Finite Group Databasebeta

← Group #98005

Character table — Group #98005

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444422444444488888888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-1
χ41111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-111111111
χ7111111111111111111111111-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-111-1-1-1111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i11-11-1-11-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii11-11-1-11-1−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111iiii−i−i−i−i−i−i−i−iiiii-1-111-11-11ii−i−i−i−iii
χ1211111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111−i−i−i−iiiiiiiii−i−i−i−i-1-111-11-11−i−iiiii−i−i
χ1311111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-11-1-11−i−iii−i−iii
χ1411111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-11-1-11ii−i−iii−i−i
χ1511111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111iiii−i−i−i−i−i−i−i−iiiii-11-1-1111-1−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111−i−i−i−iiiiiiiii−i−i−i−i-11-1-1111-1ii−i−i−i−iii
χ17222222222222222222-2-2-2-2-2-2222200-2000000000000000000000-2-200000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-200-20000000000000000000002200000000000
χ192222222222-2-222-2-2-2-222-2-222000022-2-2-20000000000000000-2000020000000000
χ202222222222-2-222-2-2-2-222-2-2220000-2-2-222000000000000000020000-20000000000
χ212222222222-2-222-2-2-2-2-2-222-2-20000002000000000000000000022000-2-200000000
χ222222222222-2-222-2-2-2-2-2-222-2-200000020000000000000000000-2-20002200000000
χ2322222222-2-222-2-222-2-22222-2-2000022-2220000000000000000-20000-20000000000
χ2422222222-2-222-2-222-2-22222-2-20000-2-2-2-2-200000000000000002000020000000000
χ2522222222-2-222-2-222-2-2-2-2-2-222000000200000000000000000002-2000-2200000000
χ2622222222-2-222-2-222-2-2-2-2-2-22200000020000000000000000000-220002-200000000
χ2722222222-2-2-2-2-2-2-2-222-2-2222222-2-200-2000000000000000000000-2200000000000
χ2822222222-2-2-2-2-2-2-2-222-2-22222-2-22200-20000000000000000000002-200000000000
χ292222-2-2-2-22222-2-2-2-22-20000002-22-2000000000000022−2−222−2−20000000000002−22−2
χ302222-2-2-2-22222-2-2-2-22-20000002-22-20000000000000−2−222−2−222000000000000−22−22
χ312222-2-2-2-22222-2-2-2-22-2000000-22-22000000000000022−2−222−2−2000000000000−22−22
χ322222-2-2-2-22222-2-2-2-22-2000000-22-220000000000000−2−222−2−2220000000000002−22−2
χ332222-2-2-2-2-2-2-2-222222-20000002-2-220000000000000i2i2−i2−i2−i2−i2i2i2000000000000i2−i2−i2i2
χ342222-2-2-2-2-2-2-2-222222-20000002-2-220000000000000−i2−i2i2i2i2i2−i2−i2000000000000−i2i2i2−i2
χ352222-2-2-2-2-2-2-2-222222-2000000-222-20000000000000i2i2−i2−i2−i2−i2i2i2000000000000−i2i2i2−i2
χ362222-2-2-2-2-2-2-2-222222-2000000-222-20000000000000−i2−i2i2i2i2i2−i2−i2000000000000i2−i2−i2i2
χ3722-2-22-22-2002i−2i002i−2i002-22i−2i0000002i−2i02-21+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ3822-2-22-22-2002i−2i002i−2i002-22i−2i0000002i−2i02-2−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ3922-2-22-22-2002i−2i002i−2i002-22i−2i000000−2i2i0-221+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ4022-2-22-22-2002i−2i002i−2i002-22i−2i000000−2i2i0-22−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ4122-2-22-22-200−2i2i00−2i2i002-2−2i2i0000002i−2i0-221−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ4222-2-22-22-200−2i2i00−2i2i002-2−2i2i0000002i−2i0-22−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ4322-2-22-22-200−2i2i00−2i2i002-2−2i2i000000−2i2i02-21−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ4422-2-22-22-200−2i2i00−2i2i002-2−2i2i000000−2i2i02-2−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ454444-4-4-4-444-4-4-4-444-4400000000000000000000000000000000000000000000000
χ464444-4-4-4-4-4-44444-4-4-4400000000000000000000000000000000000000000000000
χ4744-4-44-44-4004i−4i004i−4i00-44−4i4i0000000000000000000000000000000000000000000
χ4844-4-44-44-400−4i4i00−4i4i00-444i−4i0000000000000000000000000000000000000000000
χ4944-4-4-44-44004i−4i00−4i4i00000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000000000
χ5044-4-4-44-44004i−4i00−4i4i0000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000000000000000
χ5144-4-4-44-4400−4i4i004i−4i00000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000000000000000
χ5244-4-4-44-4400−4i4i004i−4i0000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000
χ534-44-44-4-444i−4i004i−4i00000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ544-44-44-4-444i−4i004i−4i0000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000
χ554-44-44-4-44−4i4i00−4i4i00000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000
χ564-44-44-4-44−4i4i00−4i4i0000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000
χ574-44-4-444-44i−4i00−4i4i00000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ584-44-4-444-44i−4i00−4i4i0000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ594-44-4-444-4−4i4i004i−4i00000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ604-44-4-444-4−4i4i004i−4i0000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ614-4-4444-4-4000000000000004i−4i0000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000
χ624-4-4444-4-4000000000000004i−4i000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000
χ634-4-4444-4-400000000000000−4i4i0000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000000000000000000
χ644-4-4444-4-400000000000000−4i4i000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000
χ658-8-88-8-888000000000000000000000000000000000000000000000000000000000

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