Finite Group DatabasebetaFinite Group Databasebeta| order | 32634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C37 · Schur multiplier (H2) = C3 |
| direct product | C3×C37×D49⋊C3 |
| unambiguous semidirect product | D49⋊(C32×C37) |
| unambiguous semidirect product | (C49⋊C3)⋊(C2×C3×C37) |
| unambiguous semidirect product | (C3×D49)⋊(C3×C37) |
| Fitting | C3×C37×C49 ⋊ C2×C3 |
| derived, Sylow | C49 ⋊ C2×C32×C37 |
| Hall | C3×C37×C49⋊C3 ⋊ C2 |
| Hall | C37×D49 ⋊ C32 |
| Hall | C37×C49 ⋊ C2×C32 |
| Hall | C3×C49⋊C3 ⋊ C2×C37 |
| Hall | D49 ⋊ C32×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C37 | D49⋊C3 |
| commutator, cosocle, hypocenter | C49 | C2×C32×C37 |
| Frattini | C7 | C3×C37×AGL(1,𝔽7) |
| Fitting | C3×C37×C49 | C2×C3 |
| socle | C3×C7×C37 | AGL(1,𝔽7) |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C3×C37 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5439 |
1554 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32634, 43);