Finite Group DatabasebetaFinite Group Databasebeta| order | 32004 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | D7×#11765917⋊C2 |
| unambiguous semidirect product | (C7×#11765917⋊C2)⋊C2 |
| unambiguous semidirect product | (D7×#11765917)⋊C2 |
| unambiguous semidirect product | (#11765917⋊D7)⋊C2 |
| derived, Hall | C7×C127 ⋊ C22×C9 |
| Hall | C7×#11765917 ⋊ C22 |
| Hall | D7×D127 ⋊ C9 |
| Hall | #11765917 ⋊ C2×D7 |
| Sylow | C127 ⋊ C2×C9×D7 |
| Sylow | C7 ⋊ C2×#11765917⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D7×D127⋊C3 |
| commutator, hypocenter | C7×C127 | C22×C9 |
| Fitting, socle, cosocle | C3×C7×C127 | C22×C3 |
| prime radical | C3×D7×D127 | C3 |
| LCS | G ▷ C7×C127 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8001 |
405 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32004, 43);