Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
| direct product | C2×C127⋊C64 |
| unambiguous semidirect product | (C2×C127)⋊C64 |
| derived, Sylow | C127 ⋊ C2×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D127 |
| commutator, hypocenter | C127 | C2×C64 |
| Frattini | C32 | C2×D127 |
| Fitting | C2×C32×C127 | C2 |
| socle, prime radical | C22×C127 | C32 |
| cosocle | C32×C127 | C22 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C2×C32 | |
40 conjugacy classes of subgroups.
4160 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 2719);