Finite Group DatabasebetaFinite Group Databasebeta| order | 32178 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C31 · Schur multiplier (H2) = C1 |
| direct product | C3×C31×D173 |
| unambiguous semidirect product | C173⋊(C2×C3×C31) |
| Fitting, socle, Hall | C3×C31×C173 ⋊ C2 |
| derived, Sylow | C173 ⋊ C2×C3×C31 |
| Hall | C31×C173 ⋊ C2×C3 |
| Hall | C3×C173 ⋊ C2×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C31 | D173 |
| commutator, cosocle, hypocenter | C173 | C2×C3×C31 |
| Frattini | C1 | G |
| Fitting, socle | C3×C31×C173 | C2 |
| LCS | G ▷ C173 | |
| UCS | C1 ◁ C3×C31 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16089 |
8184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32178, 3);