Finite Group DatabasebetaFinite Group Databasebeta| order | 32004 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C9×C127 · Schur multiplier (H2) = C2 |
| direct product | C7×C22⋊C9×C127 |
| unambiguous semidirect product | C22⋊(C7×C9×C127) |
| derived, Sylow | C22 ⋊ C7×C9×C127 |
| Hall | C22×C7×C127 ⋊ C9 |
| Hall | C22×C127 ⋊ C7×C9 |
| Hall | C22×C7 ⋊ C9×C127 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7×C127 | A4 |
| commutator, hypocenter | C22 | C7×C9×C127 |
| Frattini | C3 | C7×A4×C127 |
| Fitting, socle, prime radical | C22×C3×C7×C127 | C3 |
| cosocle | C22×C3 | C3×C7×C127 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C3×C7×C127 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16002 |
10668 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32004, 68);