Finite Group DatabasebetaFinite Group Databasebeta| order | 1266 |
| isoclinism | isoclinic class of C211⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×C211⋊C3 |
| unambiguous semidirect product | (C2×C211)⋊C3 |
| Fitting, socle, Hall | C2×C211 ⋊ C3 |
| derived, Sylow | C211 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C211⋊C3 |
| commutator, cosocle, hypocenter | C211 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C211 | C3 |
| LCS | G ▷ C211 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 213 |
| transitive degree | μt(G) = 422 |
146 conjugacy classes — view the full character table.
| maximal subgroup of | (C211⋊C3)⋊C4, C4×C211⋊C3, C2×D211⋊C3, … |
| maximal normal subgroup of | (C211⋊C3)⋊C4, C4×C211⋊C3, C2×D211⋊C3, … |
| maximal quotient of | C4×C211⋊C3, C22×C211⋊C3, C2×C211⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1266, 2);