Finite Group DatabasebetaFinite Group Databasebeta| order | 32046 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C3⋊(C7⋊D763) |
| unambiguous semidirect product | C7⋊D2289 |
| unambiguous semidirect product | C109⋊(C3⋊(C7⋊D7)) |
| Fitting, socle, derived, Hall | C3×C72×C109 ⋊ C2 |
| Hall | C72×C109 ⋊ D3 |
| Hall | C3×C109 ⋊ C7⋊D7 |
| Hall | C3×C72 ⋊ D109 |
| Sylow | C109 ⋊ C3⋊(C7⋊D7) |
| Sylow | C72 ⋊ D327 |
| Sylow | C3 ⋊ C7⋊D763 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C72×C109 | C2 |
| LCS | G ▷ C3×C72×C109 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16023 |
Polycyclic presentation:
2,3,7^2,109|b^a=b^2,c^a=c^6,d^a=d^6,e^a=e^1088013 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32046, 100);