Finite Group DatabasebetaFinite Group Databasebeta| order | 32004 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | Dic7×#11765919 |
| derived, Hall | C7×C127 ⋊ C4×C9 |
| Hall | C7×#11765919 ⋊ C4 |
| Hall | Dic7×C127 ⋊ C9 |
| Sylow | C127 ⋊ C9×Dic7 |
| Sylow | C7 ⋊ C4×#11765919 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D7×#11765919 |
| commutator, hypocenter | C7×C127 | C4×C9 |
| Fitting, socle | C2×C7×C127 | C2×C9 |
| prime radical, cosocle | C2×C7×C127⋊C3 | C2×C3 |
| LCS | G ▷ C7×C127 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3556 |
230 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32004, 98);