Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 16128 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C64×C127 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C32 | C22×C127 |
| socle, prime radical | C22×C127 | C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
40 conjugacy classes of subgroups.
16256 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C64×C127, C127×#7510, C127×C22⋊C64, … |
| maximal normal subgroup of | C4×C64×C127, C127×#7510, C127×C22⋊C64, … |
| maximal quotient of | C4×C64×C127, C127×C22⋊C64, C127×C4⋊C64, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 159);