Finite Group Databasebeta

← Group #221313

Character table — Group #221313

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222244444444444444444444444448888888888888888888888888161616161616161616161616
order12224444444424444444444888888888888882224444444448888888888888244488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-111-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111
χ51111111111111111111-1-1-1-1-1-1-1-1-1-1111111111-111-1111-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1
χ61111111111111111111-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111
χ71111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-11111111-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-111
χ81111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-11111-1-1-1-1-111111111-1-111-1-11111-1-1
χ9111111111111111-1-1-1-11111-1-1-1-1-1-111111111-111-11111-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111
χ10111111111111111-1-1-1-11111-1-1-1-1-1-111111111-11-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1
χ11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111111111-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ12111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-11111-11111-1-1-1-1111111-1-1-1-111-1-111
χ13111111111111111-1-1-1-1-1-1-1-111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ14111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ15111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1111111
χ16111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1
χ171111-1-111-1-1-1-1-11111-1-111-1-11111-1-1iiii−i−i−i−i1-11-111-1-1ii−i−i-1ii−i−iii−i−iii−i−i-111-1i−i1-1i−ii−i
χ181111-1-111-1-1-1-1-11111-1-111-1-11111-1-1iiii−i−i−i−i1-1-1-11-111ii−i−i-1ii−i−iii−i−i−i−iii1-1-11−ii-11−ii−ii
χ191111-1-111-1-1-1-1-11111-1-111-1-11111-1-1−i−i−i−iiiii1-11-111-1-1−i−iii-1−i−iii−i−iii−i−iii-111-1−ii1-1−ii−ii
χ201111-1-111-1-1-1-1-11111-1-111-1-11111-1-1−i−i−i−iiiii1-1-1-11-111−i−iii-1−i−iii−i−iiiii−i−i1-1-11i−i-11i−ii−i
χ211111-1-111-1-1-1-1-11111-1-1-1-111-1-1-1-111iiii−i−i−i−i111-1-11-1-1−i−iii1ii−i−i−i−iiiii−i−i-11-11−ii-11i−i−ii
χ221111-1-111-1-1-1-1-11111-1-1-1-111-1-1-1-111iiii−i−i−i−i11-1-1-1-111−i−iii1ii−i−i−i−iii−i−iii1-11-1i−i1-1−iii−i
χ231111-1-111-1-1-1-1-11111-1-1-1-111-1-1-1-111−i−i−i−iiiii111-1-11-1-1ii−i−i1−i−iiiii−i−i−i−iii-11-11i−i-11−iii−i
χ241111-1-111-1-1-1-1-11111-1-1-1-111-1-1-1-111−i−i−i−iiiii11-1-1-1-111ii−i−i1−i−iiiii−i−iii−i−i1-11-1−ii1-1i−i−ii
χ251111-1-111-1-1-1-1-111-1-11111-1-1-1-1-1-111iiii−i−i−i−i-1-11111-1-1−i−iii1−i−iiiii−i−iii−i−i1-11-1−ii-11−iii−i
χ261111-1-111-1-1-1-1-111-1-11111-1-1-1-1-1-111iiii−i−i−i−i-1-1-111-111−i−iii1−i−iiiii−i−i−i−iii-11-11i−i1-1i−i−ii
χ271111-1-111-1-1-1-1-111-1-11111-1-1-1-1-1-111−i−i−i−iiiii-1-11111-1-1ii−i−i1ii−i−i−i−iii−i−iii1-11-1i−i-11i−i−ii
χ281111-1-111-1-1-1-1-111-1-11111-1-1-1-1-1-111−i−i−i−iiiii-1-1-111-111ii−i−i1ii−i−i−i−iiiii−i−i-11-11−ii1-1−iii−i
χ291111-1-111-1-1-1-1-111-1-111-1-1111111-1-1iiii−i−i−i−i-1111-11-1-1ii−i−i-1−i−iii−i−iiiii−i−i1-1-11i−i1-1−ii−ii
χ301111-1-111-1-1-1-1-111-1-111-1-1111111-1-1iiii−i−i−i−i-11-11-1-111ii−i−i-1−i−iii−i−iii−i−iii-111-1−ii-11i−ii−i
χ311111-1-111-1-1-1-1-111-1-111-1-1111111-1-1−i−i−i−iiiii-1111-11-1-1−i−iii-1ii−i−iii−i−i−i−iii1-1-11−ii1-1i−ii−i
χ321111-1-111-1-1-1-1-111-1-111-1-1111111-1-1−i−i−i−iiiii-11-11-1-111−i−iii-1ii−i−iii−i−iii−i−i-111-1i−i-11−ii−ii
χ332222222222-2-2-2-2-22222222222-2-22200000000-2-20-2-20000000-2000000000000000000000000
χ342222222222-2-2-2-2-22222-2-2-2-2-2-222-2-200000000-220-2200000002000000000000000000000000
χ352222222222-2-2-2-2-2-2-2-2-22222-2-222-2-2000000002-202-200000002000000000000000000000000
χ362222222222-2-2-2-2-2-2-2-2-2-2-2-2-222-2-22200000000220220000000-2000000000000000000000000
χ37222222-2-2-2-2-2-222-2000000000000002i2i−2i−2i2i2i−2i−2i00200-22-200000000000002i−2i2i−2i000000000000
χ38222222-2-2-2-2-2-222-2000000000000002i2i−2i−2i2i2i−2i−2i00-2002-220000000000000−2i2i−2i2i000000000000
χ39222222-2-2-2-2-2-222-200000000000000−2i−2i2i2i−2i−2i2i2i00200-22-20000000000000−2i2i−2i2i000000000000
χ40222222-2-2-2-2-2-222-200000000000000−2i−2i2i2i−2i−2i2i2i00-2002-2200000000000002i−2i2i−2i000000000000
χ412222-2-222-2-2222-2-222-2-222-2-222-2-2-2-200000000-2202-200000002000000000000000000000000
χ422222-2-222-2-2222-2-222-2-2-2-222-2-2222200000000-2-20220000000-2000000000000000000000000
χ432222-2-222-2-2222-2-2-2-22222-2-2-2-2222200000000220-2-20000000-2000000000000000000000000
χ442222-2-222-2-2222-2-2-2-222-2-22222-2-2-2-2000000002-20-2200000002000000000000000000000000
χ452222-2-2-2-22222-22-20000000000000022-2-2-2-22200200-2-2200000000000002-2-22000000000000
χ462222-2-2-2-22222-22-20000000000000022-2-2-2-22200-20022-20000000000000-222-2000000000000
χ472222-2-2-2-22222-22-200000000000000-2-22222-2-200200-2-220000000000000-222-2000000000000
χ482222-2-2-2-22222-22-200000000000000-2-22222-2-200-20022-200000000000002-2-22000000000000
χ4922-2-22i−2i2-22i−2i000002i−2i2-22-22i−2i2i−2i002-21+i−1−i1+i−1−i1−i−1+i1−i−1+i000000001−i−1+i1+i−1−i01−i−1+i1+i−1−i1+i−1−i1−i−1+i0000000000000000
χ5022-2-22i−2i2-22i−2i000002i−2i2-22-22i−2i2i−2i002-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000−1+i1−i−1−i1+i0−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000000000000000
χ5122-2-22i−2i2-22i−2i000002i−2i2-2-22−2i2i−2i2i00-221+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000−1+i1−i−1−i1+i01−i−1+i1+i−1−i−1−i1+i−1+i1−i0000000000000000
χ5222-2-22i−2i2-22i−2i000002i−2i2-2-22−2i2i−2i2i00-22−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000001−i−1+i1+i−1−i0−1+i1−i−1−i1+i1+i−1−i1−i−1+i0000000000000000
χ5322-2-22i−2i2-22i−2i00000−2i2i-222-22i−2i−2i2i00-221+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000−1+i1−i−1−i1+i0−1+i1−i−1−i1+i1+i−1−i1−i−1+i0000000000000000
χ5422-2-22i−2i2-22i−2i00000−2i2i-222-22i−2i−2i2i00-22−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000001−i−1+i1+i−1−i01−i−1+i1+i−1−i−1−i1+i−1+i1−i0000000000000000
χ5522-2-22i−2i2-22i−2i00000−2i2i-22-22−2i2i2i−2i002-21+i−1−i1+i−1−i1−i−1+i1−i−1+i000000001−i−1+i1+i−1−i0−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000000000000000
χ5622-2-22i−2i2-22i−2i00000−2i2i-22-22−2i2i2i−2i002-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000−1+i1−i−1−i1+i01−i−1+i1+i−1−i1+i−1−i1−i−1+i0000000000000000
χ5722-2-2−2i2i2-2−2i2i000002i−2i-222-2−2i2i2i−2i00-221−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000−1−i1+i−1+i1−i0−1−i1+i−1+i1−i1−i−1+i1+i−1−i0000000000000000
χ5822-2-2−2i2i2-2−2i2i000002i−2i-222-2−2i2i2i−2i00-22−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000001+i−1−i1−i−1+i01+i−1−i1−i−1+i−1+i1−i−1−i1+i0000000000000000
χ5922-2-2−2i2i2-2−2i2i000002i−2i-22-222i−2i−2i2i002-21−i−1+i1−i−1+i1+i−1−i1+i−1−i000000001+i−1−i1−i−1+i0−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000000000000000
χ6022-2-2−2i2i2-2−2i2i000002i−2i-22-222i−2i−2i2i002-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000−1−i1+i−1+i1−i01+i−1−i1−i−1+i1−i−1+i1+i−1−i0000000000000000
χ6122-2-2−2i2i2-2−2i2i00000−2i2i2-22-2−2i2i−2i2i002-21−i−1+i1−i−1+i1+i−1−i1+i−1−i000000001+i−1−i1−i−1+i01+i−1−i1−i−1+i1−i−1+i1+i−1−i0000000000000000
χ6222-2-2−2i2i2-2−2i2i00000−2i2i2-22-2−2i2i−2i2i002-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000−1−i1+i−1+i1−i0−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000000000000000
χ6322-2-2−2i2i2-2−2i2i00000−2i2i2-2-222i−2i2i−2i00-221−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000−1−i1+i−1+i1−i01+i−1−i1−i−1+i−1+i1−i−1−i1+i0000000000000000
χ6422-2-2−2i2i2-2−2i2i00000−2i2i2-2-222i−2i2i−2i00-22−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000001+i−1−i1−i−1+i0−1−i1+i−1+i1−i1−i−1+i1+i−1−i0000000000000000
χ65444444-4-4-4-444-4-4400000000000000000000000000000000000000000000000000000000000
χ664444-4-4-4-444-4-44-4400000000000000000000000000000000000000000000000000000000000
χ6744-4-44i−4i-44−4i4i00000000000000000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i0000000000000000000000000000000000000
χ6844-4-44i−4i-44−4i4i0000000000000000000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i0000000000000000000000000000000000000
χ6944-4-4−4i4i-444i−4i00000000000000000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i0000000000000000000000000000000000000
χ7044-4-4−4i4i-444i−4i0000000000000000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i0000000000000000000000000000000000000
χ718-88-80000000000000000000004i2−4i200000000000000000000000000000000000000000000000
χ728-88-8000000000000000000000−4i24i200000000000000000000000000000000000000000000000
χ738-8-880000008i−8i00000000000000000000000000000000000000000000000000000000000000
χ748-8-88000000−8i8i00000000000000000000000000000000000000000000000000000000000000

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