Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| isoclinism | isoclinic class of D127 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C210 |
| direct product | C23×C8×D127 |
| Fitting | C23×C8×C127 ⋊ C2 |
| derived, Sylow | C127 ⋊ C24×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C8 | D127 |
| commutator, hypocenter | C127 | C24×C8 |
| Frattini | C4 | C24×D127 |
| Fitting | C23×C8×C127 | C2 |
| socle | C24×C127 | C2×C4 |
| prime radical | C24×D127 | C4 |
| cosocle | C4×C127 | C25 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C23×C8 | |
1976 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, 19208);