Finite Group DatabasebetaFinite Group Databasebeta| order | 32574 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C89 · Schur multiplier (H2) = C1 |
| direct product | C89×D61⋊C3 |
| unambiguous semidirect product | D61⋊(C3×C89) |
| unambiguous semidirect product | (C61⋊C3)⋊(C2×C89) |
| unambiguous semidirect product | (C89×D61)⋊C3 |
| Fitting, socle, Hall | C61×C89 ⋊ C2×C3 |
| derived, Sylow | C61 ⋊ C2×C3×C89 |
| Hall | C89×C61⋊C3 ⋊ C2 |
| Hall | C89×D61 ⋊ C3 |
| Hall | C61⋊C3 ⋊ C2×C89 |
| Hall | D61 ⋊ C3×C89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C89 | D61⋊C3 |
| commutator, cosocle, hypocenter | C61 | C2×C3×C89 |
| Frattini | C1 | G |
| Fitting, socle | C61×C89 | C2×C3 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C89 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5429 |
1424 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32574, 11);