Finite Group DatabasebetaFinite Group Databasebeta| order | 32178 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C173 · Schur multiplier (H2) = C1 |
| direct product | C173×D93 |
| unambiguous semidirect product | C3⋊(D31×C173) |
| unambiguous semidirect product | C31⋊(D3×C173) |
| Fitting, socle, Hall | C3×C31×C173 ⋊ C2 |
| derived, Hall | C3×C31 ⋊ C2×C173 |
| Hall | C31×C173 ⋊ D3 |
| Hall | C3×C173 ⋊ D31 |
| Sylow | C31 ⋊ D3×C173 |
| Sylow | C3 ⋊ D31×C173 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C173 | D93 |
| commutator, cosocle, hypocenter | C3×C31 | C2×C173 |
| Frattini | C1 | G |
| Fitting, socle | C3×C31×C173 | C2 |
| LCS | G ▷ C3×C31 | |
| UCS | C1 ◁ C173 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16089 |
8304 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32178, 8);