Finite Group DatabasebetaFinite Group Databasebeta| order | 2156 |
| isoclinism | isoclinic class of D11×C7⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C7 |
| direct product | D11×C7⋊D7 |
| unambiguous semidirect product | (C7×D11)⋊D7 |
| Fitting, socle, derived, Hall | C72×C11 ⋊ C22 |
| Sylow | C72 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C11 | C22 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 539 |
182 conjugacy classes — view the full character table.
| maximal subgroup of | C7⋊D7×D121, C11×D11×C7⋊D7, D11×C7⋊D77, … |
| maximal normal subgroup of | C11×D11×C7⋊D7, C13×D11×C7⋊D7, C17×D11×C7⋊D7, … |
| maximal quotient of | C7⋊D7×D121, C11×D11×C7⋊D7, D11×C7⋊D77, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2156, 18);