Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1665 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C127 · Schur multiplier (H2) = C22 |
| direct product | C127×#1668 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C127 | #121 |
| commutator, Frattini, cosocle | C42 | C23×C127 |
| prime radical | #493×C127 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C127 ◁ C42×C127 ◁ G | |
188 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
3683 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C127×#12328, C127×#12329, C127×#12330, … |
| maximal normal subgroup of | C127×#12328, C127×#12329, C127×#12330, … |
| maximal quotient of | C127×#8645, C127×#9222, C127×#9564, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 400);