Finite Group DatabasebetaFinite Group Databasebeta| order | 2172 |
| isoclinism | isoclinic class of D3×D181 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D181 |
| unambiguous semidirect product | (D3×C181)⋊C2 |
| unambiguous semidirect product | (C3×D181)⋊C2 |
| unambiguous semidirect product | D543⋊C2 |
| Fitting, socle, derived, Hall | C3×C181 ⋊ C22 |
| Sylow | C181 ⋊ C2×D3 |
| Sylow | C3 ⋊ C2×D181 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C181 | C22 |
| LCS | G ▷ C3×C181 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 184 |
| transitive degree | μt(G) = 543 |
276 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D181⋊C5, C5×D3×D181, D15×D181, … |
| maximal normal subgroup of | D3×D181⋊C5, C5×D3×D181, D3×C7×D181, … |
| maximal quotient of | C5×D3×D181, D15×D181, D3×D905, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2172, 12);