Finite Group Databasebeta

← Group #145076

Character table — Group #145076

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222224444444444444444444444441616161616161616161616161616161632323232
order1222224444444488884488888816161616161616161616161616161616248888888888161616164444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1
χ922222222222222-2-2-2-222-2-2-2-2-2-200000000000000002200000000-2-200000000
χ1022222222222222-2-2-2-222-2-2-2-2-2-20000000000000000-2-2000000002200000000
χ1122222222-2-2-2-2-2-200002-200000022222222−2−2−2−2−2−2−2−200000000002i−2ii2i2−i2−i20000
χ1222222222-2-2-2-2-2-200002-200000022222222−2−2−2−2−2−2−2−20000000000−2i2i−i2−i2i2i20000
χ1322222222-2-2-2-2-2-200002-2000000−2−2−2−2−2−2−2−22222222200000000002i−2i−i2−i2i2i20000
χ1422222222-2-2-2-2-2-200002-2000000−2−2−2−2−2−2−2−2222222220000000000−2i2ii2i2−i2−i20000
χ15222222-2-2222-2-222222-2-2-2-222-2-200000000000000000022-2-200000000000000
χ16222222-2-2222-2-222222-2-2-2-222-2-2000000000000000000-2-22200000000000000
χ17222222-2-2222-2-22-2-2-2-2-2-222-2-222000000000000000000000000000000002-200
χ18222222-2-2222-2-22-2-2-2-2-2-222-2-22200000000000000000000000000000000-2200
χ192222-2-2222-2-2-2-222222-2222-2-2-2-200000000000000000000000000000000002i−2i
χ202222-2-2222-2-2-2-222222-2222-2-2-2-20000000000000000000000000000000000−2i2i
χ212222-2-2222-2-2-2-22-2-2-2-2-22-2-2222200000000000000000000002i2i−2i−2i0000000000
χ222222-2-2222-2-2-2-22-2-2-2-2-22-2-222220000000000000000000000−2i−2i2i2i0000000000
χ232222-2-2-2-22-2-222222222-2-2-2-2-22200000000000000000000000000002-22-20000
χ242222-2-2-2-22-2-222222222-2-2-2-2-2220000000000000000000000000000-22-220000
χ252222-2-2-2-22-2-2222-2-2-2-22-22222-2-22i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i00000000000000000000
χ262222-2-2-2-22-2-2222-2-2-2-22-22222-2-2−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i00000000000000000000
χ272222-2-2-2-2-222-2-2-2000022000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i22-20000000000i2−i2−i2i20000
χ282222-2-2-2-2-222-2-2-2000022000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2-220000000000−i2i2i2−i20000
χ292222-2-2-2-2-222-2-2-2000022000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i22-20000000000−i2i2i2−i20000
χ302222-2-2-2-2-222-2-2-2000022000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2-220000000000i2−i2−i2i20000
χ3122-2-22-200-22-2002-2-22200002-20022−2−222−2−222−2−222−2−200002i−2ii2−i2i2−i20000000000
χ3222-2-22-200-22-2002-2-22200002-20022−2−222−2−222−2−222−2−20000−2i2i−i2i2−i2i20000000000
χ3322-2-22-200-22-2002-2-22200002-200−2−222−2−222−2−222−2−22200002i−2i−i2i2−i2i20000000000
χ3422-2-22-200-22-2002-2-22200002-200−2−222−2−222−2−222−2−2220000−2i2ii2−i2i2−i20000000000
χ3522-2-2-2200-2-2200222-2-200002-200i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2002i−2i002−2−220000000000
χ3622-2-2-2200-2-2200222-2-200002-200i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200−2i2i00−222−20000000000
χ3722-2-2-2200-2-2200222-2-200002-200−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2002i−2i00−222−20000000000
χ3822-2-2-2200-2-2200222-2-200002-200−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200−2i2i002−2−220000000000
χ39444444-4-4-4-4-444-40000-44000000000000000000000000000000000000000000
χ404444-4-444-44444-40000-4-4000000000000000000000000000000000000000000
χ4144-4-44-4004-4400-400000000000022-2-222-2-2-2-222-2-22200000000000000000000
χ4244-4-44-4004-4400-4000000000000-2-222-2-22222-2-222-2-200000000000000000000
χ4344-4-44-400-44-400444-4-40000-4400000000000000000000000000000000000000
χ4444-4-4-440044-400-40000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ4544-4-4-440044-400-4000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i00000000000000000000
χ4644-4-4-4400-4-44004-4-4440000-4400000000000000000000000000000000000000
χ474-44-400000004i−4i02i2−2i22i2−2i200000022−222ζ−2ζ2ζ−2ζ2ζ7−2ζ72ζ7−2ζ72ζ5−2ζ52ζ5−2ζ52ζ3−2ζ32ζ3−2ζ300000000000000000000
χ484-44-400000004i−4i02i2−2i22i2−2i200000022−22−2ζ2ζ−2ζ2ζ−2ζ72ζ7−2ζ72ζ7−2ζ52ζ5−2ζ52ζ5−2ζ32ζ3−2ζ32ζ300000000000000000000
χ494-44-400000004i−4i0−2i22i2−2i22i2000000−22222ζ5−2ζ52ζ5−2ζ52ζ3−2ζ32ζ3−2ζ3−2ζ2ζ−2ζ2ζ−2ζ72ζ7−2ζ72ζ700000000000000000000
χ504-44-400000004i−4i0−2i22i2−2i22i2000000−2222−2ζ52ζ5−2ζ52ζ5−2ζ32ζ3−2ζ32ζ32ζ−2ζ2ζ−2ζ2ζ7−2ζ72ζ7−2ζ700000000000000000000
χ514-44-40000000−4i4i02i2−2i22i2−2i2000000−22222ζ3−2ζ32ζ3−2ζ32ζ5−2ζ52ζ5−2ζ5−2ζ72ζ7−2ζ72ζ7−2ζ2ζ−2ζ2ζ00000000000000000000
χ524-44-40000000−4i4i02i2−2i22i2−2i2000000−2222−2ζ32ζ3−2ζ32ζ3−2ζ52ζ5−2ζ52ζ52ζ7−2ζ72ζ7−2ζ72ζ−2ζ2ζ−2ζ00000000000000000000
χ534-44-40000000−4i4i0−2i22i2−2i22i200000022−222ζ7−2ζ72ζ7−2ζ72ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ5−2ζ52ζ5−2ζ500000000000000000000
χ544-44-40000000−4i4i0−2i22i2−2i22i200000022−22−2ζ72ζ7−2ζ72ζ7−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ52ζ5−2ζ52ζ500000000000000000000
χ554-4-44004i−4i0000002i2−2i2−2i22i20022−220000ζ+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+ζ7−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
χ564-4-44004i−4i0000002i2−2i2−2i22i20022−220000−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−ζ7ζ+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
χ574-4-44004i−4i000000−2i22i22i2−2i200−22220000ζ+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+ζ7ζ+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
χ584-4-44004i−4i000000−2i22i22i2−2i200−22220000−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−ζ7−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
χ594-4-4400−4i4i0000002i2−2i2−2i22i200−22220000ζ−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+ζ7−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
χ604-4-4400−4i4i0000002i2−2i2−2i22i200−22220000−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−ζ7ζ−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
χ614-4-4400−4i4i000000−2i22i22i2−2i20022−220000ζ−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+ζ7ζ−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
χ624-4-4400−4i4i000000−2i22i22i2−2i20022−220000−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−ζ7−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.