Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C127 · Schur multiplier (H2) = C26 |
| direct product | C2×#413×C127 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C127 | C22⋊C4 |
| commutator | C22 | C23×C4×C127 |
| Frattini, cosocle | C2×C4 | C24×C127 |
| socle | C22×C127 | C2×C22⋊C4 |
| prime radical | C22×#41×C127 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C127 ◁ C23×C4×C127 ◁ G | |
756 conjugacy classes of subgroups.
5588 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C127×#10744, C127×#10746, C127×#10747, … |
| maximal normal subgroup of | C127×#10744, C127×#10746, C127×#10747, … |
| maximal quotient of | C2×C127×#1458, C2×C127×#1459, C127×#17349, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 1619);