Finite Group DatabasebetaFinite Group Databasebeta| order | 1256 |
| isoclinism | isoclinic class of D157 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×Dic157 |
| derived, Sylow | C157 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D157 |
| commutator, hypocenter | C157 | C2×C4 |
| Frattini | C2 | C2×D157 |
| Fitting, socle, prime radical | C22×C157 | C2 |
| cosocle | C2×C157 | C22 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C22 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1256 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×Dic157, #14578931, C22⋊Dic157, … |
| maximal normal subgroup of | C4×Dic157, #14578931, C22⋊Dic157, … |
| maximal quotient of | C4×Dic157, C22⋊Dic157, C4⋊Dic157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1256, 8);