Finite Group DatabasebetaFinite Group Databasebeta| order | 32004 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×ΓL(1,𝔽8)⋊Dic127 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C3×Dic127) |
| derived, Hall | C7×C127 ⋊ C32×C4 |
| Hall | C3×ΓL(1,𝔽8)×C127 ⋊ C4 |
| Hall | Dic889 ⋊ C32 |
| Sylow | C127 ⋊ C3×ΓL(1,𝔽8)⋊C4 |
| Hall | C3×ΓL(1,𝔽8) ⋊ Dic127 |
| Sylow | C7 ⋊ C32×Dic127 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10668 |
1932 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32004, 115);