Finite Group DatabasebetaFinite Group Databasebeta| order | 2156 |
| isoclinism | isoclinic class of D7×D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D7×D11 |
| unambiguous semidirect product | (C11×D7)⋊(C2×C7) |
| unambiguous semidirect product | (C7×D11)⋊(C2×C7) |
| unambiguous semidirect product | D77⋊(C2×C7) |
| Fitting, socle, Hall | C72×C11 ⋊ C22 |
| derived | C7×C11 ⋊ C22×C7 |
| Sylow | C72 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×C7×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D7×D11 |
| commutator, cosocle, hypocenter | C7×C11 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C72×C11 | C22 |
| LCS | G ▷ C7×C11 | |
| UCS | C1 ◁ C7 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 154 |
245 conjugacy classes — view the full character table.
| maximal subgroup of | C7×D7×D121, C7×C11×D7×D11, C7×D11×D77, … |
| maximal normal subgroup of | C7×C11×D7×D11, C7×C13×D7×D11, C7×D7×C17×D11, … |
| maximal quotient of | C7×D7×D121, C7×C11×D7×D11, C7×D11×D77, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2156, 17);