Finite Group DatabasebetaFinite Group Databasebeta| order | 2156 |
| isoclinism | isoclinic class of D11×D49 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D11×D49 |
| unambiguous semidirect product | (C11×D49)⋊C2 |
| unambiguous semidirect product | (D11×C49)⋊C2 |
| unambiguous semidirect product | D539⋊C2 |
| Fitting, derived, Hall | C11×C49 ⋊ C22 |
| Sylow | C49 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C11×C49 | C22 |
| Frattini | C7 | D7×D11 |
| socle | C7×C11 | C2×D7 |
| LCS | G ▷ C11×C49 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 60 |
| transitive degree | μt(G) = 539 |
182 conjugacy classes — view the full character table.
| maximal subgroup of | D49×D121, C11×D11×D49, D49×C11⋊D11, … |
| maximal normal subgroup of | C11×D11×D49, C13×D11×D49, C17×D11×D49 |
| maximal quotient of | D49×D121, C11×D11×D49, D49×C11⋊D11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2156, 6);