Finite Group DatabasebetaFinite Group Databasebeta| order | 2056 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊D257 |
| Fitting | C22×C257 ⋊ C2 |
| Sylow | C257 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D257 |
| commutator, socle, cosocle | C2×C257 | C22 |
| Fitting | C22×C257 | C2 |
| hypercenter | C22 | D257 |
| hypocenter | C257 | D4 |
| LCS | G ▷ C2×C257 ▷ C257 | |
| UCS | C1 ◁ C2 ◁ C22 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 261 |
| transitive degree | μt(G) = 1028 |
Polycyclic presentation:
2^3,257|b^a=bc,d^b=d^256517 conjugacy classes — view the full character table.
| maximal subgroup of | D4×D257, C2×C22⋊D257, #16861617, … |
| maximal normal subgroup of | D4×D257, C2×C22⋊D257, #16861617, … |
| maximal quotient of | #16861595, C22⋊Dic257, #16861597, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2056, 9);