Finite Group DatabasebetaFinite Group Databasebeta| order | 1256 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊D157 |
| Fitting | C22×C157 ⋊ C2 |
| Sylow | C157 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D157 |
| commutator, socle, cosocle | C2×C157 | C22 |
| Fitting | C22×C157 | C2 |
| hypercenter | C22 | D157 |
| hypocenter | C157 | D4 |
| LCS | G ▷ C2×C157 ▷ C157 | |
| UCS | C1 ◁ C2 ◁ C22 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 161 |
| transitive degree | μt(G) = 628 |
Polycyclic presentation:
2^3,157|b^a=bc,d^b=d^156317 conjugacy classes — view the full character table.
| maximal subgroup of | D4×D157, C2×C22⋊D157, #14578953, … |
| maximal normal subgroup of | D4×D157, C2×C22⋊D157, #14578953, … |
| maximal quotient of | #14578931, C22⋊Dic157, #14578933, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1256, 9);