Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C127 · Schur multiplier (H2) = C2×C4 |
| direct product | C8×M16×C127 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C8×C127 | C22 |
| commutator | C2 | C2×C4×C8×C127 |
| Frattini, cosocle | C42 | C23×C127 |
| socle | C22×C127 | C2×C42 |
| prime radical | C23×C127 | C42 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C8×C127 ◁ G | |
224 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
10160 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C127×#7163, C127×#7165, C127×#7209, … |
| maximal normal subgroup of | C127×#7163, C127×#7165, C127×#7209, … |
| maximal quotient of | C8×#97×C127, C127×#7848, C127×#8132, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 181);