Finite Group Databasebeta

← Group #145508

Character table — Group #145508

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222222222444444444444444444444488888888888888883232323232323232
order122222444444448888888844444444448888888888881616161616161616161616161616161622448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1111-1-1
χ922222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ1022222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000
χ1122222222-2-2-2-22200000000-2-22222-2-2-2-20000000000002222−2−2−2−22222−2−2−2−200000000
χ1222222222-2-2-2-22200000000-2-22222-2-2-2-2000000000000−2−2−2−22222−2−2−2−2222200000000
χ1322222222-2-2-2-22200000000-2-2-2-2-2-222220000000000002222−2−2−2−2−2−2−2−2222200000000
χ1422222222-2-2-2-22200000000-2-2-2-2-2-22222000000000000−2−2−2−222222222−2−2−2−200000000
χ15222222-2-22222-2-222222222-2-200000000-2-2-2-20000000022-2-222-2-20000000000000000
χ16222222-2-22222-2-222222222-2-200000000-2-2-2-200000000-2-222-2-2220000000000000000
χ17222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-200000000222200000000000000002i2i−2i−2i2i2i−2i−2i00000000
χ18222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-20000000022220000000000000000−2i−2i2i2i−2i−2i2i2i00000000
χ19222222-2-2-2-2-2-2-2-200000000220000000000002i2i2i2i−2i−2i−2i−2i22−2−2−2−222i2i2−i2−i2−i2−i2i2i200000000
χ20222222-2-2-2-2-2-2-2-200000000220000000000002i2i2i2i−2i−2i−2i−2i−2−22222−2−2−i2−i2i2i2i2i2−i2−i200000000
χ21222222-2-2-2-2-2-2-2-20000000022000000000000−2i−2i−2i−2i2i2i2i2i22−2−2−2−222−i2−i2i2i2i2i2−i2−i200000000
χ22222222-2-2-2-2-2-2-2-20000000022000000000000−2i−2i−2i−2i2i2i2i2i−2−22222−2−2i2i2−i2−i2−i2−i2i2i200000000
χ232222-2-22-222-2-22-22222-2-2-2-22-20000000022-2-20000000000000000000000000000002i−2i
χ242222-2-22-222-2-22-22222-2-2-2-22-20000000022-2-2000000000000000000000000000000−2i2i
χ252222-2-22-222-2-22-2-2-2-2-222222-200000000-2-222000000000000000000000000020-20000
χ262222-2-22-222-2-22-2-2-2-2-222222-200000000-2-2220000000000000000000000000-2020000
χ272222-2-2-2222-2-2-222222-2-2-2-2-2200000000-2-22200000000000000000000000000002i−2i00
χ282222-2-2-2222-2-2-222222-2-2-2-2-2200000000-2-2220000000000000000000000000000−2i2i00
χ292222-2-2-2222-2-2-22-2-2-2-22222-220000000022-2-200000000000000000000000020-200000
χ302222-2-2-2222-2-2-22-2-2-2-22222-220000000022-2-2000000000000000000000000-20200000
χ312-2-222-2220000-2-222−2−22−22−20000002i2i−2i−2i2−22−2i2i2−i2−i2i2i2−i2−i2ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ500000000
χ322-2-222-2220000-2-222−2−22−22−20000002i2i−2i−2i2−22−2i2i2−i2−i2i2i2−i2−i2−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ500000000
χ332-2-222-2220000-2-222−2−22−22−2000000−2i−2i2i2i2−22−2−i2−i2i2i2−i2−i2i2i2ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ500000000
χ342-2-222-2220000-2-222−2−22−22−2000000−2i−2i2i2i2−22−2−i2−i2i2i2−i2−i2i2i2−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ500000000
χ352-2-222-2220000-2-2−2−222−22−220000002i2i−2i−2i−22−22−i2−i2i2i2−i2−i2i2i2ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ700000000
χ362-2-222-2220000-2-2−2−222−22−220000002i2i−2i−2i−22−22−i2−i2i2i2−i2−i2i2i2−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ700000000
χ372-2-222-2220000-2-2−2−222−22−22000000−2i−2i2i2i−22−22i2i2−i2−i2i2i2−i2−i2ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ700000000
χ382-2-222-2220000-2-2−2−222−22−22000000−2i−2i2i2i−22−22i2i2−i2−i2i2i2−i2−i2−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ700000000
χ392-2-222-2-2-200002222−2−22−22−20022-2-20000−22−2222−2−2−2−222ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ500000000
χ402-2-222-2-2-200002222−2−22−22−20022-2-20000−22−2222−2−2−2−222−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ500000000
χ412-2-222-2-2-200002222−2−22−22−200-2-2220000−22−22−2−22222−2−2ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ500000000
χ422-2-222-2-2-200002222−2−22−22−200-2-2220000−22−22−2−22222−2−2−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ500000000
χ432-2-222-2-2-2000022−2−222−22−220022-2-200002−22−2−2−22222−2−2ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ700000000
χ442-2-222-2-2-2000022−2−222−22−220022-2-200002−22−2−2−22222−2−2−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ700000000
χ452-2-222-2-2-2000022−2−222−22−2200-2-22200002−22−222−2−2−2−222ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ700000000
χ462-2-222-2-2-2000022−2−222−22−2200-2-22200002−22−222−2−2−2−222−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ700000000
χ474444-4-44-4-4-4444-400000000-4400000000000000000000000000000000000000000000
χ484444-4-4-44-4-444-44000000004-400000000000000000000000000000000000000000000
χ4944-4-40000004i−4i002i2−2i22i2−2i222−22−2222002-22-22i−2i2i−2i00002ζ2−2ζ22ζ2−2ζ22ζ6−2ζ62ζ6−2ζ6000000000000000000000000
χ5044-4-40000004i−4i002i2−2i22i2−2i222−22−222200-22-22−2i2i−2i2i0000−2ζ22ζ2−2ζ22ζ2−2ζ62ζ6−2ζ62ζ6000000000000000000000000
χ5144-4-40000004i−4i00−2i22i2−2i22i2−222222−22002-22-22i−2i2i−2i0000−2ζ22ζ2−2ζ22ζ2−2ζ62ζ6−2ζ62ζ6000000000000000000000000
χ5244-4-40000004i−4i00−2i22i2−2i22i2−222222−2200-22-22−2i2i−2i2i00002ζ2−2ζ22ζ2−2ζ22ζ6−2ζ62ζ6−2ζ6000000000000000000000000
χ5344-4-4000000−4i4i002i2−2i22i2−2i2−222222−22002-22-2−2i2i−2i2i00002ζ6−2ζ62ζ6−2ζ62ζ2−2ζ22ζ2−2ζ2000000000000000000000000
χ5444-4-4000000−4i4i002i2−2i22i2−2i2−222222−2200-22-222i−2i2i−2i0000−2ζ62ζ6−2ζ62ζ6−2ζ22ζ2−2ζ22ζ2000000000000000000000000
χ5544-4-4000000−4i4i00−2i22i2−2i22i222−22−2222002-22-2−2i2i−2i2i0000−2ζ62ζ6−2ζ62ζ6−2ζ22ζ2−2ζ22ζ2000000000000000000000000
χ5644-4-4000000−4i4i00−2i22i2−2i22i222−22−222200-22-222i−2i2i−2i00002ζ6−2ζ62ζ6−2ζ62ζ2−2ζ22ζ2−2ζ2000000000000000000000000
χ574-44-400004-40000000044-4-4002-2-222-2-2200002-2-222-2-22000000000000000000000000
χ584-44-400004-40000000044-4-400-222-2-222-20000-222-2-222-2000000000000000000000000
χ594-44-400004-400000000-4-444002-2-222-2-220000-222-2-222-2000000000000000000000000
χ604-44-400004-400000000-4-44400-222-2-222-200002-2-222-2-22000000000000000000000000
χ614-44-40000-4400004i−4i−4i4i0000002-2-22-222-200002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ624-44-40000-4400004i−4i−4i4i000000-222-22-2-220000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ634-44-40000-440000−4i4i4i−4i0000002-2-22-222-20000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ644-44-40000-440000−4i4i4i−4i000000-222-22-2-2200002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ654-4-44-444-40000-442222−22−22−2222−2222000000000022−22−222200000000000000000000000000000000
χ664-4-44-444-40000-44−22−22222222−2222−220000000000−222222−2200000000000000000000000000000000
χ674-4-44-44-4400004-42222−22−22−2222−22220000000000−222222−2200000000000000000000000000000000
χ684-4-44-44-4400004-4−22−22222222−2222−22000000000022−22−222200000000000000000000000000000000

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