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×#2889 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C127 | C22×C22⋊C4 |
| commutator | C22 | C23×C4×C127 |
| Frattini, cosocle | C2×C4 | C24×C127 |
| prime radical | C2×2−1+4×C127 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C127 ◁ C2×#41×C127 ◁ G | |
704 conjugacy classes of subgroups; only the 340 normal subgroups are shown.
This group has 704 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×#13096, C127×#13098, C127×#21780, … |
| maximal normal subgroup of | C127×#13096, C127×#13098, C127×#21780, … |
| maximal quotient of | C127×#17351, C127×#17352, C127×#17368, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 1621);