Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C127 · Schur multiplier (H2) = C27 |
| direct product | C4×#120×C127 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C127 | C23 |
| commutator | C22 | C23×C4×C127 |
| Frattini, cosocle | C23 | C24×C127 |
| socle | C23×C127 | C24 |
| prime radical | C2×#120×C127 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C127 ◁ G | |
1224 conjugacy classes of subgroups; only the 368 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 368 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
7112 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C127×#8965, C127×#8967, C127×#11471, … |
| maximal normal subgroup of | C127×#8965, C127×#8967, C127×#11471, … |
| maximal quotient of | C4×#386×C127, C4×#385×C127, C4×#379×C127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 1031);