Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C127 · Schur multiplier (H2) = C24 |
| direct product | C127×#2971 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C127 | C24 |
| commutator | C22 | C23×C4×C127 |
| Frattini, cosocle | C2×C4 | C24×C127 |
| socle | C22×C127 | C23×C4 |
| prime radical | C2×#41×C127 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C127 ◁ G | |
402 conjugacy classes of subgroups; only the 276 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 276 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
6350 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C127×#9160, C127×#9162, C127×#9350, … |
| maximal normal subgroup of | C127×#9160, C127×#9162, C127×#9350, … |
| maximal quotient of | C127×#20480, C127×#20494, Q8×#97×C127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 1703);