Finite Group Databasebeta

← Group #488585

Character table — Group #488585

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size11112222444444444448888888888888161616161616161616161616161632323232
order12224444222448888884444816161616161616162244444488161616162488
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ51111111111111111111-1-1-1-11111111111-111-1-11-1-1-1-1-1-1-111-1-1
χ61111111111111111111-1-1-1-1111111111-11-1-111-11-1-1-1-1-1-1-1-111
χ71111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11-111-1-11-1-1-11111-1-111
χ81111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-11-1-111-11-1-1111111-1-1
χ911111-1-111-1-1-11-1-111111-11-1-11111-1-1-1-1111-1-1-1-111-111-1-11-11-1
χ1011111-1-111-1-1-11-1-111111-11-1-11111-1-1-1-1-1-1-11111-11-111-1-1-11-11
χ1111111-1-111-1-1-11-1-111111-11-1-1-1-1-1-11111111-1-1-1-111-1-1-111-11-11
χ1211111-1-111-1-1-11-1-111111-11-1-1-1-1-1-11111-1-1-11111-11-1-1-1111-11-1
χ1311111-1-111-1-1-11-1-11111-11-11-11111-1-1-1-11-11-111-1-1-11-1-1111-1-11
χ1411111-1-111-1-1-11-1-11111-11-11-11111-1-1-1-1-11-11-1-111-11-1-111-111-1
χ1511111-1-111-1-1-11-1-11111-11-11-1-1-1-1-111111-11-111-1-1-1111-1-1-111-1
χ1611111-1-111-1-1-11-1-11111-11-11-1-1-1-1-11111-11-11-1-111-1111-1-11-1-11
χ172222222222222-2-2-2-2-2-22222-20000000000000000-2-200000000
χ182222222222222-2-2-2-2-2-2-2-2-2-2-200000000000000002200000000
χ1922222222-22-2-2-22222-2-20000-20000000002002-20-20000000000
χ2022222222-22-2-2-22222-2-20000-2000000000-200-22020000000000
χ2122222222-22-2-2-2-2-2-2-222000020000000020-2200-200000000000
χ2222222222-22-2-2-2-2-2-2-2220000200000000-202-200200000000000
χ2322222-2-222-2-2-2222-2-2-2-22-22-220000000000000000-2200000000
χ2422222-2-222-2-2-2222-2-2-2-2-22-22200000000000000002-200000000
χ2522222-2-22-2-222-222-2-2220000-20000000020-2-200200000000000
χ2622222-2-22-2-222-222-2-2220000-200000000-202200-200000000000
χ2722222-2-22-2-222-2-2-222-2-200002000000000200-220-20000000000
χ2822222-2-22-2-222-2-2-222-2-200002000000000-2002-2020000000000
χ292222-222-2-2-22-220000002-2-22022−2−222−2−200000000002−22−20000
χ302222-222-2-2-22-220000002-2-220−2−222−2−2220000000000−22−220000
χ312222-222-2-2-22-22000000-222-2022−2−222−2−20000000000−22−220000
χ322222-222-2-2-22-22000000-222-20−2−222−2−22200000000002−22−20000
χ332222-2-2-2-2-22-22200000022-2-2022−2−2−2−22200000000002−2−220000
χ342222-2-2-2-2-22-22200000022-2-20−2−22222−2−20000000000−222−20000
χ352222-2-2-2-2-22-222000000-2-222022−2−2−2−2220000000000−222−20000
χ362222-2-2-2-2-22-222000000-2-2220−2−22222−2−200000000002−2−220000
χ374444-444-44-4-44-40000000000000000000000000000000000000
χ384444-4-4-4-4444-4-40000000000000000000000000000000000000
χ3944-4-404i−4i0000002i2−2i222−220000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7000000000000000000
χ4044-4-404i−4i0000002i2−2i222−220000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7000000000000000000
χ4144-4-404i−4i000000−2i22i2−22220000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7000000000000000000
χ4244-4-404i−4i000000−2i22i2−22220000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7000000000000000000
χ4344-4-40−4i4i0000002i2−2i2−22220000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7000000000000000000
χ4444-4-40−4i4i0000002i2−2i2−22220000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7000000000000000000
χ4544-4-40−4i4i000000−2i22i222−220000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7000000000000000000
χ4644-4-40−4i4i000000−2i22i222−220000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7000000000000000000
χ478-88-8800-8000000000000000000000000000000000000000000
χ488-88-8-8008000000000000000000000000000000000000000000
χ498-8-88000000000000042−420000000000000000000000000000000
χ508-8-880000000000000−42420000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.