Finite Group Databasebeta

← Group #224613

Character table — Group #224613

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size111111112222222222224444444444444444444444444488888888888888888888888888816161616161616161616
order12222222444444444444444444444444444444888888884444444888888888888888888882244448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111-1-1111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ711111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111
χ811111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-111111111111111-1-111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11111-1-1ii−i−iii−i−iiiii−i−i−i−iii−i−i111-1-1-1ii−i−i
χ10111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i111-1-111−i−iiiii−i−iiiii−i−i−i−i−i−iii-1-1-1111−i−iii
χ11111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11111-1-1−i−iii−i−iii−i−i−i−iiiii−i−iii111-1-1-1−i−iii
χ12111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii111-1-111ii−i−i−i−iii−i−i−i−iiiiiii−i−i-1-1-1111ii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111iiii−i−i−i−i1-1-111-1-1ii−i−iii−i−i−i−i−i−iiiiiii−i−i-1-11-111−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111iiii−i−i−i−i1-1-1-1-111−i−iiiii−i−i−i−i−i−iiiii−i−iii11-11-1-1ii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111−i−i−i−iiiii1-1-111-1-1−i−iii−i−iiiiiii−i−i−i−i−i−iii-1-11-111ii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111−i−i−i−iiiii1-1-1-1-111ii−i−i−i−iiiiiii−i−i−i−iii−i−i11-11-1-1−i−iii
χ1711111111-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-111111111-11-111111111-1-1-1-111-1-111-1-1-1-1-1-11-1-1-11-11-11-1
χ1811111111-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-111111111-11-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1111-11-11-11
χ1911111111-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-11111-1-111-1-11111111-1-1-11-1-11-11
χ2011111111-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1111-111-11-1
χ2111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1111111111-1-1-1-1-1-111-1-111-1-1-1-1-11-1-1-11-11-11
χ2211111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111-1111-11-11-1
χ2311111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1111111-1-111-1-11111-11-1-1-111-11-1
χ2411111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111111-1-111-1-1-1-1-1-11-1111-1-11-11
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111iiii−i−i−i−i-11-111-1-1ii−i−i−i−iiiii−i−i−i−iii−i−iii1-1-11-11i−i−ii
χ2611111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111iiii−i−i−i−i-11-1-1-111−i−iii−i−iiiii−i−i−i−iiiii−i−i-111-11-1−iii−i
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111−i−i−i−iiiii-11-111-1-1−i−iiiii−i−i−i−iiiii−i−iii−i−i1-1-11-11−iii−i
χ2811111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111−i−i−i−iiiii-11-1-1-111ii−i−iii−i−i−i−iiiii−i−i−i−iii-111-11-1i−i−ii
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1iiii−i−i−i−i-1-1111-1-1ii−i−i−i−iii−i−iiiii−i−i−i−iii-11-111-1−iii−i
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1iiii−i−i−i−i-1-11-1-111−i−iii−i−iii−i−iiiii−i−iii−i−i1-11-1-11i−i−ii
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1−i−i−i−iiiii-1-1111-1-1−i−iiiii−i−iii−i−i−i−iiiii−i−i-11-111-1i−i−ii
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1−i−i−i−iiiii-1-11-1-111ii−i−iii−i−iii−i−i−i−iii−i−iii1-11-1-11−iii−i
χ3322222222222222-2-222-2-22222-2-222-2-222-2-222-2-200000000-2-2-20000000000000000000000000000000000
χ3422222222222222-2-222-2-2-2-2-2-2-2-222-2-2-2-222-2-22200000000-2220000000000000000000000000000000000
χ35222222222222-2-222-2-2222222-2-2-2-222-2-222-2-22200000000-2-2-20000000000000000000000000000000000
χ36222222222222-2-222-2-222-2-2-2-2-2-2-2-22222-2-222-2-200000000-2220000000000000000000000000000000000
χ3722222222-2-2-2-222-2-222-2-222-2-2-2-2-2-22222-2-2-2-222000000002-220000000000000000000000000000000000
χ3822222222-2-2-2-222-2-222-2-2-2-222-2-2-2-222-2-22222-2-20000000022-20000000000000000000000000000000000
χ3922222222-2-2-2-2-2-222-2-22222-2-2-2-222-2-2-2-22222-2-2000000002-220000000000000000000000000000000000
χ4022222222-2-2-2-2-2-222-2-222-2-222-2-222-2-222-2-2-2-2220000000022-20000000000000000000000000000000000
χ41222-2-22-2-2000022-2-2-2-22200002-200000000000022-2-222-2-20002i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ42222-2-22-2-2000022-2-2-2-22200002-200000000000022-2-222-2-2000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ43222-2-22-2-2000022-2-2-2-22200002-2000000000000-2-222-2-2220002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ44222-2-22-2-2000022-2-2-2-22200002-2000000000000-2-222-2-222000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ45222-2-22-2-20000-2-22222-2-200002-20000000000002i2i−2i−2i−2i−2i2i2i0002i−2i−2i2i-222-200000000000000000000000000
χ46222-2-22-2-20000-2-22222-2-200002-20000000000002i2i−2i−2i−2i−2i2i2i000−2i2i2i−2i2-2-2200000000000000000000000000
χ47222-2-22-2-20000-2-22222-2-200002-2000000000000−2i−2i2i2i2i2i−2i−2i0002i−2i−2i2i2-2-2200000000000000000000000000
χ48222-2-22-2-20000-2-22222-2-200002-2000000000000−2i−2i2i2i2i2i−2i−2i000−2i2i2i−2i-222-200000000000000000000000000
χ4922-22-2-22-222-2-2002i−2i002i−2i2-22-200002i−2i002i−2i002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000001+i−1−i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ5022-22-2-22-222-2-2002i−2i002i−2i2-22-200002i−2i002i−2i002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000−1−i1+i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ5122-22-2-22-222-2-2002i−2i002i−2i-22-2200002i−2i00−2i2i00−2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000001+i−1−i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ5222-22-2-22-222-2-2002i−2i002i−2i-22-2200002i−2i00−2i2i00−2i2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000−1−i1+i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ5322-22-2-22-222-2-200−2i2i00−2i2i2-22-20000−2i2i00−2i2i00−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000001−i−1+i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ5422-22-2-22-222-2-200−2i2i00−2i2i2-22-20000−2i2i00−2i2i00−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000−1+i1−i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ5522-22-2-22-222-2-200−2i2i00−2i2i-22-220000−2i2i002i−2i002i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000001−i−1+i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ5622-22-2-22-222-2-200−2i2i00−2i2i-22-220000−2i2i002i−2i002i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000−1+i1−i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ5722-22-2-22-2-2-222002i−2i002i−2i2-2-220000−2i2i002i−2i00−2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000−1−i1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000000000
χ5822-22-2-22-2-2-222002i−2i002i−2i2-2-220000−2i2i002i−2i00−2i2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000001+i−1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000000000
χ5922-22-2-22-2-2-222002i−2i002i−2i-222-20000−2i2i00−2i2i002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000−1−i1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000000000
χ6022-22-2-22-2-2-222002i−2i002i−2i-222-20000−2i2i00−2i2i002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000001+i−1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000000000
χ6122-22-2-22-2-2-22200−2i2i00−2i2i2-2-2200002i−2i00−2i2i002i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000−1+i1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000000000
χ6222-22-2-22-2-2-22200−2i2i00−2i2i2-2-2200002i−2i00−2i2i002i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000001−i−1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000000000
χ6322-22-2-22-2-2-22200−2i2i00−2i2i-222-200002i−2i002i−2i00−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000−1+i1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000000000
χ6422-22-2-22-2-2-22200−2i2i00−2i2i-222-200002i−2i002i−2i00−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000001−i−1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000000000
χ65444-4-44-4-400004444-4-4-4-40000-44000000000000000000000000000000000000000000000000000000000
χ66444-4-44-4-40000-4-4-4-444440000-44000000000000000000000000000000000000000000000000000000000
χ6744-4-44-4-440000004i−4i00−4i4i0000000000000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i0000000000000000000000000000000000000
χ6844-4-44-4-440000004i−4i00−4i4i000000000000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i0000000000000000000000000000000000000
χ6944-4-44-4-44000000−4i4i004i−4i0000000000000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i0000000000000000000000000000000000000
χ7044-4-44-4-44000000−4i4i004i−4i000000000000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i0000000000000000000000000000000000000
χ714-444-4-4-444-44-44i−4i004i−4i000000004i−4i0000000000000000000000000000000000000000000000000000000
χ724-444-4-4-444-44-4−4i4i00−4i4i00000000−4i4i0000000000000000000000000000000000000000000000000000000
χ734-444-4-4-44-44-444i−4i004i−4i00000000−4i4i0000000000000000000000000000000000000000000000000000000
χ744-444-4-4-44-44-44−4i4i00−4i4i000000004i−4i0000000000000000000000000000000000000000000000000000000
χ754-44-44-44-400004i−4i00−4i4i0000000000000000000000000000000000000000000000000002−2i−2+2i2+2i−2−2i0000000000
χ764-44-44-44-400004i−4i00−4i4i000000000000000000000000000000000000000000000000000−2+2i2−2i−2−2i2+2i0000000000
χ774-44-44-44-40000−4i4i004i−4i0000000000000000000000000000000000000000000000000002+2i−2−2i2−2i−2+2i0000000000
χ784-44-44-44-40000−4i4i004i−4i000000000000000000000000000000000000000000000000000−2−2i2+2i−2+2i2−2i0000000000
χ794-4-4444-4-44-4-440000000000000000004i−4i004i−4i00000000000000000000000000000000000000000000000
χ804-4-4444-4-44-4-44000000000000000000−4i4i00−4i4i00000000000000000000000000000000000000000000000
χ814-4-4444-4-4-444-40000000000000000004i−4i00−4i4i00000000000000000000000000000000000000000000000
χ824-4-4444-4-4-444-4000000000000000000−4i4i004i−4i00000000000000000000000000000000000000000000000
χ838-8-8-8-8888000000000000000000000000000000000000000000000000000000000000000000000000000

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