Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| automorphism | ? |
| homology | Abelianization (H1) = C127 · Schur multiplier (H2) = C1 |
| affine general linear | AGL(1,𝔽128) |
| unambiguous semidirect product | C27⋊C127 |
| Fitting, socle, derived, Sylow | C27 ⋊ C127 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C27 | C127 |
| LCS | G ▷ C27 | |
| UCS | C1 | |
234 conjugacy classes of subgroups.
Polycyclic presentation:
127,2^7|b^a=bcdefg,c^a=dfgh,d^a=cdef,e^a=cdf,f^a=cfgh,g^a=cdefh,h^a=bh128 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 19325);