Finite Group Databasebeta

← Group #165021

Character table — Group #165021

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size111111112222222222224444444444444444444444444488888888888888888888888888816161616161616161616
order12222222444444444444224444444444444444888888882444444888888888888888888882444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-11-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111
χ511111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1111-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-111111111-11-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111
χ811111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-11111111111111111-1-11111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1iiii−i−i−i−i11111-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−i1-1-1-111ii−i−i
χ10111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1iiii−i−i−i−i11-1-1111ii−i−iiiii−i−i−i−i−i−i−i−iiiii-1111-1-1−i−iii
χ11111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1−i−i−i−iiiii11111-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii1-1-1-111−i−iii
χ12111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1−i−i−i−iiiii11-1-1111−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1111-1-1ii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111iiii−i−i−i−i-1111-1-1-1ii−i−i−i−i−i−iiiiiiiii−i−i−i−i1-111-1-1−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111iiii−i−i−i−i-11-1-1-111ii−i−i−i−i−i−iiiii−i−i−i−iiiii-11-1-111ii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111−i−i−i−iiiii-1111-1-1-1−i−iiiiiii−i−i−i−i−i−i−i−iiiii1-111-1-1ii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111−i−i−i−iiiii-11-1-1-111−i−iiiiiii−i−i−i−iiiii−i−i−i−i-11-1-111−i−iii
χ1711111111-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-111111111-1-111111-1-1-1-111-1-111-1-111-1-111-1-1-1-11-11-11-11-1
χ1811111111-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-11-1-1-1-1-1-111-1-111-1-1-1-111-1-11111-11-11-11-11
χ1911111111-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-111-1-111-1-111-1-11-11-1-11-11
χ2011111111-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-111-1-11111-1-111-1-111-11-111-11-1
χ2111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111111111111-111-111-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-11-11-11-11
χ2211111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111111-11-11-11-1
χ2311111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11-111-111111111-1-111-1-1-1-111-1-111-1-1-11-111-11-1
χ2411111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111-1-111-1-111-1-111-1-1111-11-1-11-11
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111iiii−i−i−i−i-1-1111-1-1−i−iiiii−i−i−i−iiiii−i−i−i−iii-11-111-1i−i−ii
χ2611111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111iiii−i−i−i−i-1-1-1-1111−i−iiiii−i−i−i−iii−i−iiiii−i−i1-11-1-11−iii−i
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111−i−i−i−iiiii-1-1111-1-1ii−i−i−i−iiiii−i−i−i−iiiii−i−i-11-111-1−iii−i
χ2811111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111−i−i−i−iiiii-1-1-1-1111ii−i−i−i−iiiii−i−iii−i−i−i−iii1-11-1-11i−i−ii
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1iiii−i−i−i−i1-111-1-1-1−i−iii−i−iiiii−i−iii−i−i−i−iii-111-1-11−iii−i
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1iiii−i−i−i−i1-1-1-1-111−i−iii−i−iiiii−i−i−i−iiiii−i−i1-1-111-1i−i−ii
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1−i−i−i−iiiii1-111-1-1-1ii−i−iii−i−i−i−iii−i−iiiii−i−i-111-1-11i−i−ii
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1−i−i−i−iiiii1-1-1-1-111ii−i−iii−i−i−i−iiiii−i−i−i−iii1-1-111-1−iii−i
χ332222222222222222-2-2-2-22222-2-2-2-22222-2-222-2-200000000-2-200-200000000000000000000000000000000
χ342222222222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-222-2-222000000002-200200000000000000000000000000000000
χ35222222222222-2-2-2-2222222-2-222-2-222-2-222-2-22200000000-2-200-200000000000000000000000000000000
χ36222222222222-2-2-2-22222-2-2-2-222-2-2-2-222-2-222-2-2000000002-200200000000000000000000000000000000
χ3722222222-2-2-2-22222-2-2-2-222-2-222-2-2-2-222-2-2-2-222000000002200-200000000000000000000000000000000
χ3822222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-222-2-22222-2-200000000-2200200000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-2000000002200-200000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-22222-2-222-2-2-2-22222-2-2-2-22200000000-2200200000000000000000000000000000000
χ41222-2-22-2-200002i2i−2i−2i2i2i−2i−2i0000002-200000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3002i−2i02-20000000000002ζ3−2ζ3002ζ−2ζ000000000000
χ42222-2-22-2-200002i2i−2i−2i2i2i−2i−2i0000002-200000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300−2i2i0-22000000000000−2ζ32ζ300−2ζ2ζ000000000000
χ43222-2-22-2-200002i2i−2i−2i2i2i−2i−2i0000002-20000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3002i−2i02-2000000000000−2ζ32ζ300−2ζ2ζ000000000000
χ44222-2-22-2-200002i2i−2i−2i2i2i−2i−2i0000002-20000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300−2i2i0-220000000000002ζ3−2ζ3002ζ−2ζ000000000000
χ45222-2-22-2-20000−2i−2i2i2i−2i−2i2i2i0000002-200000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ002i−2i0-22000000000000−2ζ2ζ00−2ζ32ζ3000000000000
χ46222-2-22-2-20000−2i−2i2i2i−2i−2i2i2i0000002-200000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00−2i2i02-20000000000002ζ−2ζ002ζ3−2ζ3000000000000
χ47222-2-22-2-20000−2i−2i2i2i−2i−2i2i2i0000002-20000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ002i−2i0-220000000000002ζ−2ζ002ζ3−2ζ3000000000000
χ48222-2-22-2-20000−2i−2i2i2i−2i−2i2i2i0000002-20000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00−2i2i02-2000000000000−2ζ2ζ00−2ζ32ζ3000000000000
χ4922-22-2-22-22i2i−2i−2i00002-22-22-2002i−2i002i−2i002-2002i−2ii2−i2i2−i2i2−i2i2−i200000002−22−2i2−i22−2i2−i22−2000000000000000000
χ5022-22-2-22-22i2i−2i−2i00002-22-22-2002i−2i002i−2i002-2002i−2i−i2i2−i2i2−i2i2−i2i20000000−22−22−i2i2−22−i2i2−22000000000000000000
χ5122-22-2-22-22i2i−2i−2i00002-22-2-22002i−2i00−2i2i00-2200−2i2ii2−i2i2−i2i2−i2i2−i200000002−22−2−i2i2−22−i2i2−22000000000000000000
χ5222-22-2-22-22i2i−2i−2i00002-22-2-22002i−2i00−2i2i00-2200−2i2i−i2i2−i2i2−i2i2−i2i20000000−22−22i2−i22−2i2−i22−2000000000000000000
χ5322-22-2-22-22i2i−2i−2i0000-22-222-200−2i2i002i−2i00-2200−2i2i2−22−2−22−220000000−i2i2i2−i22−2−i2i2−22i2−i2000000000000000000
χ5422-22-2-22-22i2i−2i−2i0000-22-222-200−2i2i002i−2i00-2200−2i2i−22−222−22−20000000i2−i2−i2i2−22i2−i22−2−i2i2000000000000000000
χ5522-22-2-22-22i2i−2i−2i0000-22-22-2200−2i2i00−2i2i002-2002i−2i2−22−2−22−220000000−i2i2i2−i2−22i2−i22−2−i2i2000000000000000000
χ5622-22-2-22-22i2i−2i−2i0000-22-22-2200−2i2i00−2i2i002-2002i−2i−22−222−22−20000000i2−i2−i2i22−2−i2i2−22i2−i2000000000000000000
χ5722-22-2-22-2−2i−2i2i2i00002-22-22-200−2i2i00−2i2i002-200−2i2ii2−i2i2−i2i2−i2i2−i20000000−22−22i2−i2−22i2−i2−22000000000000000000
χ5822-22-2-22-2−2i−2i2i2i00002-22-22-200−2i2i00−2i2i002-200−2i2i−i2i2−i2i2−i2i2−i2i200000002−22−2−i2i22−2−i2i22−2000000000000000000
χ5922-22-2-22-2−2i−2i2i2i00002-22-2-2200−2i2i002i−2i00-22002i−2ii2−i2i2−i2i2−i2i2−i20000000−22−22−i2i22−2−i2i22−2000000000000000000
χ6022-22-2-22-2−2i−2i2i2i00002-22-2-2200−2i2i002i−2i00-22002i−2i−i2i2−i2i2−i2i2−i2i200000002−22−2i2−i2−22i2−i2−22000000000000000000
χ6122-22-2-22-2−2i−2i2i2i0000-22-222-2002i−2i00−2i2i00-22002i−2i2−22−2−22−220000000i2−i2−i2i22−2i2−i2−22−i2i2000000000000000000
χ6222-22-2-22-2−2i−2i2i2i0000-22-222-2002i−2i00−2i2i00-22002i−2i−22−222−22−20000000−i2i2i2−i2−22−i2i22−2i2−i2000000000000000000
χ6322-22-2-22-2−2i−2i2i2i0000-22-22-22002i−2i002i−2i002-200−2i2i2−22−2−22−220000000i2−i2−i2i2−22−i2i22−2i2−i2000000000000000000
χ6422-22-2-22-2−2i−2i2i2i0000-22-22-22002i−2i002i−2i002-200−2i2i−22−222−22−20000000−i2i2i2−i22−2i2−i2−22−i2i2000000000000000000
χ65444-4-44-4-400004i4i−4i−4i−4i−4i4i4i000000-440000000000000000000000000000000000000000000000000000000
χ66444-4-44-4-40000−4i−4i4i4i4i4i−4i−4i000000-440000000000000000000000000000000000000000000000000000000
χ6744-4-44-4-44000000004i−4i−4i4i0000000000000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i0000000000000000000000000000000000000
χ6844-4-44-4-44000000004i−4i−4i4i000000000000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i0000000000000000000000000000000000000
χ6944-4-44-4-4400000000−4i4i4i−4i0000000000000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i0000000000000000000000000000000000000
χ7044-4-44-4-4400000000−4i4i4i−4i000000000000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i0000000000000000000000000000000000000
χ714-444-4-4-444i−4i4i−4i4-44-40000004i−4i00000000000000000000000000000000000000000000000000000000000
χ724-444-4-4-444i−4i4i−4i-44-44000000−4i4i00000000000000000000000000000000000000000000000000000000000
χ734-444-4-4-44−4i4i−4i4i4-44-4000000−4i4i00000000000000000000000000000000000000000000000000000000000
χ744-444-4-4-44−4i4i−4i4i-44-440000004i−4i00000000000000000000000000000000000000000000000000000000000
χ754-44-44-44-400004i−4i−4i4i0000000000000000000000000000000000000000000000000002+2i−2−2i002−2i−2+2i0000000000
χ764-44-44-44-400004i−4i−4i4i000000000000000000000000000000000000000000000000000−2−2i2+2i00−2+2i2−2i0000000000
χ774-44-44-44-40000−4i4i4i−4i0000000000000000000000000000000000000000000000000002−2i−2+2i002+2i−2−2i0000000000
χ784-44-44-44-40000−4i4i4i−4i000000000000000000000000000000000000000000000000000−2+2i2−2i00−2−2i2+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 ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.