Finite Group DatabasebetaFinite Group Databasebeta| order | 32056 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C4007⋊C8 |
| derived, Sylow | C4007 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D4007 |
| commutator, hypocenter | C4007 | C8 |
| Fitting, cosocle | C4×C4007 | C2 |
| socle, prime radical | C2×C4007 | C4 |
| LCS | G ▷ C4007 | |
| UCS | C1 ◁ C4 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32056 |
Polycyclic presentation:
2^3,4007|a^2=b,b^2=c,d^a=d^40068020 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32056, 6);