Finite Group Databasebeta

← Group #365321

Character table — Group #365321

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222222222224444444444444444888888888888888888888888888888881616161616161616
order12224444222222444444888888888888888844444444888888882244444444444444888888888888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ911111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ1011111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1111111-1-1-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1
χ171111-1-1-1-111-1-1-1-111-1-111iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−iii−i−i11-1-11-11-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-111-1-11-11-1i−ii−i
χ181111-1-1-1-111-1-1-1-111-1-111iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−iii−i−i11-1-11-11-1ii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111-1-111-11-11−ii−ii
χ191111-1-1-1-111-1-1-1-111-1-111iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−iii−i−i11-1-1-11-11−i−iiiii−i−iii−i−i−i−iii-1-11111-1-111-1-1-11-11−ii−ii
χ201111-1-1-1-111-1-1-1-111-1-111iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−iii−i−i11-1-1-11-11−i−iii−i−iii−i−iii−i−iii-1-111-1-111-1-1111-11-1i−ii−i
χ211111-1-1-1-111-1-1-1-111-1-111iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiiiii−i−i-1-1111-11-1−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1-1-1111-1-11i−i−ii
χ221111-1-1-1-111-1-1-1-111-1-111iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiiiii−i−i-1-1111-11-1−i−iii−i−iiiii−i−iii−i−i-1-111-1-11111-1-1-111-1−iii−i
χ231111-1-1-1-111-1-1-1-111-1-111iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiiiii−i−i-1-111-11-11ii−i−iii−i−i−i−iii−i−iii11-1-111-1-1-1-111-111-1−iii−i
χ241111-1-1-1-111-1-1-1-111-1-111iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiiiii−i−i-1-111-11-11ii−i−i−i−iiiii−i−i−i−iii11-1-1-1-11111-1-11-1-11i−i−ii
χ251111-1-1-1-111-1-1-1-111-1-111−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−i−iii11-1-11-11-1−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111-1-111-11-11i−ii−i
χ261111-1-1-1-111-1-1-1-111-1-111−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−i−iii11-1-11-11-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-111-1-11-11-1−ii−ii
χ271111-1-1-1-111-1-1-1-111-1-111−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−i−iii11-1-1-11-11ii−i−iii−i−iii−i−iii−i−i-1-111-1-111-1-1111-11-1−ii−ii
χ281111-1-1-1-111-1-1-1-111-1-111−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−i−iii11-1-1-11-11ii−i−i−i−iii−i−iiiii−i−i-1-11111-1-111-1-1-11-11i−ii−i
χ291111-1-1-1-111-1-1-1-111-1-111−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i−i−iii-1-1111-11-1ii−i−iii−i−i−i−iii−i−iii-1-111-1-11111-1-1-111-1i−i−ii
χ301111-1-1-1-111-1-1-1-111-1-111−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i−i−iii-1-1111-11-1ii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1-1-1111-1-11−iii−i
χ311111-1-1-1-111-1-1-1-111-1-111−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i−i−iii-1-111-11-11−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-11111-1-11-1-11−iii−i
χ321111-1-1-1-111-1-1-1-111-1-111−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i−i−iii-1-111-11-11−i−iii−i−iiiii−i−iii−i−i11-1-111-1-1-1-111-111-1i−i−ii
χ332222222222-2-2-2-2-2-222-2-222-2-222-2-200000000000000002-22-2000000002i−2i2i−2i0000000000002i−2i2i−2i0000000000000000
χ342222222222-2-2-2-2-2-222-2-222-2-222-2-200000000000000002-22-200000000−2i2i−2i2i000000000000−2i2i−2i2i0000000000000000
χ352222222222-2-2-2-2-2-222-2-2-2-222-2-2220000000000000000-22-22000000002i−2i2i−2i000000000000−2i2i−2i2i0000000000000000
χ362222222222-2-2-2-2-2-222-2-2-2-222-2-2220000000000000000-22-2200000000−2i2i−2i2i0000000000002i−2i2i−2i0000000000000000
χ3722222222-2-22-2-222-2-2-22-2222222220000000000000000-2-2-2-200002-2-220000000000002-22-200000000000000000000
χ3822222222-2-22-2-222-2-2-22-2222222220000000000000000-2-2-2-20000-222-2000000000000-22-2200000000000000000000
χ3922222222-2-22-2-222-2-2-22-2-2-2-2-2-2-2-2-20000000000000000222200002-2-22000000000000-22-2200000000000000000000
χ4022222222-2-22-2-222-2-2-22-2-2-2-2-2-2-2-2-2000000000000000022220000-222-20000000000002-22-200000000000000000000
χ4122222222-2-2-222-2-22-2-2-2222-2-222-2-22222222222-2-222-2-2-22-22-2-2-2-20000000000000000000000000000000000000000
χ4222222222-2-2-222-2-22-2-2-2222-2-222-2-2-2-2-2-2-2-2-2-2-2-222-2-222-22-2222220000000000000000000000000000000000000000
χ4322222222-2-2-222-2-22-2-2-22-2-222-2-22222222222-2-222-2-2222-22-2-2-2-2-20000000000000000000000000000000000000000
χ4422222222-2-2-222-2-22-2-2-22-2-222-2-222-2-2-2-2-2-2-2-222-2-222-2-22-22-222220000000000000000000000000000000000000000
χ452222-2-2-2-2222222-2-2-2-2-2-22i2i−2i−2i−2i−2i2i2i00000000000000002i−2i−2i2i000000002-2-22000000000000−2i2i2i−2i0000000000000000
χ462222-2-2-2-2222222-2-2-2-2-2-22i2i−2i−2i−2i−2i2i2i00000000000000002i−2i−2i2i00000000-222-20000000000002i−2i−2i2i0000000000000000
χ472222-2-2-2-2222222-2-2-2-2-2-2−2i−2i2i2i2i2i−2i−2i0000000000000000−2i2i2i−2i000000002-2-220000000000002i−2i−2i2i0000000000000000
χ482222-2-2-2-2222222-2-2-2-2-2-2−2i−2i2i2i2i2i−2i−2i0000000000000000−2i2i2i−2i00000000-222-2000000000000−2i2i2i−2i0000000000000000
χ492222-2-2-2-2-2-22-2-22-2222-222i2i−2i−2i−2i−2i2i2i2222-2-2-2-22i2i−2i−2i−2i−2i2i2i−2i2i2i−2i-2-2220000000000000000000000000000000000000000
χ502222-2-2-2-2-2-22-2-22-2222-222i2i−2i−2i−2i−2i2i2i-2-2-2-22222−2i−2i2i2i2i2i−2i−2i−2i2i2i−2i22-2-20000000000000000000000000000000000000000
χ512222-2-2-2-2-2-22-2-22-2222-22−2i−2i2i2i2i2i−2i−2i2222-2-2-2-2−2i−2i2i2i2i2i−2i−2i2i−2i−2i2i-2-2220000000000000000000000000000000000000000
χ522222-2-2-2-2-2-22-2-22-2222-22−2i−2i2i2i2i2i−2i−2i-2-2-2-222222i2i−2i−2i−2i−2i2i2i2i−2i−2i2i22-2-20000000000000000000000000000000000000000
χ532222-2-2-2-2-2-2-222-22-2222-22i2i2i2i−2i−2i−2i−2i0000000000000000−2i−2i2i2i000022-2-20000000000002i−2i−2i2i00000000000000000000
χ542222-2-2-2-2-2-2-222-22-2222-22i2i2i2i−2i−2i−2i−2i0000000000000000−2i−2i2i2i0000-2-222000000000000−2i2i2i−2i00000000000000000000
χ552222-2-2-2-2-2-2-222-22-2222-2−2i−2i−2i−2i2i2i2i2i00000000000000002i2i−2i−2i000022-2-2000000000000−2i2i2i−2i00000000000000000000
χ562222-2-2-2-2-2-2-222-22-2222-2−2i−2i−2i−2i2i2i2i2i00000000000000002i2i−2i−2i0000-2-2220000000000002i−2i−2i2i00000000000000000000
χ5722-2-222-2-22-222-2-2-2-22-2220000000022-2-222-2-20000000000002-22-2000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ5822-2-222-2-22-222-2-2-2-22-2220000000022-2-222-2-20000000000002-22-200000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ5922-2-222-2-22-222-2-2-2-22-22200000000-2-222-2-222000000000000-22-22000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ6022-2-222-2-22-222-2-2-2-22-22200000000-2-222-2-222000000000000-22-2200000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ6122-2-222-2-2-22-22-222-2-22-220000000022-2-222-2-2000000000000-22-220000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000
χ6222-2-222-2-2-22-22-222-2-22-220000000022-2-222-2-2000000000000-22-22000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ6322-2-222-2-2-22-22-222-2-22-2200000000-2-222-2-2220000000000002-22-20000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000
χ6422-2-222-2-2-22-22-222-2-22-2200000000-2-222-2-2220000000000002-22-2000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000
χ6522-2-2-2-2222-2-2-222-2-2-22220000000022-2-2-2-2220000000000002-2-22000000002-2-222-2-22000000000000000000000000
χ6622-2-2-2-2222-2-2-222-2-2-22220000000022-2-2-2-2220000000000002-2-2200000000-222-2-222-2000000000000000000000000
χ6722-2-2-2-2222-2-2-222-2-2-222200000000-2-22222-2-2000000000000-222-2000000002-2-22-222-2000000000000000000000000
χ6822-2-2-2-2222-2-2-222-2-2-222200000000-2-22222-2-2000000000000-222-200000000-222-22-2-22000000000000000000000000
χ6922-2-2-2-222-222-22-22-22-2-220000000022-2-2-2-222000000000000-222-20000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000
χ7022-2-2-2-222-222-22-22-22-2-220000000022-2-2-2-222000000000000-222-2000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000
χ7122-2-2-2-222-222-22-22-22-2-2200000000-2-22222-2-20000000000002-2-220000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000
χ7222-2-2-2-222-222-22-22-22-2-2200000000-2-22222-2-20000000000002-2-22000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000
χ7344-4-444-4-44-4-4-444444-4-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ7444-4-444-4-4-444-44-4-44-444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ7544-4-4-4-4444-444-4-444-44-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ7644-4-4-4-444-44-44-44-444-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ774-44-44i−4i4i−4i000000000000004ζ3−4ζ3004ζ−4ζ2i2−2i22i2−2i222−2222−22002+2i−2−2i002−2i−2+2i000000000000000000000000000000000000000000000000
χ784-44-44i−4i4i−4i000000000000004ζ3−4ζ3004ζ−4ζ−2i22i2−2i22i2−2222−222200−2−2i2+2i00−2+2i2−2i000000000000000000000000000000000000000000000000
χ794-44-44i−4i4i−4i00000000000000−4ζ34ζ300−4ζ4ζ2i2−2i22i2−2i222−2222−2200−2−2i2+2i00−2+2i2−2i000000000000000000000000000000000000000000000000
χ804-44-44i−4i4i−4i00000000000000−4ζ34ζ300−4ζ4ζ−2i22i2−2i22i2−2222−2222002+2i−2−2i002−2i−2+2i000000000000000000000000000000000000000000000000
χ814-44-4−4i4i−4i4i000000000000004ζ−4ζ004ζ3−4ζ32i2−2i22i2−2i2−2222−2222002−2i−2+2i002+2i−2−2i000000000000000000000000000000000000000000000000
χ824-44-4−4i4i−4i4i000000000000004ζ−4ζ004ζ3−4ζ3−2i22i2−2i22i222−2222−2200−2+2i2−2i00−2−2i2+2i000000000000000000000000000000000000000000000000
χ834-44-4−4i4i−4i4i00000000000000−4ζ4ζ00−4ζ34ζ32i2−2i22i2−2i2−2222−222200−2+2i2−2i00−2−2i2+2i000000000000000000000000000000000000000000000000
χ844-44-4−4i4i−4i4i00000000000000−4ζ4ζ00−4ζ34ζ3−2i22i2−2i22i222−2222−22002−2i−2+2i002+2i−2−2i000000000000000000000000000000000000000000000000
χ854-4-444i−4i−4i4i0000000000004ζ3−4ζ3004ζ−4ζ002i2−2i2−2i22i222−22−22222+2i−2−2i002−2i−2+2i00000000000000000000000000000000000000000000000000
χ864-4-444i−4i−4i4i0000000000004ζ3−4ζ3004ζ−4ζ00−2i22i22i2−2i2−222222−22−2−2i2+2i00−2+2i2−2i00000000000000000000000000000000000000000000000000
χ874-4-444i−4i−4i4i000000000000−4ζ34ζ300−4ζ4ζ002i2−2i2−2i22i222−22−2222−2−2i2+2i00−2+2i2−2i00000000000000000000000000000000000000000000000000
χ884-4-444i−4i−4i4i000000000000−4ζ34ζ300−4ζ4ζ00−2i22i22i2−2i2−222222−222+2i−2−2i002−2i−2+2i00000000000000000000000000000000000000000000000000
χ894-4-44−4i4i4i−4i0000000000004ζ−4ζ004ζ3−4ζ3002i2−2i2−2i22i2−222222−222−2i−2+2i002+2i−2−2i00000000000000000000000000000000000000000000000000
χ904-4-44−4i4i4i−4i0000000000004ζ−4ζ004ζ3−4ζ300−2i22i22i2−2i222−22−2222−2+2i2−2i00−2−2i2+2i00000000000000000000000000000000000000000000000000
χ914-4-44−4i4i4i−4i000000000000−4ζ4ζ00−4ζ34ζ3002i2−2i2−2i22i2−222222−22−2+2i2−2i00−2−2i2+2i00000000000000000000000000000000000000000000000000
χ924-4-44−4i4i4i−4i000000000000−4ζ4ζ00−4ζ34ζ300−2i22i22i2−2i222−22−22222−2i−2+2i002+2i−2−2i00000000000000000000000000000000000000000000000000

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