Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #99 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C127 · Schur multiplier (H2) = C27 |
| direct product | C22×#99×C127 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C127 | C22⋊C4 |
| commutator | C22 | C23×C4×C127 |
| Frattini, cosocle | C23 | C24×C127 |
| prime radical | C23×D4×C127 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C127 ◁ C25×C127 ◁ G | |
1112 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 360 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 | C127×#10745, C127×#10754, C127×#10761, … |
| maximal normal subgroup of | C127×#10745, C127×#10754, C127×#10761, … |
| maximal quotient of | C22×#323×C127, C22×#324×C127, C2×C127×#1459, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 1613);