Finite Group DatabasebetaFinite Group Databasebeta| order | 32004 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊(#11765917⋊C7) |
| unambiguous semidirect product | (C22⋊#11765917)⋊C7 |
| derived, Hall | C22×C127 ⋊ C7×C9 |
| Hall | C22⋊#11765917 ⋊ C7 |
| Hall | C22×C127⋊C7 ⋊ C9 |
| Hall | C127⋊C7 ⋊ C22⋊C9 |
| Sylow | C127 ⋊ C7×C22⋊C9 |
| Sylow | C22 ⋊ #11765917⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C22⋊((C127⋊C3)⋊C7) |
| commutator, hypocenter | C22×C127 | C7×C9 |
| Fitting, socle, cosocle | C22×C3×C127 | C3×C7 |
| prime radical | C22×C3×C127⋊C7 | C3 |
| LCS | G ▷ C22×C127 | |
| UCS | C1 ◁ C3 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2286 |
Polycyclic presentation:
3,7,2^2,127,3|a^3=f,c^a=d,d^a=cd,e^a=e^107,e^b=e^4156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32004, 35);