Finite Group DatabasebetaFinite Group Databasebeta| order | 32004 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊#22547877 |
| derived, Hall | C22×C7×C127 ⋊ C9 |
| Hall | C7×C127 ⋊ C22⋊C9 |
| Hall | C22×C127 ⋊ C7⋊C9 |
| Sylow | C127 ⋊ C22⋊(C7⋊C9) |
| Hall | C22×C7 ⋊ #11765917 |
| Sylow | C7 ⋊ C22⋊#11765917 |
| Sylow | C22 ⋊ #22547877 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C22⋊#14581887 |
| commutator, hypocenter | C22×C7×C127 | C9 |
| Fitting, socle, prime radical, cosocle | C22×C3×C7×C127 | C3 |
| LCS | G ▷ C22×C7×C127 | |
| UCS | C1 ◁ C3 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16002 |
Polycyclic presentation:
3,2^2,7,127,3|a^3=f,b^a=c,c^a=bc,d^a=d^2,e^a=e^193564 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32004, 65);