Finite Group DatabasebetaFinite Group Databasebeta| order | 32004 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D2667 |
| unambiguous semidirect product | (C3×D3)⋊D889 |
| unambiguous semidirect product | (D3×C7)⋊D381 |
| unambiguous semidirect product | (D3×C127)⋊D21 |
| Fitting, socle, derived, Hall | C32×C7×C127 ⋊ C22 |
| Hall | C32×C127 ⋊ C2×D7 |
| Hall | C7×C127 ⋊ D32 |
| Sylow | C127 ⋊ D3×D21 |
| Hall | C32×C7 ⋊ C2×D127 |
| Sylow | C32 ⋊ C2×D889 |
| Sylow | C7 ⋊ D3×D381 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C7×C127 | C22 |
| LCS | G ▷ C32×C7×C127 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5334 |
4005 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32004, 279);