Finite Group DatabasebetaFinite Group Databasebeta| order | 32128 |
| automorphism | ? |
| homology | Abelianization (H1) = C128 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C251⋊C128 |
| derived, Sylow | C251 ⋊ C128 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C64 | D251 |
| commutator, hypocenter | C251 | C128 |
| Fitting, cosocle | C64×C251 | C2 |
| socle, prime radical | C2×C251 | C64 |
| LCS | G ▷ C251 | |
| UCS | C1 ◁ C64 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32128 |
Polycyclic presentation:
2^7,251|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,f^2=g,h^a=h^2508128 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32128, 2329);