Finite Group Databasebeta

← Group #164439

Character table — Group #164439

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size111111112222222222224444444444444444444444444488888888888888888888888888816161616161616161616
order12222222444444444444444444444444444444888888884444444888888888888888888884444448888
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
χ51111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1111111111-111-111-1-1-1-11111-1-1-1-111111111-1-11-11-1-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-111111
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11-111-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-11-11111
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-111111111111111-11-11-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i1-111-1-1-1ii−i−iii−i−iii−i−iiiii−i−i−i−i-11-1-111i−ii−i
χ10111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i1-1-1-1-111ii−i−iii−i−iii−i−i−i−i−i−iiiii1-111-1-1−ii−ii
χ11111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii1-111-1-1-1−i−iii−i−iii−i−iii−i−i−i−iiiii-11-1-111−ii−ii
χ12111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii1-1-1-1-111−i−iii−i−iii−i−iiiiiii−i−i−i−i1-111-1-1i−ii−i
χ13111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111iiii−i−i−i−i11111-1-1−i−iiiii−i−i−i−iiiiiii−i−i−i−i1-1-111-1−ii−ii
χ14111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111iiii−i−i−i−i11-1-1111−i−iiiii−i−i−i−iii−i−i−i−iiiii-111-1-11i−ii−i
χ15111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111−i−i−i−iiiii11111-1-1ii−i−i−i−iiiii−i−i−i−i−i−iiiii1-1-111-1i−ii−i
χ16111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111−i−i−i−iiiii11-1-1111ii−i−i−i−iiiii−i−iiiii−i−i−i−i-111-1-11−ii−ii
χ1711111111-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-111111111-1-111111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-111-1-1
χ1811111111-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-1-111
χ1911111111-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-111
χ2011111111-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111111-1-1-1-111-1-111-1-1-1-1111111-1-1
χ2111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-11111111111-1111-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-11-11-1-111
χ2211111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-11111111111-11-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111-11-111-1-1
χ2311111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1111-111-1-1-1-111111111-1-111-1-111-1-1-11-1111-1-1
χ2411111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-11111111111-1-111-1-1111-11-1-1-111
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111iiii−i−i−i−i-1111-1-1-1−i−iii−i−iiiii−i−iii−i−i−i−iii-1111-1-1i−i−ii
χ2611111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111iiii−i−i−i−i-11-1-1-111−i−iii−i−iiiii−i−i−i−iiiii−i−i1-1-1-111−iii−i
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111−i−i−i−iiiii-1111-1-1-1ii−i−iii−i−i−i−iii−i−iiiii−i−i-1111-1-1−iii−i
χ2811111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111−i−i−i−iiiii-11-1-1-111ii−i−iii−i−i−i−iiiii−i−i−i−iii1-1-1-111i−i−ii
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1iiii−i−i−i−i-1-1111-1-1ii−i−i−i−iii−i−iiiii−i−i−i−iii1-11-1-11−iii−i
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1iiii−i−i−i−i-1-1-1-1111ii−i−i−i−iii−i−iii−i−iiiii−i−i-11-111-1i−i−ii
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1−i−i−i−iiiii-1-1111-1-1−i−iiiii−i−iii−i−i−i−iiiii−i−i1-11-1-11i−i−ii
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1−i−i−i−iiiii-1-1-1-1111−i−iiiii−i−iii−i−iii−i−i−i−iii-11-111-1−iii−i
χ3322222222222222-2-222-2-2-2-222-2-222-2-22222-2-22200000000-2-200-200000000000000000000000000000000
χ3422222222222222-2-222-2-2-2-2-2-222-2-22222-2-2-2-2-2-200000000-2200200000000000000000000000000000000
χ35222222222222-2-222-2-222-2-222-2-222-2-2-2-2-2-222-2-200000000-2200200000000000000000000000000000000
χ36222222222222-2-222-2-222-2-2-2-222-2-222-2-222222200000000-2-200-200000000000000000000000000000000
χ3722222222-2-2-2-222-2-222-2-2-2-222-2-2-2-222-2-22222-2-2000000002200-200000000000000000000000000000000
χ3822222222-2-2-2-222-2-222-2-2-2-2-2-22222-2-2-2-2-2-22222000000002-200200000000000000000000000000000000
χ3922222222-2-2-2-2-2-222-2-222-2-222-2-2-2-22222-2-2-2-222000000002-200200000000000000000000000000000000
χ4022222222-2-2-2-2-2-222-2-222-2-2-2-22222-2-22222-2-2-2-2000000002200-200000000000000000000000000000000
χ4122-2-2-22-2200002i−2i2i−2i2i−2i2i−2i2-200000000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3002i−2i02-20000000000002ζ3−2ζ3002ζ−2ζ000000000000
χ4222-2-2-22-2200002i−2i2i−2i2i−2i2i−2i2-200000000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300−2i2i0-22000000000000−2ζ32ζ300−2ζ2ζ000000000000
χ4322-2-2-22-2200002i−2i2i−2i2i−2i2i−2i2-20000000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3002i−2i02-2000000000000−2ζ32ζ300−2ζ2ζ000000000000
χ4422-2-2-22-2200002i−2i2i−2i2i−2i2i−2i2-20000000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300−2i2i0-220000000000002ζ3−2ζ3002ζ−2ζ000000000000
χ4522-2-2-22-220000−2i2i−2i2i−2i2i−2i2i2-200000000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ002i−2i0-22000000000000−2ζ2ζ00−2ζ32ζ3000000000000
χ4622-2-2-22-220000−2i2i−2i2i−2i2i−2i2i2-200000000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00−2i2i02-20000000000002ζ−2ζ002ζ3−2ζ3000000000000
χ4722-2-2-22-220000−2i2i−2i2i−2i2i−2i2i2-20000000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ002i−2i0-220000000000002ζ−2ζ002ζ3−2ζ3000000000000
χ4822-2-2-22-220000−2i2i−2i2i−2i2i−2i2i2-20000000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00−2i2i02-2000000000000−2ζ2ζ00−2ζ32ζ3000000000000
χ492-222-2-2-222i2i−2i−2i002i−2i00−2i2i00002-2002i−2i002i−2i2-22-21−i−1+i1−i−1+i1+i−1−i1+i−1−i00000001+i−1−i1−i−1+i1+i−1−i1−i−1+i1−i−1+i1+i−1−i000000000000000000
χ502-222-2-2-222i2i−2i−2i002i−2i00−2i2i00002-2002i−2i002i−2i2-22-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i−1+i1−i−1−i1+i000000000000000000
χ512-222-2-2-222i2i−2i−2i002i−2i00−2i2i0000-2200−2i2i00−2i2i2-2-221−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i−1+i1−i−1−i1+i000000000000000000
χ522-222-2-2-222i2i−2i−2i002i−2i00−2i2i0000-2200−2i2i00−2i2i2-2-22−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000001+i−1−i1−i−1+i−1−i1+i−1+i1−i1−i−1+i1+i−1−i000000000000000000
χ532-222-2-2-222i2i−2i−2i00−2i2i002i−2i00002-2002i−2i00−2i2i-22-221+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i000000000000000000
χ542-222-2-2-222i2i−2i−2i00−2i2i002i−2i00002-2002i−2i00−2i2i-22-22−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000001−i−1+i1+i−1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i000000000000000000
χ552-222-2-2-222i2i−2i−2i00−2i2i002i−2i0000-2200−2i2i002i−2i-222-21+i−1−i1+i−1−i1−i−1+i1−i−1+i00000001−i−1+i1+i−1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i000000000000000000
χ562-222-2-2-222i2i−2i−2i00−2i2i002i−2i0000-2200−2i2i002i−2i-222-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i000000000000000000
χ572-222-2-2-22−2i−2i2i2i002i−2i00−2i2i00002-200−2i2i002i−2i-22-221−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i000000000000000000
χ582-222-2-2-22−2i−2i2i2i002i−2i00−2i2i00002-200−2i2i002i−2i-22-22−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000001+i−1−i1−i−1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i000000000000000000
χ592-222-2-2-22−2i−2i2i2i002i−2i00−2i2i0000-22002i−2i00−2i2i-222-21−i−1+i1−i−1+i1+i−1−i1+i−1−i00000001+i−1−i1−i−1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i000000000000000000
χ602-222-2-2-22−2i−2i2i2i002i−2i00−2i2i0000-22002i−2i00−2i2i-222-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i000000000000000000
χ612-222-2-2-22−2i−2i2i2i00−2i2i002i−2i00002-200−2i2i00−2i2i2-22-21+i−1−i1+i−1−i1−i−1+i1−i−1+i00000001−i−1+i1+i−1−i1−i−1+i1+i−1−i1+i−1−i1−i−1+i000000000000000000
χ622-222-2-2-22−2i−2i2i2i00−2i2i002i−2i00002-200−2i2i00−2i2i2-22-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i−1−i1+i−1+i1−i000000000000000000
χ632-222-2-2-22−2i−2i2i2i00−2i2i002i−2i0000-22002i−2i002i−2i2-2-221+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i−1−i1+i−1+i1−i000000000000000000
χ642-222-2-2-22−2i−2i2i2i00−2i2i002i−2i0000-22002i−2i002i−2i2-2-22−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000001−i−1+i1+i−1−i−1+i1−i−1−i1+i1+i−1−i1−i−1+i000000000000000000
χ65444-44-4-4-44-44-400000000004-4004-40000000000000000000000000000000000000000000000000000000
χ66444-44-4-4-44-44-40000000000-4400-440000000000000000000000000000000000000000000000000000000
χ67444-44-4-4-4-44-4400000000004-400-440000000000000000000000000000000000000000000000000000000
χ68444-44-4-4-4-44-440000000000-44004-40000000000000000000000000000000000000000000000000000000
χ6944-4-4-44-4400004i−4i−4i4i4i−4i−4i4i-440000000000000000000000000000000000000000000000000000000000000
χ7044-4-4-44-440000−4i4i4i−4i−4i4i4i−4i-440000000000000000000000000000000000000000000000000000000000000
χ714-44-4-444-44i−4i−4i4i4i−4i00−4i4i0000000000004-4000000000000000000000000000000000000000000000000000
χ724-44-4-444-44i−4i−4i4i−4i4i004i−4i000000000000-44000000000000000000000000000000000000000000000000000
χ734-44-4-444-4−4i4i4i−4i4i−4i00−4i4i000000000000-44000000000000000000000000000000000000000000000000000
χ744-44-4-444-4−4i4i4i−4i−4i4i004i−4i0000000000004-4000000000000000000000000000000000000000000000000000
χ754-4-4444-4-400004400-4-4000000000000000000000000000000000000000000000000022−220022−220000000000
χ764-4-4444-4-400004400-4-40000000000000000000000000000000000000000000000000−222200−22220000000000
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χ784-4-4444-4-40000-4-400440000000000000000000000000000000000000000000000000−2i22i2002i2−2i20000000000
χ794-4-4-44-4440000004400-4-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000
χ804-4-4-44-4440000004400-4-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000
χ814-4-4-44-444000000-4-4004400000000000000000022−22−2222−222222−220000000000000000000000000000000000000
χ824-4-4-44-444000000-4-40044000000000000000000−222222−2222−22−22220000000000000000000000000000000000000
χ8388-88-8-88-8000000000000000000000000000000000000000000000000000000000000000000000000000

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