Finite Group Databasebeta

← Group #164471

Character table — Group #164471

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size111111112222222222224444444444444444444444444488888888888888888888888888816161616161616161616
order12222222444444444444444444444444444444888888884444444888888888888888888882444448888
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
χ5111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1111111111111-1-11111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1iiii−i−i−i−i11111-1-1ii−i−iii−i−iiiii−i−i−i−iii−i−i-1111-1-1ii−i−i
χ10111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1iiii−i−i−i−i111-1-111−i−iiiii−i−iiiii−i−i−i−i−i−iii1-1-1-111−i−iii
χ11111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1−i−i−i−iiiii11111-1-1−i−iii−i−iii−i−i−i−iiiii−i−iii-1111-1-1−i−iii
χ12111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1−i−i−i−iiiii111-1-111ii−i−i−i−iii−i−i−i−iiiiiii−i−i1-1-1-111ii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111iiii−i−i−i−i-1-1111-1-1ii−i−iii−i−i−i−i−i−iiiiiii−i−i-11-1-111−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111iiii−i−i−i−i-1-11-1-111−i−iiiii−i−i−i−i−i−iiiii−i−iii1-111-1-1ii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−i−i−i−iiiii-1-1111-1-1−i−iii−i−iiiiiii−i−i−i−i−i−iii-11-1-111ii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−i−i−i−iiiii-1-11-1-111ii−i−i−i−iiiiiii−i−i−i−iii−i−i1-111-1-1−i−iii
χ1711111111-1-1-1-111111111-1-1-1-111-1-111-1-11111-1-1111111111-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-11-11-11-11-1
χ1811111111-1-1-1-111111111-1-1-1-111-1-111-1-11111-1-1111111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-111-11-11-11-11
χ1911111111-1-1-1-111111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-11-1-1111111111111-1-111-1-111-1-1-1-1-1-11-11-1-11-11
χ2011111111-1-1-1-111111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-111-1-111111111-11-111-11-1
χ2111111111-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-11111111111-11-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-11-11-11-11
χ2211111111-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-11111111111-11-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1111-11-11-11-1
χ2311111111-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-11-111111111111111-1-111-1-1-1-1-1-1-1-1-11-111-11-1
χ2411111111-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1111111-1-111-1-11111111-11-1-11-11
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111iiii−i−i−i−i1-1-111-1-1−i−iii−i−iiiii−i−i−i−iiiii−i−i1-11-1-11i−i−ii
χ2611111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111iiii−i−i−i−i1-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii−i−iii-11-111-1−iii−i
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111−i−i−i−iiiii1-1-111-1-1ii−i−iii−i−i−i−iiiii−i−i−i−iii1-11-1-11−iii−i
χ2811111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111−i−i−i−iiiii1-1-1-1-111−i−iiiii−i−i−i−iiiii−i−iii−i−i-11-111-1i−i−ii
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1iiii−i−i−i−i-11-111-1-1−i−iii−i−iii−i−iiiii−i−iii−i−i1-1-111-1−iii−i
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1iiii−i−i−i−i-11-1-1-111ii−i−i−i−iii−i−iiiii−i−i−i−iii-111-1-11i−i−ii
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1−i−i−i−iiiii-11-111-1-1ii−i−iii−i−iii−i−i−i−iii−i−iii1-1-111-1i−i−ii
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1−i−i−i−iiiii-11-1-1-111−i−iiiii−i−iii−i−i−i−iiiii−i−i-111-1-11−iii−i
χ3322222222222222-2-222-2-222-2-222222222-2-2-2-2-2-200000000-2-2-20000000000000000000000000000000000
χ3422222222222222-2-222-2-222-2-2-2-2-2-2-2-2-2-2-2-222220000000022-20000000000000000000000000000000000
χ35222222222222-2-222-2-222-2-2222222-2-2-2-2-2-2222200000000-2-2-20000000000000000000000000000000000
χ36222222222222-2-222-2-222-2-222-2-2-2-22222-2-2-2-2-2-20000000022-20000000000000000000000000000000000
χ3722222222-2-2-2-222-2-222-2-2-2-22222-2-222-2-2-2-2-2-22200000000-2220000000000000000000000000000000000
χ3822222222-2-2-2-222-2-222-2-2-2-222-2-222-2-222-2-222-2-2000000002-220000000000000000000000000000000000
χ3922222222-2-2-2-2-2-222-2-22222-2-222-2-2-2-222-2-222-2-200000000-2220000000000000000000000000000000000
χ4022222222-2-2-2-2-2-222-2-22222-2-2-2-22222-2-2-2-2-2-222000000002-220000000000000000000000000000000000
χ4122-22-2-2-2222-2-22i−2i002i−2i002i−2i002-22-22i−2i2i−2i0000001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000001+i−1−i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ4222-22-2-2-2222-2-22i−2i002i−2i002i−2i002-22-22i−2i2i−2i000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000−1−i1+i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ4322-22-2-2-2222-2-22i−2i002i−2i002i−2i00-22-22−2i2i−2i2i0000001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000001+i−1−i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ4422-22-2-2-2222-2-22i−2i002i−2i002i−2i00-22-22−2i2i−2i2i000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000−1−i1+i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ4522-22-2-2-2222-2-2−2i2i00−2i2i00−2i2i002-22-2−2i2i−2i2i0000001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000001−i−1+i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ4622-22-2-2-2222-2-2−2i2i00−2i2i00−2i2i002-22-2−2i2i−2i2i000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000−1+i1−i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ4722-22-2-2-2222-2-2−2i2i00−2i2i00−2i2i00-22-222i−2i2i−2i0000001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000001−i−1+i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ4822-22-2-2-2222-2-2−2i2i00−2i2i00−2i2i00-22-222i−2i2i−2i000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000−1+i1−i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ4922-22-2-2-22-2-2222i−2i002i−2i00−2i2i002-2-222i−2i−2i2i0000001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000−1−i1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000000000
χ5022-22-2-2-22-2-2222i−2i002i−2i00−2i2i002-2-222i−2i−2i2i000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000001+i−1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000000000
χ5122-22-2-2-22-2-2222i−2i002i−2i00−2i2i00-222-2−2i2i2i−2i0000001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000−1−i1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000000000
χ5222-22-2-2-22-2-2222i−2i002i−2i00−2i2i00-222-2−2i2i2i−2i000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000001+i−1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000000000
χ5322-22-2-2-22-2-222−2i2i00−2i2i002i−2i002-2-22−2i2i2i−2i0000001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000−1+i1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000000000
χ5422-22-2-2-22-2-222−2i2i00−2i2i002i−2i002-2-22−2i2i2i−2i000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000001−i−1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000000000
χ5522-22-2-2-22-2-222−2i2i00−2i2i002i−2i00-222-22i−2i−2i2i0000001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000−1+i1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000000000
χ5622-22-2-2-22-2-222−2i2i00−2i2i002i−2i00-222-22i−2i−2i2i000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000001−i−1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000000000
χ572-2-222-22-200002i−2i2i−2i−2i2i2i−2i0000000000002-200002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30002-22i−2i00000000000000002ζ−2ζ2ζ3−2ζ30000000000
χ582-2-222-22-200002i−2i2i−2i−2i2i2i−2i0000000000002-200002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000-22−2i2i0000000000000000−2ζ2ζ−2ζ32ζ30000000000
χ592-2-222-22-200002i−2i2i−2i−2i2i2i−2i0000000000002-20000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30002-22i−2i0000000000000000−2ζ2ζ−2ζ32ζ30000000000
χ602-2-222-22-200002i−2i2i−2i−2i2i2i−2i0000000000002-20000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000-22−2i2i00000000000000002ζ−2ζ2ζ3−2ζ30000000000
χ612-2-222-22-20000−2i2i−2i2i2i−2i−2i2i0000000000002-200002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0002-2−2i2i00000000000000002ζ3−2ζ32ζ−2ζ0000000000
χ622-2-222-22-20000−2i2i−2i2i2i−2i−2i2i0000000000002-200002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000-222i−2i0000000000000000−2ζ32ζ3−2ζ2ζ0000000000
χ632-2-222-22-20000−2i2i−2i2i2i−2i−2i2i0000000000002-20000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0002-2−2i2i0000000000000000−2ζ32ζ3−2ζ2ζ0000000000
χ642-2-222-22-20000−2i2i−2i2i2i−2i−2i2i0000000000002-20000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000-222i−2i00000000000000002ζ3−2ζ32ζ−2ζ0000000000
χ6544-4-444-4-40000004400-4-400000000000000000000000000000000022−2222−2200000000000000000000000000
χ6644-4-444-4-40000004400-4-4000000000000000000000000000000000−2222−222200000000000000000000000000
χ6744-4-444-4-4000000-4-400440000000000000000000000000000000002i2−2i2−2i22i200000000000000000000000000
χ6844-4-444-4-4000000-4-40044000000000000000000000000000000000−2i22i22i2−2i200000000000000000000000000
χ694-444-44-4-400004400-4-40000000000000000000022−22−2222−222222−220000000000000000000000000000000000000
χ704-444-44-4-400004400-4-400000000000000000000−222222−2222−22−22220000000000000000000000000000000000000
χ714-444-44-4-40000-4-40044000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000
χ724-444-44-4-40000-4-4004400000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000
χ734-44-44-4-444-44-4004i−4i00−4i4i004i−4i00000000000000000000000000000000000000000000000000000000000
χ744-44-44-4-444-44-400−4i4i004i−4i00−4i4i00000000000000000000000000000000000000000000000000000000000
χ754-44-44-4-44-44-44004i−4i00−4i4i00−4i4i00000000000000000000000000000000000000000000000000000000000
χ764-44-44-4-44-44-4400−4i4i004i−4i004i−4i00000000000000000000000000000000000000000000000000000000000
χ774-4-444-44-400004i−4i−4i4i−4i4i−4i4i000000000000-440000000000000000000000000000000000000000000000000
χ784-4-444-44-40000−4i4i4i−4i4i−4i4i−4i000000000000-440000000000000000000000000000000000000000000000000
χ794-4-4-4-44444-4-4400000000000000000000004-44-4000000000000000000000000000000000000000000000
χ804-4-4-4-44444-4-440000000000000000000000-44-44000000000000000000000000000000000000000000000
χ814-4-4-4-4444-444-400000000000000000000004-4-44000000000000000000000000000000000000000000000
χ824-4-4-4-4444-444-40000000000000000000000-444-4000000000000000000000000000000000000000000000
χ83888-8-8-88-8000000000000000000000000000000000000000000000000000000000000000000000000000

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