Finite Group DatabasebetaFinite Group Databasebeta| order | 1086 |
| isoclinism | isoclinic class of C181⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×C181⋊C3 |
| unambiguous semidirect product | (C2×C181)⋊C3 |
| Fitting, socle, Hall | C2×C181 ⋊ C3 |
| derived, Sylow | C181 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C181⋊C3 |
| commutator, cosocle, hypocenter | C181 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C181 | C3 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 183 |
| transitive degree | μt(G) = 362 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | Dic181⋊C3, C4×C181⋊C3, C2×D181⋊C3, … |
| maximal normal subgroup of | Dic181⋊C3, C4×C181⋊C3, C2×D181⋊C3, … |
| maximal quotient of | C4×C181⋊C3, C22×C181⋊C3, C2×#13108656, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1086, 2);