Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C127 · Schur multiplier (H2) = C25 |
| direct product | C4×C22⋊Q8×C127 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C127 | C23 |
| commutator | C22 | C23×C4×C127 |
| Frattini, cosocle | C23 | C24×C127 |
| socle | C23×C127 | C24 |
| prime radical | C24×C127 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C127 ◁ G | |
656 conjugacy classes of subgroups.
7112 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C127×#7566, C127×#7583, C127×#7589, … |
| maximal normal subgroup of | C127×#7566, C127×#7583, C127×#7589, … |
| maximal quotient of | C4×#385×C127, C4×#387×C127, C4×#389×C127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 1034);