Finite Group DatabasebetaFinite Group Databasebeta| order | 2172 |
| isoclinism | isoclinic class of #10624382 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#10624382 |
| Fitting, socle, Hall | C3×C181 ⋊ C4 |
| derived, Sylow | C181 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #10624382 |
| commutator, hypocenter | C181 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C181 | C4 |
| prime radical | C3×D181 | C2 |
| cosocle | D181 | C2×C3 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 184 |
| transitive degree | μt(G) = 543 |
147 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2172, 10);