Finite Group DatabasebetaFinite Group Databasebeta| order | 32178 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C173 · Schur multiplier (H2) = C1 |
| direct product | C173×D31⋊C3 |
| unambiguous semidirect product | D31⋊(C3×C173) |
| unambiguous semidirect product | (C31⋊C3)⋊(C2×C173) |
| unambiguous semidirect product | (D31×C173)⋊C3 |
| Fitting, socle, Hall | C31×C173 ⋊ C2×C3 |
| derived, Sylow | C31 ⋊ C2×C3×C173 |
| Hall | C31⋊C3×C173 ⋊ C2 |
| Hall | D31×C173 ⋊ C3 |
| Hall | C31⋊C3 ⋊ C2×C173 |
| Hall | D31 ⋊ C3×C173 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C173 | D31⋊C3 |
| commutator, cosocle, hypocenter | C31 | C2×C3×C173 |
| Frattini | C1 | G |
| Fitting, socle | C31×C173 | C2×C3 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C173 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5363 |
1903 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32178, 11);