Finite Group DatabasebetaFinite Group Databasebeta| order | 2056 |
| isoclinism | isoclinic class of #11759967 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×#11759967 |
| unambiguous semidirect product | D257⋊C4 |
| Fitting, socle | C2×C257 ⋊ C4 |
| derived, Sylow | C257 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #11759967 |
| commutator, hypocenter | C257 | C2×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C257 | C4 |
| prime radical | C2×D257 | C2 |
| cosocle | D257 | C22 |
| LCS | G ▷ C257 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 514 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#11759967, C22⋊#11759967, C4⋊#11759967, … |
| maximal normal subgroup of | C4×#11759967, C22⋊#11759967, C4⋊#11759967, … |
| maximal quotient of | C4×#11759967, C22⋊#11759967, C4⋊#11759967, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2056, 14);