Finite Group DatabasebetaFinite Group Databasebeta| order | 2056 |
| isoclinism | isoclinic class of D257 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C257 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D257 |
| commutator, hypocenter | C257 | C8 |
| Fitting, cosocle | C4×C257 | C2 |
| socle, prime radical | C2×C257 | C4 |
| LCS | G ▷ C257 | |
| UCS | C1 ◁ C4 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 265 |
| transitive degree | μt(G) = 2056 |
Polycyclic presentation:
2^3,257|a^2=b,b^2=c,d^a=d^256520 conjugacy classes — view the full character table.
| maximal subgroup of | C8×D257, C2×#14523339, #16861601, … |
| maximal normal subgroup of | C8×D257, C2×#14523339, #16861601, … |
| maximal quotient of | #16861593, C2×#14523339 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2056, 6);