Finite Group DatabasebetaFinite Group Databasebeta| order | 2172 |
| isoclinism | isoclinic class of D181⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×D181⋊C3 |
| unambiguous semidirect product | D181⋊(C2×C3) |
| unambiguous semidirect product | (C181⋊C3)⋊C22 |
| unambiguous semidirect product | (C2×D181)⋊C3 |
| unambiguous semidirect product | (C2×C181⋊C3)⋊C2 |
| Fitting, socle | C2×C181 ⋊ C2×C3 |
| derived, Sylow | C181 ⋊ C22×C3 |
| Hall | C2×D181 ⋊ C3 |
| Hall | C181⋊C3 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D181⋊C3 |
| commutator, cosocle, hypocenter | C181 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C181 | C2×C3 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 362 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2172, 9);