Finite Group DatabasebetaFinite Group Databasebeta| order | 32004 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | D32×C127⋊C7 |
| unambiguous semidirect product | (C3×D3)⋊(C2×C127⋊C7) |
| unambiguous semidirect product | (C3⋊D3)⋊(C2×C127⋊C7) |
| unambiguous semidirect product | (D32×C127)⋊C7 |
| Fitting, socle, derived, Hall | C32×C127 ⋊ C22×C7 |
| Hall | C32×C127⋊C7 ⋊ C22 |
| Hall | D32×C127 ⋊ C7 |
| Sylow | C127 ⋊ D32×C7 |
| Sylow | C32 ⋊ C22×C127⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C127 | C22×C7 |
| LCS | G ▷ C32×C127 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 762 |
225 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32004, 170);