Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C127 · Schur multiplier (H2) = C22×C4 |
| direct product | C127×#1393 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C127 | #99 |
| commutator | C2×C4 | C42×C127 |
| Frattini, cosocle | C22×D4 | C22×C127 |
| prime radical | C22×D4×C127 | C22 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C127 ◁ C23×C127 ◁ C22×D4×C127 ◁ G | |
232 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
3302 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C127×#7402, C127×#7403, C127×#7408, … |
| maximal normal subgroup of | C127×#7402, C127×#7403, C127×#7408, … |
| maximal quotient of | C127×#7189, C127×#7205, C127×#7213, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 125);