Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C127 · Schur multiplier (H2) = C25 |
| direct product | C4×AGL(1,ℤ/8)×C127 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C127 | C2×D4 |
| commutator | C4 | C23×C4×C127 |
| Frattini, cosocle | C2×C4 | C24×C127 |
| socle | C22×C127 | C22×D4 |
| prime radical | C2×AGL(1,ℤ/8)×C127 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C127 ◁ C2×C42×C127 ◁ G | |
548 conjugacy classes of subgroups.
5588 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C127×#8954, C127×#8956, C127×#9095, … |
| maximal normal subgroup of | C127×#8954, C127×#8956, C127×#9095, … |
| maximal quotient of | C8×AGL(1,ℤ/8)×C127, C127×#17869, C127×#17871, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 1676);