112×C49, C2×C49×C11⋊D11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2156, 7);