Finite Group DatabasebetaFinite Group Databasebeta| order | 32046 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C109 · Schur multiplier (H2) = C1 |
| direct product | C109×D49⋊C3 |
| unambiguous semidirect product | D49⋊(C3×C109) |
| unambiguous semidirect product | (C49⋊C3)⋊(C2×C109) |
| Fitting, Hall | C49×C109 ⋊ C2×C3 |
| derived, Sylow | C49 ⋊ C2×C3×C109 |
| Hall | C109×C49⋊C3 ⋊ C2 |
| Hall | D49×C109 ⋊ C3 |
| Hall | C49⋊C3 ⋊ C2×C109 |
| Hall | D49 ⋊ C3×C109 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C109 | D49⋊C3 |
| commutator, cosocle, hypocenter | C49 | C2×C3×C109 |
| Frattini | C7 | AGL(1,𝔽7)×C109 |
| Fitting | C49×C109 | C2×C3 |
| socle | C7×C109 | AGL(1,𝔽7) |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C109 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5341 |
1526 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32046, 18);