Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #327 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C127 · Schur multiplier (H2) = C23 |
| direct product | C2×#328×C127 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C127 | C22⋊C4 |
| commutator | C2×C4 | C22×C4×C127 |
| Frattini, cosocle | C22×C4 | C23×C127 |
| prime radical | C24×C127 | D4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C127 ◁ C23×C4×C127 ◁ G | |
336 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
4826 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#328×C127, C127×#8217, C127×#8219, … |
| maximal normal subgroup of | C4×#328×C127, C127×#8217, C127×#8219, … |
| maximal quotient of | C2×C127×#1271, C2×C127×#1272, C127×#7566, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 231);