Finite Group Databasebeta

← Group #153318

Character table — Group #153318

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222222222444444444444444444444488888888888888883232323232323232
order12222244448888161616161616161644448888881616161616161616161616163232323232323232323232323232323224444488
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1
χ51111111111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1111-1-1
χ81111111111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-1-111
χ922222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ1022222222222222-2-2-2-2-2-2-2-2-2-2-2-22-2-2-2-22-2-2-2-222222222000000000000000000000000
χ112222222222-2-2-2-2000000002222-2-2-2-2-2-20000000000002222−2−2−2−22222−2−2−2−200000000
χ122222222222-2-2-2-2000000002222-2-2-2-2-2-2000000000000−2−2−2−22222−2−2−2−2222200000000
χ132222222222-2-2-2-200000000-2-2-2-2-22222-20000000000002222−2−2−2−2−2−2−2−2222200000000
χ142222222222-2-2-2-200000000-2-2-2-2-22222-2000000000000−2−2−2−222222222−2−2−2−200000000
χ152222-2-222-2-22222222222220000-20000-2-2-2-2-2000000000000000000000000200-20000
χ162222-2-222-2-22222222222220000-20000-2-2-2-2-2000000000000000000000000-20020000
χ172222-2-222-2-22222-2-2-2-2-2-2-2-20000-20000-222220000000000000000000000000000002i−2i
χ182222-2-222-2-22222-2-2-2-2-2-2-2-20000-20000-22222000000000000000000000000000000−2i2i
χ192222-2-2-2-222000022−2−222−2−20000022-2-2022−2−22222−2−2−2−2ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ700000000
χ202222-2-2-2-222000022−2−222−2−20000022-2-2022−2−22222−2−2−2−2−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ700000000
χ212222-2-2-2-222000022−2−222−2−200000-2-222022−2−2−2−2−2−22222ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ700000000
χ222222-2-2-2-222000022−2−222−2−200000-2-222022−2−2−2−2−2−22222−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ700000000
χ232222-2-2-2-2220000−2−222−2−2220000022-2-20−2−222−2−2−2−22222ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ500000000
χ242222-2-2-2-2220000−2−222−2−2220000022-2-20−2−222−2−2−2−22222−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ500000000
χ252222-2-2-2-2220000−2−222−2−22200000-2-2220−2−2222222−2−2−2−2ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ500000000
χ262222-2-2-2-2220000−2−222−2−22200000-2-2220−2−2222222−2−2−2−2−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ500000000
χ272-2-222-22-22-2000022−2−2−2−2222i2i−2i−2i0000002−22−2i2i2−i2−i2i2i2−i2−i2ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ500000000
χ282-2-222-22-22-2000022−2−2−2−2222i2i−2i−2i0000002−22−2i2i2−i2−i2i2i2−i2−i2−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ500000000
χ292-2-222-22-22-2000022−2−2−2−222−2i−2i2i2i0000002−22−2−i2−i2i2i2−i2−i2i2i2ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ500000000
χ302-2-222-22-22-2000022−2−2−2−222−2i−2i2i2i0000002−22−2−i2−i2i2i2−i2−i2i2i2−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ500000000
χ312-2-222-22-22-20000−2−22222−2−22i2i−2i−2i000000−22−22−i2−i2i2i2−i2−i2i2i2ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ700000000
χ322-2-222-22-22-20000−2−22222−2−22i2i−2i−2i000000−22−22−i2−i2i2i2−i2−i2i2i2−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ700000000
χ332-2-222-22-22-20000−2−22222−2−2−2i−2i2i2i000000−22−22i2i2−i2−i2i2i2−i2−i2ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ700000000
χ342-2-222-22-22-20000−2−22222−2−2−2i−2i2i2i000000−22−22i2i2−i2−i2i2i2−i2−i2−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ700000000
χ352-2-222-2-22-22-2-2222222-2-2-2-2000020000-2-222-200000000000000000000000002i−2i00000
χ362-2-222-2-22-22-2-2222222-2-2-2-2000020000-2-222-20000000000000000000000000−2i2i00000
χ372-2-222-2-22-22-2-222-2-2-2-22222000020000-22-2-2200000000000000000000000000002-200
χ382-2-222-2-22-22-2-222-2-2-2-22222000020000-22-2-220000000000000000000000000000-2200
χ392-2-22-22-222-222-2-200000000000020000-200002i2i−2i−2i−2i−2i2i2ii2−i2−i2i2−i2i2i2−i22−2−222−2−2200000000
χ402-2-22-22-222-222-2-200000000000020000-200002i2i−2i−2i−2i−2i2i2i−i2i2i2−i2i2−i2−i2i2−222−2−222−200000000
χ412-2-22-22-222-222-2-200000000000020000-20000−2i−2i2i2i2i2i−2i−2ii2−i2−i2i2−i2i2i2−i2−222−2−222−200000000
χ422-2-22-22-222-222-2-200000000000020000-20000−2i−2i2i2i2i2i−2i−2i−i2i2i2−i2i2−i2−i2i22−2−222−2−2200000000
χ432-2-22-22-222-2-2-2222222-2-2-2-20000-2000022-2-22000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ442-2-22-22-222-2-2-2222222-2-2-2-20000-2000022-2-2200000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ452-2-22-22-222-2-2-222-2-2-2-222220000-200002-222-200000000000000002-2-22-222-200000000
χ462-2-22-22-222-2-2-222-2-2-2-222220000-200002-222-20000000000000000-222-22-2-2200000000
χ47444444-4-4-4-400002222−22−222222−22−220000000000−22−22222200000000000000000000000000000000
χ48444444-4-4-4-40000−22−222222−22−22222200000000002222−22−2200000000000000000000000000000000
χ494444-4-444-4-4-4-4-4-4000000000000400004000000000000000000000000000000000000
χ5044-4-400000022−2222−222ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52-22-200022−2200000ζ−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+ζ7000000000000000000000000
χ5144-4-400000022−2222−222ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5-22-22000−222200000−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−ζ7000000000000000000000000
χ5244-4-400000022−2222−22−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52-22-200022−2200000−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−ζ7000000000000000000000000
χ5344-4-400000022−2222−22−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5-22-22000−222200000ζ−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+ζ7000000000000000000000000
χ5444-4-4000000−2222−22222ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72-22-2000−222200000ζ+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−ζ7000000000000000000000000
χ5544-4-4000000−2222−22222ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7-22-2200022−2200000−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+ζ7000000000000000000000000
χ5644-4-4000000−2222−2222−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72-22-2000−222200000−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+ζ7000000000000000000000000
χ5744-4-4000000−2222−2222−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7-22-2200022−2200000ζ+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−ζ7000000000000000000000000
χ584-44-400000022−22−22222ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72i−2i−2i2i02i2−2i20000000ζ−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+ζ7000000000000000000000000
χ594-44-400000022−22−22222ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7−2i2i2i−2i0−2i22i20000000−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−ζ7000000000000000000000000
χ604-44-400000022−22−2222−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72i−2i−2i2i02i2−2i20000000−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−ζ7000000000000000000000000
χ614-44-400000022−22−2222−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2i2i2i−2i0−2i22i20000000ζ−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+ζ7000000000000000000000000
χ624-44-4000000−222222−222ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52i−2i−2i2i0−2i22i20000000ζ+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−ζ7000000000000000000000000
χ634-44-4000000−222222−222ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2i2i2i−2i02i2−2i20000000−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+ζ7000000000000000000000000
χ644-44-4000000−222222−22−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52i−2i−2i2i0−2i22i20000000−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+ζ7000000000000000000000000
χ654-44-4000000−222222−22−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2i2i2i−2i02i2−2i20000000ζ+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−ζ7000000000000000000000000
χ664-4-444-4-44-4444-4-4000000000000-400004000000000000000000000000000000000000
χ674-4-44-444-4-4400002222−22−22−22−2222220000000000−2222−222200000000000000000000000000000000
χ684-4-44-444-4-440000−22−2222222222−22−22000000000022−2222−2200000000000000000000000000000000

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