Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C127 · Schur multiplier (H2) = C29 |
| direct product | C22×AGL(1,ℤ/8)×C127 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C127 | C2×D4 |
| commutator, Frattini, cosocle | C4 | C25×C127 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C127 ◁ C23×C4×C127 ◁ G | |
1720 conjugacy classes of subgroups.
5588 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C127×#11012, C127×#11014, C127×#11016, … |
| maximal normal subgroup of | C127×#11012, C127×#11014, C127×#11016, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 2310);