Finite Group DatabasebetaFinite Group Databasebeta| order | 2172 |
| isoclinism | isoclinic class of C22⋊(C181⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊(C181⋊C3) |
| unambiguous semidirect product | C181⋊A4 |
| Fitting, socle, derived, Hall | C22×C181 ⋊ C3 |
| Sylow | C181 ⋊ A4 |
| Sylow | C22 ⋊ C181⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C181 | C3 |
| LCS | G ▷ C22×C181 | |
| UCS | C1 | |
10 conjugacy classes of subgroups.
| minimal degree | μ(G) = 185 |
| transitive degree | μt(G) = 724 |
Polycyclic presentation:
3,2^2,181|b^a=c,c^a=bc,d^a=d^132244 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2172, 15);