Finite Group Databasebeta

← Group #164458

Character table — Group #164458

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size111111112222222222224444444444444444444444444488888888888888888888888888816161616161616161616
order12222222444444444444444444444444444444888888884444444888888888888888888882444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
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
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111111-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111111111-1-11111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111iiii−i−i−i−i111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iii−i−i-11-1-111ii−i−i
χ10111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111iiii−i−i−i−i-1-11-1-111ii−i−i−i−iiiiiii−i−i−i−i−i−iii1-111-1-1−i−iii
χ11111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111−i−i−i−iiiii111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−iii-11-1-111−i−iii
χ12111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111−i−i−i−iiiii-1-11-1-111−i−iiiii−i−i−i−i−i−iiiiiii−i−i1-111-1-1ii−i−i
χ13111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1iiii−i−i−i−i11111-1-1ii−i−iii−i−i−i−i−i−iiiiiii−i−i-1111-1-1−i−iii
χ14111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1iiii−i−i−i−i-1-111111ii−i−i−i−iii−i−i−i−iiiii−i−iii1-1-1-111ii−i−i
χ15111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1−i−i−i−iiiii11111-1-1−i−iii−i−iiiiiii−i−i−i−i−i−iii-1111-1-1ii−i−i
χ16111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1−i−i−i−iiiii-1-111111−i−iiiii−i−iiiii−i−i−i−iii−i−i1-1-1-111−i−iii
χ1711111111-1-1-1-11111111111-1-111-1-111-1-1-1-111-1-11111111111-11-111-1-1-1-1-1-1-1-111-1-111-1-11111-1-11-11-11-11-1
χ1811111111-1-1-1-11111111111-1-111-1-111-1-1-1-111-1-111111111-1-1-11-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111-11-11-11-11
χ1911111111-1-1-1-11111111111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-11-11111111111-1-111-1-111-1-1-1-1-1-11-11-1-11-11
χ2011111111-1-1-1-11111111111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-1-1-111-1-111111111-11-111-11-1
χ2111111111-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-1111111111111-1-1111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-11-11-11-11
χ2211111111-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-11111111111-1-1-1-11-1-1-1-1-1-11111-1-111-1-111-1-1-1-1111-11-11-11-1
χ2311111111-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111111111111-1-111-1-1-1-1-1-1-1-1-11-111-11-1
χ2411111111-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-111-1-111-1-11111111-11-1-11-11
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1iiii−i−i−i−i11-1-11-1-1−i−iii−i−iiiii−i−i−i−iiiii−i−i1-1-111-1i−i−ii
χ2611111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1iiii−i−i−i−i-1-1-1-1111−i−iiiii−i−iii−i−i−i−iii−i−iii-111-1-11−iii−i
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1−i−i−i−iiiii11-1-11-1-1ii−i−iii−i−i−i−iiiii−i−i−i−iii1-1-111-1−iii−i
χ2811111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1−i−i−i−iiiii-1-1-1-1111ii−i−i−i−iii−i−iiiii−i−iii−i−i-111-1-11i−i−ii
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-111iiii−i−i−i−i11-11-1-1-1−i−iii−i−iii−i−iiiii−i−iii−i−i1-11-1-11−iii−i
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-111iiii−i−i−i−i-1-1-11-111−i−iiiii−i−i−i−iiiii−i−i−i−iii-11-111-1i−i−ii
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-111−i−i−i−iiiii11-11-1-1-1ii−i−iii−i−iii−i−i−i−iii−i−iii1-11-1-11i−i−ii
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-111−i−i−i−iiiii-1-1-11-111ii−i−i−i−iiiii−i−i−i−iiiii−i−i-11-111-1−iii−i
χ3322222222222222-2-222-2-2-2-2-2-22222222222-2-2-2-20000000000-2-2-200000000000000000000000000000000
χ3422222222222222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222220000000000-22200000000000000000000000000000000
χ35222222222222-2-222-2-222-2-2222222-2-2-2-2-2-2-2-2-2-20000000000-22200000000000000000000000000000000
χ36222222222222-2-222-2-222-2-222-2-2-2-22222-2-222220000000000-2-2-200000000000000000000000000000000
χ3722222222-2-2-2-222-2-222-2-2-2-22222-2-222-2-2-2-2-2-22200000000002-2200000000000000000000000000000000
χ3822222222-2-2-2-222-2-222-2-2-2-222-2-222-2-222-2-222-2-2000000000022-200000000000000000000000000000000
χ3922222222-2-2-2-2-2-222-2-222-2-2-2-222-2-2-2-22222-2-222000000000022-200000000000000000000000000000000
χ4022222222-2-2-2-2-2-222-2-222-2-2-2-2-2-22222-2-22222-2-200000000002-2200000000000000000000000000000000
χ412-222-2-2-2200002i−2i2i−2i2i−2i2i−2i2-200000000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ32-20002i−2i00000000000000002ζ−2ζ2ζ3−2ζ30000000000
χ422-222-2-2-2200002i−2i2i−2i2i−2i2i−2i2-200000000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3-22000−2i2i0000000000000000−2ζ2ζ−2ζ32ζ30000000000
χ432-222-2-2-2200002i−2i2i−2i2i−2i2i−2i2-20000000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ32-20002i−2i0000000000000000−2ζ2ζ−2ζ32ζ30000000000
χ442-222-2-2-2200002i−2i2i−2i2i−2i2i−2i2-20000000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3-22000−2i2i00000000000000002ζ−2ζ2ζ3−2ζ30000000000
χ452-222-2-2-220000−2i2i−2i2i−2i2i−2i2i2-200000000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ2-2000−2i2i00000000000000002ζ3−2ζ32ζ−2ζ0000000000
χ462-222-2-2-220000−2i2i−2i2i−2i2i−2i2i2-200000000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ-220002i−2i0000000000000000−2ζ32ζ3−2ζ2ζ0000000000
χ472-222-2-2-220000−2i2i−2i2i−2i2i−2i2i2-20000000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ2-2000−2i2i0000000000000000−2ζ32ζ3−2ζ2ζ0000000000
χ482-222-2-2-220000−2i2i−2i2i−2i2i−2i2i2-20000000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ-220002i−2i00000000000000002ζ3−2ζ32ζ−2ζ0000000000
χ492-22-222-2-222-2-22i−2i00−2i2i0000002-22-22i−2i2i−2i2i−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000001+i−1−i1−i−1+i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ502-22-222-2-222-2-22i−2i00−2i2i0000002-22-22i−2i2i−2i2i−2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000−1−i1+i−1+i1−i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ512-22-222-2-222-2-22i−2i00−2i2i000000-22-22−2i2i−2i2i2i−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000001+i−1−i1−i−1+i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ522-22-222-2-222-2-22i−2i00−2i2i000000-22-22−2i2i−2i2i2i−2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000−1−i1+i−1+i1−i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ532-22-222-2-222-2-2−2i2i002i−2i0000002-22-2−2i2i−2i2i−2i2i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000001−i−1+i1+i−1−i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ542-22-222-2-222-2-2−2i2i002i−2i0000002-22-2−2i2i−2i2i−2i2i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000−1+i1−i−1−i1+i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ552-22-222-2-222-2-2−2i2i002i−2i000000-22-222i−2i2i−2i−2i2i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000001−i−1+i1+i−1−i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ562-22-222-2-222-2-2−2i2i002i−2i000000-22-222i−2i2i−2i−2i2i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000−1+i1−i−1−i1+i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ572-22-222-2-2-2-2222i−2i00−2i2i0000002-2-222i−2i−2i2i−2i2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000−1−i1+i−1+i1−i00001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000000000
χ582-22-222-2-2-2-2222i−2i00−2i2i0000002-2-222i−2i−2i2i−2i2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000001+i−1−i1−i−1+i0000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000000000
χ592-22-222-2-2-2-2222i−2i00−2i2i000000-222-2−2i2i2i−2i−2i2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000−1−i1+i−1+i1−i0000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000000000
χ602-22-222-2-2-2-2222i−2i00−2i2i000000-222-2−2i2i2i−2i−2i2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000001+i−1−i1−i−1+i00001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000000000
χ612-22-222-2-2-2-222−2i2i002i−2i0000002-2-22−2i2i2i−2i2i−2i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000−1+i1−i−1−i1+i00001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000000000
χ622-22-222-2-2-2-222−2i2i002i−2i0000002-2-22−2i2i2i−2i2i−2i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000001−i−1+i1+i−1−i0000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000000000
χ632-22-222-2-2-2-222−2i2i002i−2i000000-222-22i−2i−2i2i2i−2i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000−1+i1−i−1−i1+i0000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000000000
χ642-22-222-2-2-2-222−2i2i002i−2i000000-222-22i−2i−2i2i2i−2i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000001−i−1+i1+i−1−i00001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000000000
χ65444-4-4-44-400004400-4-40000000000000000000022−22−2222−222222−220000000000000000000000000000000000000
χ66444-4-4-44-400004400-4-400000000000000000000−222222−2222−22−22220000000000000000000000000000000000000
χ67444-4-4-44-40000-4-40044000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000
χ68444-4-4-44-40000-4-4004400000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000
χ6944-4-44-4-444-44-4004i−4i00−4i4i004i−4i00000000000000000000000000000000000000000000000000000000000
χ7044-4-44-4-444-44-400−4i4i004i−4i00−4i4i00000000000000000000000000000000000000000000000000000000000
χ7144-4-44-4-44-44-44004i−4i00−4i4i00−4i4i00000000000000000000000000000000000000000000000000000000000
χ7244-4-44-4-44-44-4400−4i4i004i−4i004i−4i00000000000000000000000000000000000000000000000000000000000
χ734-444-4-4-4400004i−4i−4i4i4i−4i−4i4i-440000000000000000000000000000000000000000000000000000000000000
χ744-444-4-4-440000−4i4i4i−4i−4i4i4i−4i-440000000000000000000000000000000000000000000000000000000000000
χ754-4-444-44-44-4-4400000000000000000000004i−4i4i−4i000000000000000000000000000000000000000000000
χ764-4-444-44-44-4-440000000000000000000000−4i4i−4i4i000000000000000000000000000000000000000000000
χ774-4-444-44-4-444-400000000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000
χ784-4-444-44-4-444-40000000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000
χ794-4-4-4-44440000004400-4-400000000000000000000000000000000000002i2−2i22i2−2i20000000000000000000000
χ804-4-4-4-44440000004400-4-40000000000000000000000000000000000000−2i22i2−2i22i20000000000000000000000
χ814-4-4-4-4444000000-4-40044000000000000000000000000000000000000022−22−22220000000000000000000000
χ824-4-4-4-4444000000-4-400440000000000000000000000000000000000000−222222−220000000000000000000000
χ8388-88-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000

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