Finite Group DatabasebetaFinite Group Databasebeta| order | 32004 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C7×C127 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×C7×A4×C127 |
| unambiguous semidirect product | C22⋊(C32×C7×C127) |
| unambiguous semidirect product | (C22×C3)⋊(C3×C7×C127) |
| Fitting, socle | C22×C3×C7×C127 ⋊ C3 |
| derived, Sylow | C22 ⋊ C32×C7×C127 |
| Hall | C22×C7×C127 ⋊ C32 |
| Hall | C22×C127 ⋊ C32×C7 |
| Hall | C22×C7 ⋊ C32×C127 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7×C127 | A4 |
| commutator, cosocle, hypocenter | C22 | C32×C7×C127 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C7×C127 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C3×C7×C127 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10668 |
10668 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32004, 291);