Finite Group Databasebeta

← Group #145976

Character table — Group #145976

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222224444444444444444444444441616161616161616161616161616161632323232
order122222444488888888444488881616161616161616161616161616161644881616161616161616161616164444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ9222222222222-2-222-2-2-2-2-2-22-2-2222222222-2-2-2-2-2-2-2-200000000000000000000
χ10222222222222-2-222-2-2-2-2-2-22-2-22-2-2-2-2-2-2-2-22222222200000000000000000000
χ112222222222-2-222-2-222-2-2-2-2-222-2000000000000000022-2-20000000000000000
χ122222222222-2-222-2-222-2-2-2-2-222-20000000000000000-2-2220000000000000000
χ132222222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000002i2i−2i−2i000000000000
χ142222222222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000−2i−2i2i2i000000000000
χ152222-2-222-2-20022002200000-2-202222−2−2−2−22222−2−2−2−2002i−2ii2−i2i2−i2000000000000
χ162222-2-222-2-20022002200000-2-202222−2−2−2−22222−2−2−2−200−2i2i−i2i2−i2i2000000000000
χ172222-2-222-2-20022002200000-2-20−2−2−2−22222−2−2−2−22222002i−2i−i2i2−i2i2000000000000
χ182222-2-222-2-20022002200000-2-20−2−2−2−22222−2−2−2−2222200−2i2ii2−i2i2−i2000000000000
χ192222-2-222-2-200-2-200-2-2000002202222−2−2−2−2−2−2−2−222222-2002−2−22000000000000
χ202222-2-222-2-200-2-200-2-2000002202222−2−2−2−2−2−2−2−22222-2200−222−2000000000000
χ212222-2-222-2-200-2-200-2-200000220−2−2−2−222222222−2−2−2−22-200−222−2000000000000
χ222222-2-222-2-200-2-200-2-200000220−2−2−2−222222222−2−2−2−2-22002−2−22000000000000
χ232222-2-2-2-222220022000000-200-222-2-222-2-20000000000000000i2i2−i2−i2i2i2−i2−i20000
χ242222-2-2-2-222220022000000-200-222-2-222-2-20000000000000000−i2−i2i2i2−i2−i2i2i20000
χ252222-2-2-2-222220022000000-200-2-2-222-2-2220000000000000000i2i2−i2−i2−i2−i2i2i20000
χ262222-2-2-2-222220022000000-200-2-2-222-2-2220000000000000000−i2−i2i2i2i2i2−i2−i20000
χ2722-2-22-22-22-2-2-20022000000200-2000000002i2i−2i−2i2i2i−2i−2i00000000i2−i2i2−i22−22−20000
χ2822-2-22-22-22-2-2-20022000000200-2000000002i2i−2i−2i2i2i−2i−2i00000000−i2i2−i2i2−22−220000
χ2922-2-22-22-22-2-2-20022000000200-200000000−2i−2i2i2i−2i−2i2i2i00000000i2−i2i2−i2−22−220000
χ3022-2-22-22-22-2-2-20022000000200-200000000−2i−2i2i2i−2i−2i2i2i00000000−i2i2−i2i22−22−20000
χ3122-2-2-22-222-22222-2-2-2-222-2-222-2-200000000000000000000000000000000002-2
χ3222-2-2-22-222-22222-2-2-2-222-2-222-2-20000000000000000000000000000000000-22
χ3322-2-2-22-222-222-2-2-2-222-2-2222-22-2000000000000000000000000000000002i−2i00
χ3422-2-2-22-222-222-2-2-2-222-2-2222-22-200000000000000000000000000000000−2i2i00
χ3522-2-2-22-222-2-2-22222-2-2-2-222-22-2200000000000000000000000000002i−2i−2i2i0000
χ3622-2-2-22-222-2-2-22222-2-2-2-222-22-220000000000000000000000000000−2i2i2i−2i0000
χ3722-2-2-22-222-2-2-2-2-2222222-2-2-2-2220000000000000000000000002-2-2200000000
χ3822-2-2-22-222-2-2-2-2-2222222-2-2-2-222000000000000000000000000-222-200000000
χ39444444-4-4-4-400000000000000002222−22−22−22−2222220000000000000000000000000000
χ40444444-4-4-4-40000000000000000−22−2222222222−22−220000000000000000000000000000
χ414444-4-4-4-444-4-400-4-40000004004000000000000000000000000000000000000
χ4244-4-44-44-44-44400-4-4000000-4004000000000000000000000000000000000000
χ4344-4-44-4-44-44004400-4-400000-440000000000000000000000000000000000000
χ4444-4-44-4-44-4400-4-40044000004-40000000000000000000000000000000000000
χ4544-4-4-444-4-440000000000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000
χ4644-4-4-444-4-44000000000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000
χ474-44-400000022−222i2−2i222−222i2−2i22i−2i2i−2i0000002ζ3+2ζ5−2ζ3−2ζ5002ζ+2ζ7−2ζ−2ζ7ζ+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+ζ700000000000000000000
χ484-44-400000022−222i2−2i222−222i2−2i22i−2i2i−2i000000−2ζ3−2ζ52ζ3+2ζ500−2ζ−2ζ72ζ+2ζ7−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−ζ700000000000000000000
χ494-44-400000022−22−2i22i222−22−2i22i2−2i2i−2i2i0000002ζ3+2ζ5−2ζ3−2ζ5002ζ+2ζ7−2ζ−2ζ7−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−ζ700000000000000000000
χ504-44-400000022−22−2i22i222−22−2i22i2−2i2i−2i2i000000−2ζ3−2ζ52ζ3+2ζ500−2ζ−2ζ72ζ+2ζ7ζ+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+ζ700000000000000000000
χ514-44-4000000−22222i2−2i2−22222i2−2i2−2i2i−2i2i0000002ζ+2ζ7−2ζ−2ζ700−2ζ3−2ζ52ζ3+2ζ5ζ−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−ζ700000000000000000000
χ524-44-4000000−22222i2−2i2−22222i2−2i2−2i2i−2i2i000000−2ζ−2ζ72ζ+2ζ7002ζ3+2ζ5−2ζ3−2ζ5−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+ζ700000000000000000000
χ534-44-4000000−2222−2i22i2−2222−2i22i22i−2i2i−2i0000002ζ+2ζ7−2ζ−2ζ700−2ζ3−2ζ52ζ3+2ζ5−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+ζ700000000000000000000
χ544-44-4000000−2222−2i22i2−2222−2i22i22i−2i2i−2i000000−2ζ−2ζ72ζ+2ζ7002ζ3+2ζ5−2ζ3−2ζ5ζ−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−ζ700000000000000000000
χ554-4-4400000022−222i2−2i2−2222−2i22i22i−2i−2i2i00002ζ3−2ζ5−2ζ3+2ζ5002ζ−2ζ7−2ζ+2ζ700ζ−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+ζ700000000000000000000
χ564-4-4400000022−222i2−2i2−2222−2i22i22i−2i−2i2i0000−2ζ3+2ζ52ζ3−2ζ500−2ζ+2ζ72ζ−2ζ700−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−ζ700000000000000000000
χ574-4-4400000022−22−2i22i2−22222i2−2i2−2i2i2i−2i00002ζ3−2ζ5−2ζ3+2ζ5002ζ−2ζ7−2ζ+2ζ700−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−ζ700000000000000000000
χ584-4-4400000022−22−2i22i2−22222i2−2i2−2i2i2i−2i0000−2ζ3+2ζ52ζ3−2ζ500−2ζ+2ζ72ζ−2ζ700ζ−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+ζ700000000000000000000
χ594-4-44000000−22222i2−2i222−22−2i22i2−2i2i2i−2i00002ζ−2ζ7−2ζ+2ζ700−2ζ3+2ζ52ζ3−2ζ500−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+ζ700000000000000000000
χ604-4-44000000−22222i2−2i222−22−2i22i2−2i2i2i−2i0000−2ζ+2ζ72ζ−2ζ7002ζ3−2ζ5−2ζ3+2ζ500ζ+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−ζ700000000000000000000
χ614-4-44000000−2222−2i22i222−222i2−2i22i−2i−2i2i00002ζ−2ζ7−2ζ+2ζ700−2ζ3+2ζ52ζ3−2ζ500ζ+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−ζ700000000000000000000
χ624-4-44000000−2222−2i22i222−222i2−2i22i−2i−2i2i0000−2ζ+2ζ72ζ−2ζ7002ζ3−2ζ5−2ζ3+2ζ500−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+ζ700000000000000000000

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