Finite Group DatabasebetaFinite Group Databasebeta| order | 32004 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C7⋊(C127⋊#157) |
| unambiguous semidirect product | C127⋊(C7⋊#157) |
| Fitting, socle, derived, Hall | C32×C7×C127 ⋊ C4 |
| Hall | C32×C127 ⋊ Dic7 |
| Hall | C7×C127 ⋊ #157 |
| Sylow | C127 ⋊ C7⋊#157 |
| Hall | C32×C7 ⋊ Dic127 |
| Sylow | C32 ⋊ Dic889 |
| Sylow | C7 ⋊ C127⋊#157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C7×C127 | C4 |
| prime radical, cosocle | C7×C3⋊D3×C127 | C2 |
| LCS | G ▷ C32×C7×C127 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5334 |
Polycyclic presentation:
2^2,3^2,7,127|a^2=b,c^a=cd,d^a=cd^2,e^a=e^6,f^a=f^126,c^b=c^2,d^b=d^22670 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32004, 267);