Finite Group DatabasebetaFinite Group Databasebeta| order | 32186 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C112 · Schur multiplier (H2) = C11 |
| direct product | C112×D133 |
| unambiguous semidirect product | C7⋊(C112×D19) |
| unambiguous semidirect product | C19⋊(C112×D7) |
| Fitting, socle, Hall | C7×C112×C19 ⋊ C2 |
| derived, Hall | C7×C19 ⋊ C2×C112 |
| Hall | C112×C19 ⋊ D7 |
| Hall | C7×C112 ⋊ D19 |
| Sylow | C19 ⋊ C112×D7 |
| Sylow | C7 ⋊ C112×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C112 | D133 |
| commutator, cosocle, hypocenter | C7×C19 | C2×C112 |
| Frattini | C1 | G |
| Fitting, socle | C7×C112×C19 | C2 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C112 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16093 |
8228 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32186, 16);