Finite Group DatabasebetaFinite Group Databasebeta| order | 2172 |
| isoclinism | isoclinic class of C181⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C22×C181⋊C3 |
| Fitting, socle, Hall | C22×C181 ⋊ C3 |
| derived, Sylow | C181 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C181⋊C3 |
| commutator, cosocle, hypocenter | C181 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C22×C181 | C3 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C22 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 185 |
| transitive degree | μt(G) = 724 |
252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2172, 13);