Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C127 · Schur multiplier (H2) = C25 |
| direct product | C127×#3054 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C127 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C127 |
| socle | C22×C127 | C22×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C127 ◁ C23×C4×C127 ◁ G | |
500 conjugacy classes of subgroups.
4064 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C127×#11685, C127×#11688, C127×#12998, … |
| maximal normal subgroup of | C127×#11685, C127×#11688, C127×#12998, … |
| maximal quotient of | C127×#19133, C127×#19137, C127×#19142, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 1786);