Finite Group Databasebeta

← Group #105695

Character table — Group #105695

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12224444222222444444444444444444444444888888884444888888888888888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111111111-1-1-1-1-1-1-1-111111111-1-111111111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i
χ101111111111-1-1-1-1-1-1-1-111111111-1-111111111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii
χ111111111111-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii
χ121111111111-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i
χ131111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii
χ141111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i
χ151111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i
χ161111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii
χ1711111111-1-11-11-111-1-11111-1-1-1-11-11111-1-1-1-11-1ii−i−iii−i−i11-1-1i−ii−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i1-11-1i−ii−i
χ1811111111-1-11-11-111-1-11111-1-1-1-11-11111-1-1-1-11-1ii−i−iii−i−i11-1-1i−ii−iii−i−iii−i−i-1-111-1-111−i−iii−i−iii-11-11−ii−ii
χ1911111111-1-11-11-111-1-11111-1-1-1-11-11111-1-1-1-11-1−i−iii−i−iii11-1-1−ii−ii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii1-11-1−ii−ii
χ2011111111-1-11-11-111-1-11111-1-1-1-11-11111-1-1-1-11-1−i−iii−i−iii11-1-1−ii−ii−i−iii−i−iii-1-111-1-111ii−i−iii−i−i-11-11i−ii−i
χ2111111111-1-11-11-111-1-11111-1-1-1-11-1-1-1-1-111111-1ii−i−iii−i−i-1-111i−ii−i−i−iii−i−iii11-1-111-1-1ii−i−iii−i−i-11-11−ii−ii
χ2211111111-1-11-11-111-1-11111-1-1-1-11-1-1-1-1-111111-1ii−i−iii−i−i-1-111i−ii−i−i−iii−i−iii-1-111-1-111−i−iii−i−iii1-11-1i−ii−i
χ2311111111-1-11-11-111-1-11111-1-1-1-11-1-1-1-1-111111-1−i−iii−i−iii-1-111−ii−iiii−i−iii−i−i11-1-111-1-1−i−iii−i−iii-11-11i−ii−i
χ2411111111-1-11-11-111-1-11111-1-1-1-11-1-1-1-1-111111-1−i−iii−i−iii-1-111−ii−iiii−i−iii−i−i-1-111-1-111ii−i−iii−i−i1-11-1−ii−ii
χ2511111111-1-1-11-11-1-1111111-1-1-1-1-111111-1-1-1-1-11ii−i−i−i−iii-1-111i−i−iiii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1i−i−ii-111-1
χ2611111111-1-1-11-11-1-1111111-1-1-1-1-111111-1-1-1-1-11ii−i−i−i−iii-1-111i−i−iiii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111−iii−i1-1-11
χ2711111111-1-1-11-11-1-1111111-1-1-1-1-111111-1-1-1-1-11−i−iiiii−i−i-1-111−iii−i−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111i−i−ii1-1-11
χ2811111111-1-1-11-11-1-1111111-1-1-1-1-111111-1-1-1-1-11−i−iiiii−i−i-1-111−iii−i−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1−iii−i-111-1
χ2911111111-1-1-11-11-1-1111111-1-1-1-1-11-1-1-1-11111-11ii−i−i−i−iii11-1-1i−i−ii−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1−iii−i1-1-11
χ3011111111-1-1-11-11-1-1111111-1-1-1-1-11-1-1-1-11111-11ii−i−i−i−iii11-1-1i−i−ii−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111i−i−ii-111-1
χ3111111111-1-1-11-11-1-1111111-1-1-1-1-11-1-1-1-11111-11−i−iiiii−i−i11-1-1−iii−iii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111−iii−i-111-1
χ3211111111-1-1-11-11-1-1111111-1-1-1-1-11-1-1-1-11111-11−i−iiiii−i−i11-1-1−iii−iii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1i−i−ii1-1-11
χ33222222222222222222-2-2-2-222-2-2-2-200000000-2-2222222220000-2-2-2-200000000000000000000000000000000
χ34222222222222222222-2-2-2-222-2-2-2-200000000-2-2-2-2-2-2-2-2-2-20000222200000000000000000000000000000000
χ352222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-22200000000222222-2-2-2-20000-2-22200000000000000000000000000000000
χ362222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2220000000022-2-2-2-22222000022-2-200000000000000000000000000000000
χ3722222222-2-22-22-222-2-2-2-2-2-2-2-222-2200000000-222i2i−2i−2i2i2i−2i−2i0000−2i2i−2i2i00000000000000000000000000000000
χ3822222222-2-22-22-222-2-2-2-2-2-2-2-222-2200000000-22−2i−2i2i2i−2i−2i2i2i00002i−2i2i−2i00000000000000000000000000000000
χ3922222222-2-2-22-22-2-222-2-2-2-2-2-2222-2000000002-22i2i−2i−2i−2i−2i2i2i0000−2i2i2i−2i00000000000000000000000000000000
χ4022222222-2-2-22-22-2-222-2-2-2-2-2-2222-2000000002-2−2i−2i2i2i2i2i−2i−2i00002i−2i−2i2i00000000000000000000000000000000
χ412222-2-2-2-2222222-2-2-2-222-2-2-2-22-22200000000-2-200000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ422222-2-2-2-2222222-2-2-2-222-2-2-2-22-22200000000-2-20000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ432222-2-2-2-2222222-2-2-2-2-2-222-2-2-22-2-222-2-222-2-222000000002-22-2000000000000000000000000000000000000
χ442222-2-2-2-2222222-2-2-2-2-2-222-2-2-22-2-2-2-222-2-2222200000000-22-22000000000000000000000000000000000000
χ452222-2-2-2-222-2-2-2-2222222-2-2-2-22-2-2-2000000002200000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ462222-2-2-2-222-2-2-2-2222222-2-2-2-22-2-2-200000000220000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ472222-2-2-2-222-2-2-2-22222-2-222-2-2-222222-2-222-2-2-2-200000000-22-22000000000000000000000000000000000000
χ482222-2-2-2-222-2-2-2-22222-2-222-2-2-2222-2-222-2-222-2-2000000002-22-2000000000000000000000000000000000000
χ492222-2-2-2-2-2-22-22-2-2-22222-2-222-222-200000000-2200000000000000002-2-222-2-22000000000000000000000000
χ502222-2-2-2-2-2-22-22-2-2-22222-2-222-222-200000000-220000000000000000-222-2-222-2000000000000000000000000
χ512222-2-2-2-2-2-22-22-2-2-222-2-222222-2-2222-2-2-2-2222-2000000002-2-22000000000000000000000000000000000000
χ522222-2-2-2-2-2-22-22-2-2-222-2-222222-2-22-2-22222-2-22-200000000-222-2000000000000000000000000000000000000
χ532222-2-2-2-2-2-2-22-2222-2-222-2-222-22-22000000002-200000000000000002-2-22-222-2000000000000000000000000
χ542222-2-2-2-2-2-2-22-2222-2-222-2-222-22-22000000002-20000000000000000-222-22-2-22000000000000000000000000
χ552222-2-2-2-2-2-2-22-2222-2-2-2-222222-22-222-2-2-2-222-2200000000-222-2000000000000000000000000000000000000
χ562222-2-2-2-2-2-2-22-2222-2-2-2-222222-22-2-2-22222-2-2-22000000002-2-22000000000000000000000000000000000000
χ5722-2-222-2-22-222-2-22-22-200002-2000000000000002-22-22-22-200000000000000002−22−22−22−22−22−22−22−200000000
χ5822-2-222-2-22-222-2-22-22-200002-2000000000000002-22-22-22-20000000000000000−22−22−22−22−22−22−22−2200000000
χ5922-2-222-2-22-222-2-22-22-200002-200000000000000-22-22-22-2200000000000000002−22−22−22−2−22−22−22−2200000000
χ6022-2-222-2-22-222-2-22-22-200002-200000000000000-22-22-22-220000000000000000−22−22−22−222−22−22−22−200000000
χ6122-2-222-2-22-2-2-222-22-2200002-2000000000000002-22-2-22-220000000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i200000000
χ6222-2-222-2-22-2-2-222-22-2200002-2000000000000002-22-2-22-220000000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i200000000
χ6322-2-222-2-22-2-2-222-22-2200002-200000000000000-22-222-22-20000000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i200000000
χ6422-2-222-2-22-2-2-222-22-2200002-200000000000000-22-222-22-20000000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i200000000
χ6522-2-222-2-2-222-2-222-2-220000-22000000000000002i−2i−2i2i2i−2i−2i2i00000000000000002−2−222−2−22i2−i2−i2i2i2−i2−i2i200000000
χ6622-2-222-2-2-222-2-222-2-220000-22000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000−222−2−222−2−i2i2i2−i2−i2i2i2−i200000000
χ6722-2-222-2-2-222-2-222-2-220000-2200000000000000−2i2i2i−2i−2i2i2i−2i00000000000000002−2−222−2−22−i2i2i2−i2−i2i2i2−i200000000
χ6822-2-222-2-2-222-2-222-2-220000-2200000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000−222−2−222−2i2−i2−i2i2i2−i2−i2i200000000
χ6922-2-222-2-2-22-222-2-222-20000-22000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000i2−i2−i2i2−i2i2i2−i2−222−22−2−2200000000
χ7022-2-222-2-2-22-222-2-222-20000-22000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000−i2i2i2−i2i2−i2−i2i22−2−22−222−200000000
χ7122-2-222-2-2-22-222-2-222-20000-2200000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000i2−i2−i2i2−i2i2i2−i22−2−22−222−200000000
χ7222-2-222-2-2-22-222-2-222-20000-2200000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000−i2i2i2−i2i2−i2−i2i2−222−22−2−2200000000
χ7344-4-4-4-4444-444-4-4-44-440000-4400000000000000000000000000000000000000000000000000000000000000
χ7444-4-4-4-4444-4-4-4444-44-40000-4400000000000000000000000000000000000000000000000000000000000000
χ7544-4-4-4-444-444-4-44-444-400004-400000000000000000000000000000000000000000000000000000000000000
χ7644-4-4-4-444-44-444-44-4-4400004-400000000000000000000000000000000000000000000000000000000000000
χ774-44-44i−4i4i−4i00000000004i−4i4-400000000004-44i−4i00000000000000000000000000000000000000000000000000
χ784-44-44i−4i4i−4i00000000004i−4i4-40000000000-44−4i4i00000000000000000000000000000000000000000000000000
χ794-44-44i−4i4i−4i0000000000−4i4i-440000004-44i−4i000000000000000000000000000000000000000000000000000000
χ804-44-44i−4i4i−4i0000000000−4i4i-44000000-44−4i4i000000000000000000000000000000000000000000000000000000
χ814-44-4−4i4i−4i4i00000000004i−4i-440000004-4−4i4i000000000000000000000000000000000000000000000000000000
χ824-44-4−4i4i−4i4i00000000004i−4i-44000000-444i−4i000000000000000000000000000000000000000000000000000000
χ834-44-4−4i4i−4i4i0000000000−4i4i4-400000000004-4−4i4i00000000000000000000000000000000000000000000000000
χ844-44-4−4i4i−4i4i0000000000−4i4i4-40000000000-444i−4i00000000000000000000000000000000000000000000000000
χ858-8-888i−8i−8i8i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-88−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).