Finite Group DatabasebetaFinite Group Databasebeta| order | 2172 |
| isoclinism | isoclinic class of D181⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic181⋊C3 |
| derived, Sylow | C181 ⋊ C3×C4 |
| Hall | Dic181 ⋊ C3 |
| Hall | C181⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D181⋊C3 |
| commutator, hypocenter | C181 | C3×C4 |
| Fitting, socle, cosocle | C2×C181 | C2×C3 |
| prime radical | C2×C181⋊C3 | C2 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 185 |
| transitive degree | μt(G) = 724 |
Polycyclic presentation:
2,3,181,2|a^2=d,c^a=c^180,c^b=c^4872 conjugacy classes — view the full character table.
| maximal subgroup of | C5×Dic181⋊C3, Dic905⋊C3, (Dic181⋊C3)⋊C5, … |
| maximal normal subgroup of | C5×Dic181⋊C3, (Dic181⋊C3)⋊C5, C7×Dic181⋊C3, … |
| maximal quotient of | C5×Dic181⋊C3, Dic905⋊C3, #16813739⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2172, 2);