Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C24×C22⋊D127 |
| Fitting | C26×C127 ⋊ C2 |
| Sylow | C127 ⋊ C24×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C25 | C2×D127 |
| commutator, cosocle | C2×C127 | C26 |
| Frattini | C2 | C25×D127 |
| Fitting | C26×C127 | C2 |
| socle | C25×C127 | C22 |
| hypercenter | C26 | D127 |
| hypocenter | C127 | C24×D4 |
| LCS | G ▷ C2×C127 ▷ C127 | |
| UCS | C1 ◁ C25 ◁ C26 | |
10552 conjugacy classes of subgroups.
4112 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 19302);