Finite Group DatabasebetaFinite Group Databasebeta| order | 32004 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#24922580 |
| derived, Hall | C7×C127 ⋊ C32×C4 |
| Hall | C3×#14581887 ⋊ C4 |
| Hall | C7×Dic127 ⋊ C32 |
| Hall | Dic127 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C127 ⋊ C3×C4×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×(C127⋊C3)⋊C4 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10668 |
942 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32004, 117);