Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C127 · Schur multiplier (H2) = C2 |
| direct product | C127×#1336 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C127 | #102 |
| commutator | C8 | C2×C8×C127 |
| Frattini, cosocle | C4×C8 | C22×C127 |
| socle | C2×C127 | D4⋊C8 |
| prime radical | #135×C127 | C4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C127 ◁ C2×C8×C127 ◁ C4×C8×C127 ◁ G | |
96 conjugacy classes of subgroups.
4064 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C127×#1336, C127×#11604, C127×#11669, … |
| maximal normal subgroup of | C2×C127×#1336, C127×#11604, C127×#11669, … |
| maximal quotient of | C127×#7070, C127×#7071, C127×#7072, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 68);