Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 64512 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C4 |
| abelian | C4×C32×C127 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C16 | C22×C127 |
| socle, prime radical | C22×C127 | C2×C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
72 conjugacy classes of subgroups.
16256 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×C32×C127, C127×#7329, C127×#7331, … |
| maximal normal subgroup of | C8×C32×C127, C127×#7329, C127×#7331, … |
| maximal quotient of | C8×C32×C127, C127×#7331, C127×#7465, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 128);