Finite Group DatabasebetaFinite Group Databasebeta| order | 32004 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊Dic2667 |
| unambiguous semidirect product | C7⋊(C3⋊Dic381) |
| unambiguous semidirect product | C127⋊(C3⋊Dic21) |
| derived, Hall | C32×C7×C127 ⋊ C4 |
| Hall | C32×C127 ⋊ Dic7 |
| Hall | C7×C127 ⋊ C3⋊Dic3 |
| Sylow | C127 ⋊ C3⋊Dic21 |
| Hall | C32×C7 ⋊ Dic127 |
| Sylow | C32 ⋊ Dic889 |
| Sylow | C7 ⋊ C3⋊Dic381 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊D2667 |
| commutator, hypocenter | C32×C7×C127 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C32×C7×C127 | C2 |
| LCS | G ▷ C32×C7×C127 | |
| UCS | C1 ◁ C2 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32004 |
Polycyclic presentation:
2,3^2,7,127,2|a^2=f,b^a=b^2,c^a=c^2,d^a=d^6,e^a=e^1268004 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32004, 141);