Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C127 · Schur multiplier (H2) = C22 |
| direct product | C127×#1331 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C127 | D8 |
| commutator | C8 | C2×C8×C127 |
| Frattini, cosocle | C4×C8 | C22×C127 |
| socle | C22×C127 | #102 |
| prime radical | C2×D8×C127 | C4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C127 ◁ C42×C127 ◁ C4×C8×C127 ◁ G | |
110 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
5588 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C127×#1331, C127×#11591, C127×#11592, … |
| maximal normal subgroup of | C2×C127×#1331, C127×#11591, C127×#11592, … |
| maximal quotient of | C127×#7068, C127×#7072, C127×#7112, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 63);