Finite Group Databasebeta

← Group #115252

Character table — Group #115252

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222244444444222244444444444488888888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91-1-11-1-11111-1-11111-1-1-1-111-1-11-11-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i11-1-1ii−i−i11-1-1
χ101-1-11-1-11111-1-11111-1-1-1-111-1-11-11-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii-1-111−i−iii-1-111
χ111-1-11-1-11111-1-11111-1-1-1-111-1-11-11-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−i-1-111ii−i−i-1-111
χ121-1-11-1-11111-1-11111-1-1-1-111-1-11-11-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii11-1-1−i−iii11-1-1
χ131-1-11-1-11111-1-11111-1-1-1-111-1-11-11-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i11-1-1−i−iii-1-111
χ141-1-11-1-11111-1-11111-1-1-1-111-1-11-11-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iii-1-111ii−i−i11-1-1
χ151-1-11-1-11111-1-11111-1-1-1-111-1-11-11-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i-1-111−i−iii11-1-1
χ161-1-11-1-11111-1-11111-1-1-1-111-1-11-11-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iii11-1-1ii−i−i-1-111
χ1722222222222222222222-2-2-2-2-2-2-2-20000000022-2-222-2-2000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-200000000-2-222-2-222000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ20222222222222-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2322222222-2-2-2-222-2-222-2-22-22-22-2-220000000000000000000000002-22-2000000000000
χ2422222222-2-2-2-222-2-222-2-22-22-22-2-22000000000000000000000000-22-22000000000000
χ2522222222-2-2-2-222-2-222-2-2-22-22-222-200000000000000000000000000002-22-200000000
χ2622222222-2-2-2-222-2-222-2-2-22-22-222-20000000000000000000000000000-22-2200000000
χ2722222222-2-2-2-2-2-222-2-2222-22-2-222-20000000000000000000000000000000000002-22-2
χ2822222222-2-2-2-2-2-222-2-2222-22-2-222-2000000000000000000000000000000000000-22-22
χ2922222222-2-2-2-2-2-222-2-222-22-222-2-22000000000000000000000000000000002-22-20000
χ3022222222-2-2-2-2-2-222-2-222-22-222-2-2200000000000000000000000000000000-22-220000
χ312-2-22-2-22222-2-22222-2-2-2-2-2-222-22-22000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ322-2-22-2-22222-2-22222-2-2-2-2-2-222-22-2200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ332-2-22-2-22222-2-2-2-2-2-2222222-2-2-22-22000000000000000022-2-2-2-2220000000000000000
χ342-2-22-2-22222-2-2-2-2-2-2222222-2-2-22-220000000000000000-2-22222-2-20000000000000000
χ352-2-22-2-22222-2-2-2-2-2-22222-2-2222-22-222-2-2-2-22200000000000000000000000000000000
χ362-2-22-2-22222-2-2-2-2-2-22222-2-2222-22-2-2-22222-2-200000000000000000000000000000000
χ372-2-22-2-222-2-22222-2-2-2-2222-2-2222-2-20000000000000000000000002i−2i−2i2i000000000000
χ382-2-22-2-222-2-22222-2-2-2-2222-2-2222-2-2000000000000000000000000−2i2i2i−2i000000000000
χ392-2-22-2-222-2-22222-2-2-2-222-222-2-2-22200000000000000000000000000002-2-2200000000
χ402-2-22-2-222-2-22222-2-2-2-222-222-2-2-2220000000000000000000000000000-222-200000000
χ412-2-22-2-222-2-222-2-22222-2-22-2-22-2-2220000000000000000000000000000000000002-2-22
χ422-2-22-2-222-2-222-2-22222-2-22-2-22-2-222000000000000000000000000000000000000-222-2
χ432-2-22-2-222-2-222-2-22222-2-2-222-222-2-2000000000000000000000000000000002i−2i−2i2i0000
χ442-2-22-2-222-2-222-2-22222-2-2-222-222-2-200000000000000000000000000000000−2i2i2i−2i0000
χ454444-4-4-4-44-44-40000000000000000000000000022−220022−22000000000000000000000000
χ464444-4-4-4-44-44-400000000000000000000000000−222200−2222000000000000000000000000
χ474444-4-4-4-4-44-4400000000000000000000000022−220022−2200000000000000000000000000
χ484444-4-4-4-4-44-44000000000000000000000000−222200−222200000000000000000000000000
χ4944-4-44-44-40000004i−4i004i−4i0000000000000000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ30000000000000000
χ5044-4-44-44-40000004i−4i004i−4i000000000000000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ30000000000000000
χ5144-4-44-44-4000000−4i4i00−4i4i0000000000000000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ0000000000000000
χ5244-4-44-44-4000000−4i4i00−4i4i000000000000000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ0000000000000000
χ5344-4-4-44-4400004-4004-400000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ5444-4-4-44-4400004-4004-40000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ5544-4-4-44-440000-4400-4400000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ5644-4-4-44-440000-4400-440000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ574-44-44-4-4400004-400-4400000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ584-44-44-4-4400004-400-440000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ594-44-44-4-440000-44004-400000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ604-44-44-4-440000-44004-40000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ614-44-4-444-40000004i−4i00−4i4i0000000000000000000000002ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ0000000000000000
χ624-44-4-444-40000004i−4i00−4i4i000000000000000000000000−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ0000000000000000
χ634-44-4-444-4000000−4i4i004i−4i0000000000000000000000002ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ30000000000000000
χ644-44-4-444-4000000−4i4i004i−4i000000000000000000000000−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ30000000000000000
χ654-4-4444-4-44-4-44000000000000000000000000002i2−2i200−2i22i2000000000000000000000000
χ664-4-4444-4-44-4-4400000000000000000000000000−2i22i2002i2−2i2000000000000000000000000
χ674-4-4444-4-4-444-40000000000000000000000002i2−2i200−2i22i200000000000000000000000000
χ684-4-4444-4-4-444-4000000000000000000000000−2i22i2002i2−2i200000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.