Finite Group Databasebeta

← Group #221113

Character table — Group #221113

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222222244444444444444444444444444444488888888888888888888161616161616161616161616
order12224444444444448888888824444444444444444488888888888822244444888888888888244488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-111-111111111111-1-1-1-111-1-111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111
χ511111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-111111111-1-1-1-11111-1-111-1-111-1-1-1-1
χ611111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-11-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-11-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-111-1111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-111
χ131111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1
χ141111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-111111111-1-1-1-111-1-1-1-111-1-111
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1-1111-1-1-1-111111111-1-1-1-11111-1-111
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1
χ171111-1-1-1-111-1-111-1-1iiii−i−i−i−i-1111-1-111-1-1iiii−i−i−i−i1111-1-1-1-1ii−i−i111-1-11-1-1ii−i−iii−i−iii−i−i-111-1i−ii−ii−i1-1
χ181111-1-1-1-111-1-111-1-1iiii−i−i−i−i-1111-1-111-1-1iiii−i−i−i−i1111-1-1-1-1ii−i−i11-1-1-1-111−i−iiiii−i−iii−i−i1-1-11−ii−ii−ii-11
χ191111-1-1-1-111-1-111-1-1iiii−i−i−i−i-1111-1-1-1-111−i−i−i−iiiii-1-1-1-11111ii−i−i1-11-111-1-1ii−i−iii−i−i−i−iii-11-11i−i−ii−ii-11
χ201111-1-1-1-111-1-111-1-1iiii−i−i−i−i-1111-1-1-1-111−i−i−i−iiiii-1-1-1-11111ii−i−i1-1-1-11-111−i−iiiii−i−i−i−iii1-11-1−iii−ii−i1-1
χ211111-1-1-1-111-1-111-1-1iiii−i−i−i−i-11-1-11111-1-1−i−i−i−iiiii-1-1-1-11111ii−i−i-1111-11-1-1ii−i−i−i−iiiii−i−i1-11-1−iii−i−ii-11
χ221111-1-1-1-111-1-111-1-1iiii−i−i−i−i-11-1-11111-1-1−i−i−i−iiiii-1-1-1-11111ii−i−i-11-11-1-111−i−iii−i−iiiii−i−i-11-11i−i−iii−i1-1
χ231111-1-1-1-111-1-111-1-1iiii−i−i−i−i-11-1-111-1-111iiii−i−i−i−i1111-1-1-1-1ii−i−i-1-11111-1-1ii−i−i−i−iii−i−iii1-1-11−ii−iii−i1-1
χ241111-1-1-1-111-1-111-1-1iiii−i−i−i−i-11-1-111-1-111iiii−i−i−i−i1111-1-1-1-1ii−i−i-1-1-111-111−i−iii−i−iii−i−iii-111-1i−ii−i−ii-11
χ251111-1-1-1-111-1-111-1-1−i−i−i−iiiii-1111-1-111-1-1−i−i−i−iiiii1111-1-1-1-1−i−iii111-1-11-1-1−i−iii−i−iii−i−iii-111-1−ii−ii−ii1-1
χ261111-1-1-1-111-1-111-1-1−i−i−i−iiiii-1111-1-111-1-1−i−i−i−iiiii1111-1-1-1-1−i−iii11-1-1-1-111ii−i−i−i−iii−i−iii1-1-11i−ii−ii−i-11
χ271111-1-1-1-111-1-111-1-1−i−i−i−iiiii-1111-1-1-1-111iiii−i−i−i−i-1-1-1-11111−i−iii1-11-111-1-1−i−iii−i−iiiii−i−i-11-11−iii−ii−i-11
χ281111-1-1-1-111-1-111-1-1−i−i−i−iiiii-1111-1-1-1-111iiii−i−i−i−i-1-1-1-11111−i−iii1-1-1-11-111ii−i−i−i−iiiii−i−i1-11-1i−i−ii−ii1-1
χ291111-1-1-1-111-1-111-1-1−i−i−i−iiiii-11-1-11111-1-1iiii−i−i−i−i-1-1-1-11111−i−iii-1111-11-1-1−i−iiiii−i−i−i−iii1-11-1i−i−iii−i-11
χ301111-1-1-1-111-1-111-1-1−i−i−i−iiiii-11-1-11111-1-1iiii−i−i−i−i-1-1-1-11111−i−iii-11-11-1-111ii−i−iii−i−i−i−iii-11-11−iii−i−ii1-1
χ311111-1-1-1-111-1-111-1-1−i−i−i−iiiii-11-1-111-1-111−i−i−i−iiiii1111-1-1-1-1−i−iii-1-11111-1-1−i−iiiii−i−iii−i−i1-1-11i−ii−i−ii1-1
χ321111-1-1-1-111-1-111-1-1−i−i−i−iiiii-11-1-111-1-111−i−i−i−iiiii1111-1-1-1-1−i−iii-1-1-111-111ii−i−iii−i−iii−i−i-111-1−ii−iii−i-11
χ332222222222-2-2-2-22222222222-2-2000000000000000000000000-2-2-2-200200-22-22-22-200000000000000000000
χ342222222222-2-2-2-22222222222-2-2000000000000000000000000-2-2-2-200-2002-22-22-2200000000000000000000
χ352222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2000000000000000000000000222200200-22-2-22-2200000000000000000000
χ362222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2000000000000000000000000222200-2002-222-22-200000000000000000000
χ3722222222-2-22222-2-200000000-2-2222222220000000022-2-222-2-20000-2-20-2-2000000000000000000000000000
χ3822222222-2-22222-2-200000000-2-22222-2-2-2-200000000-2-222-2-2220000-220-22000000000000000000000000000
χ3922222222-2-22222-2-200000000-2-2-2-2-2-2222200000000-2-222-2-22200002-202-2000000000000000000000000000
χ4022222222-2-22222-2-200000000-2-2-2-2-2-2-2-2-2-20000000022-2-222-2-2000022022000000000000000000000000000
χ412222-2-2-2-22222-2-2-2-22i2i2i2i−2i−2i−2i−2i2-2000000000000000000000000−2i−2i2i2i00200-2-222i−2i−2i2i00000000000000000000
χ422222-2-2-2-22222-2-2-2-22i2i2i2i−2i−2i−2i−2i2-2000000000000000000000000−2i−2i2i2i00-20022-2−2i2i2i−2i00000000000000000000
χ432222-2-2-2-22222-2-2-2-2−2i−2i−2i−2i2i2i2i2i2-20000000000000000000000002i2i−2i−2i00200-2-22−2i2i2i−2i00000000000000000000
χ442222-2-2-2-22222-2-2-2-2−2i−2i−2i−2i2i2i2i2i2-20000000000000000000000002i2i−2i−2i00-20022-22i−2i−2i2i00000000000000000000
χ452222-2-2-2-2-2-2-2-22222000000002-222-2-222-2-20000000022-2-2-2-2220000-2-2022000000000000000000000000000
χ462222-2-2-2-2-2-2-2-22222000000002-222-2-2-2-22200000000-2-22222-2-20000-2202-2000000000000000000000000000
χ472222-2-2-2-2-2-2-2-22222000000002-2-2-22222-2-200000000-2-22222-2-200002-20-22000000000000000000000000000
χ482222-2-2-2-2-2-2-2-22222000000002-2-2-222-2-2220000000022-2-2-2-2220000220-2-2000000000000000000000000000
χ4922-2-22i2i−2i−2i002i−2i2-2001+i1+i−1−i−1−i1−i1−i−1+i−1+i002i−2i2-22i−2i2-21+i1+i−1−i−1−i1−i1−i−1+i−1+i2-2002i−2i001+i−1−i1−i−1+i0000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i000000000000
χ5022-2-22i2i−2i−2i002i−2i2-2001+i1+i−1−i−1−i1−i1−i−1+i−1+i002i−2i2-2−2i2i-22−1−i−1−i1+i1+i−1+i−1+i1−i1−i-2200−2i2i001+i−1−i1−i−1+i0000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i000000000000
χ5122-2-22i2i−2i−2i002i−2i2-2001+i1+i−1−i−1−i1−i1−i−1+i−1+i00−2i2i-222i−2i2-2−1−i−1−i1+i1+i−1+i−1+i1−i1−i-2200−2i2i001+i−1−i1−i−1+i000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i000000000000
χ5222-2-22i2i−2i−2i002i−2i2-2001+i1+i−1−i−1−i1−i1−i−1+i−1+i00−2i2i-22−2i2i-221+i1+i−1−i−1−i1−i1−i−1+i−1+i2-2002i−2i001+i−1−i1−i−1+i000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i000000000000
χ5322-2-22i2i−2i−2i002i−2i2-200−1−i−1−i1+i1+i−1+i−1+i1−i1−i002i−2i2-22i−2i2-2−1−i−1−i1+i1+i−1+i−1+i1−i1−i2-2002i−2i00−1−i1+i−1+i1−i000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i000000000000
χ5422-2-22i2i−2i−2i002i−2i2-200−1−i−1−i1+i1+i−1+i−1+i1−i1−i002i−2i2-2−2i2i-221+i1+i−1−i−1−i1−i1−i−1+i−1+i-2200−2i2i00−1−i1+i−1+i1−i000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i000000000000
χ5522-2-22i2i−2i−2i002i−2i2-200−1−i−1−i1+i1+i−1+i−1+i1−i1−i00−2i2i-222i−2i2-21+i1+i−1−i−1−i1−i1−i−1+i−1+i-2200−2i2i00−1−i1+i−1+i1−i0000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i000000000000
χ5622-2-22i2i−2i−2i002i−2i2-200−1−i−1−i1+i1+i−1+i−1+i1−i1−i00−2i2i-22−2i2i-22−1−i−1−i1+i1+i−1+i−1+i1−i1−i2-2002i−2i00−1−i1+i−1+i1−i0000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i000000000000
χ5722-2-2−2i−2i2i2i00−2i2i2-2001−i1−i−1+i−1+i1+i1+i−1−i−1−i002i−2i-222i−2i-221−i1−i−1+i−1+i1+i1+i−1−i−1−i2-200−2i2i001−i−1+i1+i−1−i000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i000000000000
χ5822-2-2−2i−2i2i2i00−2i2i2-2001−i1−i−1+i−1+i1+i1+i−1−i−1−i002i−2i-22−2i2i2-2−1+i−1+i1−i1−i−1−i−1−i1+i1+i-22002i−2i001−i−1+i1+i−1−i000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i000000000000
χ5922-2-2−2i−2i2i2i00−2i2i2-2001−i1−i−1+i−1+i1+i1+i−1−i−1−i00−2i2i2-22i−2i-22−1+i−1+i1−i1−i−1−i−1−i1+i1+i-22002i−2i001−i−1+i1+i−1−i0000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i000000000000
χ6022-2-2−2i−2i2i2i00−2i2i2-2001−i1−i−1+i−1+i1+i1+i−1−i−1−i00−2i2i2-2−2i2i2-21−i1−i−1+i−1+i1+i1+i−1−i−1−i2-200−2i2i001−i−1+i1+i−1−i0000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i000000000000
χ6122-2-2−2i−2i2i2i00−2i2i2-200−1+i−1+i1−i1−i−1−i−1−i1+i1+i002i−2i-222i−2i-22−1+i−1+i1−i1−i−1−i−1−i1+i1+i2-200−2i2i00−1+i1−i−1−i1+i0000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i000000000000
χ6222-2-2−2i−2i2i2i00−2i2i2-200−1+i−1+i1−i1−i−1−i−1−i1+i1+i002i−2i-22−2i2i2-21−i1−i−1+i−1+i1+i1+i−1−i−1−i-22002i−2i00−1+i1−i−1−i1+i0000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i000000000000
χ6322-2-2−2i−2i2i2i00−2i2i2-200−1+i−1+i1−i1−i−1−i−1−i1+i1+i00−2i2i2-22i−2i-221−i1−i−1+i−1+i1+i1+i−1−i−1−i-22002i−2i00−1+i1−i−1−i1+i000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i000000000000
χ6422-2-2−2i−2i2i2i00−2i2i2-200−1+i−1+i1−i1−i−1−i−1−i1+i1+i00−2i2i2-2−2i2i2-2−1+i−1+i1−i1−i−1−i−1−i1+i1+i2-200−2i2i00−1+i1−i−1−i1+i000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i000000000000
χ6544444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000000000000000000
χ664444-4-4-4-4-4-444-4-44400000000-44000000000000000000000000000000000000000000000000000000000000
χ6744-4-44i4i−4i−4i00−4i4i-44002+2i2+2i−2−2i−2−2i2−2i2−2i−2+2i−2+2i00000000000000000000000000−2−2i2+2i−2+2i2−2i00000000000000000000000000000000
χ6844-4-44i4i−4i−4i00−4i4i-4400−2−2i−2−2i2+2i2+2i−2+2i−2+2i2−2i2−2i000000000000000000000000002+2i−2−2i2−2i−2+2i00000000000000000000000000000000
χ6944-4-4−4i−4i4i4i004i−4i-44002−2i2−2i−2+2i−2+2i2+2i2+2i−2−2i−2−2i00000000000000000000000000−2+2i2−2i−2−2i2+2i00000000000000000000000000000000
χ7044-4-4−4i−4i4i4i004i−4i-4400−2+2i−2+2i2−2i2−2i−2−2i−2−2i2+2i2+2i000000000000000000000000002−2i−2+2i2+2i−2−2i00000000000000000000000000000000
χ714-44-44-44-4000000002i2−2i22i2−2i22i2−2i22i2−2i200000000002-22-22-22-2002i2−2i2002i2−2i2000000000000000000000000000000000000
χ724-44-44-44-4000000002i2−2i22i2−2i22i2−2i22i2−2i20000000000-22-22-22-2200−2i22i200−2i22i2000000000000000000000000000000000000
χ734-44-44-44-400000000−2i22i2−2i22i2−2i22i2−2i22i200000000002-22-22-22-200−2i22i200−2i22i2000000000000000000000000000000000000
χ744-44-44-44-400000000−2i22i2−2i22i2−2i22i2−2i22i20000000000-22-22-22-22002i2−2i2002i2−2i2000000000000000000000000000000000000
χ754-44-4-44-440000000022−2222−22−2222−222200000000002i−2i2i−2i−2i2i−2i2i00−2i22i2002i2−2i2000000000000000000000000000000000000
χ764-44-4-44-440000000022−2222−22−2222−22220000000000−2i2i−2i2i2i−2i2i−2i002i2−2i200−2i22i2000000000000000000000000000000000000
χ774-44-4-44-4400000000−2222−222222−2222−2200000000002i−2i2i−2i−2i2i−2i2i002i2−2i200−2i22i2000000000000000000000000000000000000
χ784-44-4-44-4400000000−2222−222222−2222−220000000000−2i2i−2i2i2i−2i2i−2i00−2i22i2002i2−2i2000000000000000000000000000000000000
χ794-4-444i−4i−4i4i4-400004i−4i0000000000000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i00000000000000000000000000000000000000000000
χ804-4-444i−4i−4i4i4-400004i−4i000000000000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i00000000000000000000000000000000000000000000
χ814-4-444i−4i−4i4i-440000−4i4i4ζ3−4ζ3−4ζ34ζ34ζ−4ζ−4ζ4ζ00000000000000000000000000000000000000000000000000000000000000
χ824-4-444i−4i−4i4i-440000−4i4i−4ζ34ζ34ζ3−4ζ3−4ζ4ζ4ζ−4ζ00000000000000000000000000000000000000000000000000000000000000
χ834-4-44−4i4i4i−4i4-40000−4i4i0000000000000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i00000000000000000000000000000000000000000000
χ844-4-44−4i4i4i−4i4-40000−4i4i000000000000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i00000000000000000000000000000000000000000000
χ854-4-44−4i4i4i−4i-4400004i−4i4ζ−4ζ−4ζ4ζ4ζ3−4ζ3−4ζ34ζ300000000000000000000000000000000000000000000000000000000000000
χ864-4-44−4i4i4i−4i-4400004i−4i−4ζ4ζ4ζ−4ζ−4ζ34ζ34ζ3−4ζ300000000000000000000000000000000000000000000000000000000000000

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