Finite Group Databasebeta

← Group #147462

Character table — Group #147462

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222222222224444444444444444888888888888888888888888888888881616161616161616
order122244442222224444444444444488888888444488888888888888888888888888881616161616161616161616161616161622448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
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
χ511111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ711111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111-1-1-1-111-1-1-1-111-1iiii−i−i−i−i1-1111-1-111-1-1ii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-111-1-1ii−i−i
χ101111-1-1-1-111-1-1-1-111-1iiii−i−i−i−i1-1111-1-111-1-1ii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-1-1-1-11111-1-111−i−iii
χ111111-1-1-1-111-1-1-1-111-1iiii−i−i−i−i1-1111-1-111-1-1ii−i−i11-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1-1-111−i−iii
χ121111-1-1-1-111-1-1-1-111-1iiii−i−i−i−i1-1111-1-111-1-1ii−i−i11-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii-1-1-1-1111111-1-1ii−i−i
χ131111-1-1-1-111-1-1-1-111-1−i−i−i−iiiii1-1111-1-111-1-1−i−iii11-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i-1-1-1-1111111-1-1−i−iii
χ141111-1-1-1-111-1-1-1-111-1−i−i−i−iiiii1-1111-1-111-1-1−i−iii11-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−i
χ151111-1-1-1-111-1-1-1-111-1−i−i−i−iiiii1-1111-1-111-1-1−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-1-1-1-11111-1-111ii−i−i
χ161111-1-1-1-111-1-1-1-111-1−i−i−i−iiiii1-1111-1-111-1-1−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii
χ171-1-1111-1-11-111-1-11-11ii−i−iii−i−i1-1-111-1-1-1-111i−ii−i1-11-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i1-11-1i−ii−i
χ181-1-1111-1-11-111-1-11-11ii−i−iii−i−i1-1-111-1-1-1-111i−ii−i1-11-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i-1-111-1-111−i−iii−i−iii-11-11−ii−ii
χ191-1-1111-1-11-111-1-11-11ii−i−iii−i−i1-1-111-1-1-1-111i−ii−i1-11-1ii−i−iii−i−i-1-111-1-111−i−iii−i−iii11-1-111-1-1ii−i−iii−i−i-11-11−ii−ii
χ201-1-1111-1-11-111-1-11-11ii−i−iii−i−i1-1-111-1-1-1-111i−ii−i1-11-1ii−i−iii−i−i-1-111-1-111−i−iii−i−iii-1-111-1-111−i−iii−i−iii1-11-1i−ii−i
χ211-1-1111-1-11-111-1-11-11−i−iii−i−iii1-1-111-1-1-1-111−ii−ii1-11-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii1-11-1−ii−ii
χ221-1-1111-1-11-111-1-11-11−i−iii−i−iii1-1-111-1-1-1-111−ii−ii1-11-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−i-11-11i−ii−i
χ231-1-1111-1-11-111-1-11-11−i−iii−i−iii1-1-111-1-1-1-111−ii−ii1-11-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−i11-1-111-1-1−i−iii−i−iii-11-11i−ii−i
χ241-1-1111-1-11-111-1-11-11−i−iii−i−iii1-1-111-1-1-1-111−ii−ii1-11-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−i-1-111-1-111ii−i−iii−i−i1-11-1−ii−ii
χ251-1-11-1-1111-1-1-1111-1-111-1-1-1-11111-11111-1-1-1-11-1-111-1-1111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i1-1-111-1-11
χ261-1-11-1-1111-1-1-1111-1-111-1-1-1-11111-11111-1-1-1-11-1-111-1-1111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii-111-1-111-1
χ271-1-11-1-1111-1-1-1111-1-111-1-1-1-11111-11111-1-1-1-11-1-111-1-1111-1-1-1-111−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i-111-1-111-1
χ281-1-11-1-1111-1-1-1111-1-111-1-1-1-11111-11111-1-1-1-11-1-111-1-1111-1-1-1-111−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii1-1-111-1-11
χ291-1-11-1-1111-1-1-1111-1-1-1-11111-1-111-11111-1-1-1-1-111-11-1-11-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii1-1-11-111-1
χ301-1-11-1-1111-1-1-1111-1-1-1-11111-1-111-11111-1-1-1-1-111-11-1-11-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i-111-11-1-11
χ311-1-11-1-1111-1-1-1111-1-1-1-11111-1-111-11111-1-1-1-1-111-11-1-11-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii-111-11-1-11
χ321-1-11-1-1111-1-1-1111-1-1-1-11111-1-111-11111-1-1-1-1-111-11-1-11-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i1-1-11-111-1
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χ3422222222222222222-2-2-2-2-2-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000
χ3522222222-2-22-22-2-22-2000000002-2-2222222220000-2-2-2-2000000002-22-22-22-200000000000000000000000000000000
χ3622222222-2-22-22-2-22-2000000002-2-2222222220000-2-2-2-200000000-22-22-22-2200000000000000000000000000000000
χ3722222222-2-22-22-2-22-2000000002-2-2-2-2-2-2-2-2-2-20000222200000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ3822222222-2-22-22-2-22-2000000002-2-2-2-2-2-2-2-2-2-2000022220000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ3922222222-2-2-22-222-2-222222222-2-2200000000-2-2-2-200000000000000000000000000002−22−22−22−22−22−22−22−200000000
χ4022222222-2-2-22-222-2-222222222-2-2200000000-2-2-2-20000000000000000000000000000−22−22−22−22−22−22−22−2200000000
χ4122222222-2-2-22-222-2-2-2-2-2-2-2-2-2-2-2-2200000000222200000000000000000000000000002−22−22−22−2−22−22−22−2200000000
χ4222222222-2-2-22-222-2-2-2-2-2-2-2-2-2-2-2-220000000022220000000000000000000000000000−22−22−22−222−22−22−22−200000000
χ432222-2-2-2-222-2-2-2-222-22i2i2i2i−2i−2i−2i−2i2-22-2-222-2-2222i2i−2i−2i-2-222−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000
χ442222-2-2-2-222-2-2-2-222-2−2i−2i−2i−2i2i2i2i2i2-22-2-222-2-222−2i−2i2i2i-2-2222i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000
χ452222-2-2-2-2-2-22-22-22-222i2i2i2i−2i−2i−2i−2i-22200000000−2i−2i2i2i0000000000000000000000000000i2−i2i2−i2−i2i2−i2i22−22−2−22−2200000000
χ462222-2-2-2-2-2-22-22-22-222i2i2i2i−2i−2i−2i−2i-22200000000−2i−2i2i2i0000000000000000000000000000−i2i2−i2i2i2−i2i2−i2−22−222−22−200000000
χ472222-2-2-2-2-2-22-22-22-22−2i−2i−2i−2i2i2i2i2i-222000000002i2i−2i−2i0000000000000000000000000000i2−i2i2−i2−i2i2−i2i2−22−222−22−200000000
χ482222-2-2-2-2-2-22-22-22-22−2i−2i−2i−2i2i2i2i2i-222000000002i2i−2i−2i0000000000000000000000000000−i2i2−i2i2i2−i2i2−i22−22−2−22−2200000000
χ492222-2-2-2-2-2-2-22-22-2220000000022-222-2-222-2-20000-2-222000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ502222-2-2-2-2-2-2-22-22-2220000000022-222-2-222-2-20000-2-22200000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ512222-2-2-2-2-2-2-22-22-2220000000022-2-2-222-2-222000022-2-200000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ522222-2-2-2-2-2-2-22-22-2220000000022-2-2-222-2-222000022-2-20000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ532-2-2222-2-22-222-2-22-222i2i−2i−2i2i2i−2i−2i2-2-2-2-22222-2-22i−2i2i−2i-22-22−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ542-2-2222-2-22-222-2-22-22−2i−2i2i2i−2i−2i2i2i2-2-2-2-22222-2-2−2i2i−2i2i-22-222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ552-2-2222-2-2-222-2-22-2-2-20000000022222-2-2-2-2220000-22-22000000002-2-222-2-2200000000000000000000000000000000
χ562-2-2222-2-2-222-2-22-2-2-20000000022222-2-2-2-2220000-22-2200000000-222-2-222-200000000000000000000000000000000
χ572-2-2222-2-2-222-2-22-2-2-200000000222-2-22222-2-200002-22-200000000000000002-2-222-2-22000000000000000000000000
χ582-2-2222-2-2-222-2-22-2-2-200000000222-2-22222-2-200002-22-20000000000000000-222-2-222-2000000000000000000000000
χ592-2-2222-2-2-22-222-222-22i2i−2i−2i2i2i−2i−2i-22-200000000−2i2i−2i2i00000000000000000000000000002−2−222−2−22i2−i2−i2i2i2−i2−i2i200000000
χ602-2-2222-2-2-22-222-222-22i2i−2i−2i2i2i−2i−2i-22-200000000−2i2i−2i2i0000000000000000000000000000−222−2−222−2−i2i2i2−i2−i2i2i2−i200000000
χ612-2-2222-2-2-22-222-222-2−2i−2i2i2i−2i−2i2i2i-22-2000000002i−2i2i−2i00000000000000000000000000002−2−222−2−22−i2i2i2−i2−i2i2i2−i200000000
χ622-2-2222-2-2-22-222-222-2−2i−2i2i2i−2i−2i2i2i-22-2000000002i−2i2i−2i0000000000000000000000000000−222−2−222−2i2−i2−i2i2i2−i2−i2i200000000
χ632-2-22-2-2222-2-2-2222-2-222-2-2-2-22222-2-2-2-2-222222-2-22-222-2-2-22222-2-20000000000000000000000000000000000000000
χ642-2-22-2-2222-2-2-2222-2-2-2-22222-2-222-2-2-2-2-22222-222-2-222-222-2-2-2-2220000000000000000000000000000000000000000
χ652-2-22-2-222-222-2-2222222-2-2-2-222-2-2-200000000-222-20000000000000000000000000000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i200000000
χ662-2-22-2-222-222-2-2222222-2-2-2-222-2-2-200000000-222-20000000000000000000000000000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i200000000
χ672-2-22-2-222-222-2-22222-2-22222-2-2-2-2-2000000002-2-220000000000000000000000000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i200000000
χ682-2-22-2-222-222-2-22222-2-22222-2-2-2-2-2000000002-2-220000000000000000000000000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i200000000
χ692-2-22-2-222-22-222-2-2-22000000002-222222-2-2-2-20000-222-2000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ702-2-22-2-222-22-222-2-2-22000000002-222222-2-2-2-20000-222-200000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ712-2-22-2-222-22-222-2-2-22000000002-22-2-2-2-2222200002-2-2200000000000000002-2-22-222-2000000000000000000000000
χ722-2-22-2-222-22-222-2-2-22000000002-22-2-2-2-2222200002-2-220000000000000000-222-22-2-22000000000000000000000000
χ734444444444-4-4-4-4-4-4400000000-44-40000000000000000000000000000000000000000000000000000000000000000
χ744444-4-4-4-4444444-4-4-400000000-4-4-40000000000000000000000000000000000000000000000000000000000000000
χ7544-4-44i−4i4i−4i0000000002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i00022−222i2−2i222−222i2−2i2000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000000000000000000000000000
χ7644-4-44i−4i4i−4i0000000002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i000−2222−2i22i2−2222−2i22i200000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000000000000000000000000000
χ7744-4-44i−4i4i−4i000000000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i00022−222i2−2i222−222i2−2i200000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000000000000000000000000000
χ7844-4-44i−4i4i−4i000000000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i000−2222−2i22i2−2222−2i22i2000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000000000000000000000000000
χ7944-4-4−4i4i−4i4i0000000002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i00022−22−2i22i222−22−2i22i200000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000000000000000000000000000
χ8044-4-4−4i4i−4i4i0000000002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i000−22222i2−2i2−22222i2−2i2000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000000000000000000000000000
χ8144-4-4−4i4i−4i4i000000000−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i00022−22−2i22i222−22−2i22i2000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000000000000000000000000000
χ8244-4-4−4i4i−4i4i000000000−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i000−22222i2−2i2−22222i2−2i200000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000000000000000000000000000
χ834-44-44i−4i−4i4i0000000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i00022−22−2i22i2−22222i2−2i200000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000000000000000000000000000000000000000
χ844-44-44i−4i−4i4i0000000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i000−22222i2−2i222−22−2i22i2000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000000000000000000000000000000000
χ854-44-44i−4i−4i4i000000000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i00022−22−2i22i2−22222i2−2i2000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000000000000000000000000000000000
χ864-44-44i−4i−4i4i000000000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i000−22222i2−2i222−22−2i22i200000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000000000000000000000000000000000000000
χ874-44-4−4i4i4i−4i0000000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i00022−222i2−2i2−2222−2i22i2000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000000000000000000000000000000000000000
χ884-44-4−4i4i4i−4i0000000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i000−2222−2i22i222−222i2−2i200000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000000000000000000000000000
χ894-44-4−4i4i4i−4i000000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i00022−222i2−2i2−2222−2i22i200000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000000000000000000000000000
χ904-44-4−4i4i4i−4i000000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i000−2222−2i22i222−222i2−2i2000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000000000000000000000000000000000000000
χ914-4-4444-4-44-4-4-444-44400000000-4-440000000000000000000000000000000000000000000000000000000000000000
χ924-4-44-4-4444-444-4-4-44-400000000-4440000000000000000000000000000000000000000000000000000000000000000

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