Finite Group DatabasebetaFinite Group Databasebeta| order | 32186 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C7⋊(C11⋊D209) |
| unambiguous semidirect product | C11⋊D1463 |
| unambiguous semidirect product | C19⋊(C7⋊(C11⋊D11)) |
| Fitting, socle, derived, Hall | C7×C112×C19 ⋊ C2 |
| Hall | C112×C19 ⋊ D7 |
| Hall | C7×C112 ⋊ D19 |
| Hall | C7×C19 ⋊ C11⋊D11 |
| Sylow | C112 ⋊ D133 |
| Sylow | C19 ⋊ C7⋊(C11⋊D11) |
| Sylow | C7 ⋊ C11⋊D209 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C112×C19 | C2 |
| LCS | G ▷ C7×C112×C19 | |
| UCS | C1 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16093 |
Polycyclic presentation:
2,7,11^2,19|b^a=b^6,c^a=c^10,d^a=d^10,e^a=e^188048 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32186, 20);