Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2883 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C127 · Schur multiplier (H2) = C26 |
| direct product | C127×#2883 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C127 | C22×C22⋊C4 |
| commutator | C22 | C23×C4×C127 |
| Frattini, cosocle | C23 | C24×C127 |
| prime radical | C2×H(5,𝔽2)×C127 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C127 ◁ C22×D4×C127 ◁ G | |
800 conjugacy classes of subgroups; only the 340 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 340 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
5207 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C127×#13100, C127×#13102, C127×#21776, … |
| maximal normal subgroup of | C127×#13100, C127×#13102, C127×#21776, … |
| maximal quotient of | C127×#17350, C127×#17351, C127×#17367, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 1615);