Finite Group Databasebeta

← Group #101710

Character table — Group #101710

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444444444488888888888888888888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1ii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-11-11-1ii−i−iii−i−i1-1
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1ii−i−iii−i−iiiii−i−i−i−i-1-1-1-111111-11-1−i−iii−i−iii-11
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1ii−i−iii−i−i−i−i−i−iiiii1111-1-1-1-1-11-11ii−i−i−i−iii-11
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1ii−i−iii−i−i−i−i−i−iiiii-1-1-1-11111-11-11−i−iiiii−i−i1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1−i−iii−i−iiiiiii−i−i−i−i1111-1-1-1-1-11-11−i−iiiii−i−i-11
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1−i−iii−i−iiiiiii−i−i−i−i-1-1-1-11111-11-11ii−i−i−i−iii1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-11-11-1−i−iii−i−iii1-1
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1−i−iii−i−iii−i−i−i−iiiii-1-1-1-111111-11-1ii−i−iii−i−i-11
χ17222222222222-2-22222-2-2-2-2-2-222-200000000000000000000000022-2-20000000000
χ18222222222222-2-22222-2-2-2-2-2-222-2000000000000000000000000-2-2220000000000
χ192222222222-2-22222-2-22222-2-2-2-2-22222-2-2-2-2000000000000000000000000000000
χ202222222222-2-22222-2-22222-2-2-2-2-2-2-2-2-22222000000000000000000000000000000
χ212222222222-2-2-2-222-2-2-2-2-2-222-2-22000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000
χ222222222222-2-2-2-222-2-2-2-2-2-222-2-2200000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000
χ2322222222-2-22222-2-22222-2-222-2-2-20000000022-2-2-2-2220000000000000000000000
χ2422222222-2-22222-2-22222-2-222-2-2-200000000-2-22222-2-20000000000000000000000
χ2522222222-2-222-2-2-2-222-2-222-2-2-2-222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ2622222222-2-222-2-2-2-222-2-222-2-2-2-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ2722222222-2-2-2-222-2-2-2-222-2-2-2-22220000000000000000000000002-2-220000000000
χ2822222222-2-2-2-222-2-2-2-222-2-2-2-2222000000000000000000000000-222-20000000000
χ292222-2-2-2-2220022-2-200-2-22-2000002-22-200000000000022−2−222−2−200002−22−2000000
χ302222-2-2-2-2220022-2-200-2-22-2000002-22-2000000000000−2−222−2−2220000−22−22000000
χ312222-2-2-2-2220022-2-200-2-22-200000-22-2200000000000022−2−222−2−20000−22−22000000
χ322222-2-2-2-2220022-2-200-2-22-200000-22-22000000000000−2−222−2−22200002−22−2000000
χ332222-2-2-2-2-2-200-2-22200222-2000002i−2i−2i2i00000000000022−2−2−2−2220000i2−i2−i2i2000000
χ342222-2-2-2-2-2-200-2-22200222-2000002i−2i−2i2i000000000000−2−22222−2−20000−i2i2i2−i2000000
χ352222-2-2-2-2-2-200-2-22200222-200000−2i2i2i−2i00000000000022−2−2−2−2220000−i2i2i2−i2000000
χ362222-2-2-2-2-2-200-2-22200222-200000−2i2i2i−2i000000000000−2−22222−2−20000i2−i2−i2i2000000
χ3722-2-22-22-2002i−2i2i−2i002i−2i2i−2i002-200000000000002ζ3−2ζ32ζ−2ζ00i2−i2i2−i22−22−2000000001+i−1−i1−i−1+i00
χ3822-2-22-22-2002i−2i2i−2i002i−2i2i−2i002-200000000000002ζ3−2ζ32ζ−2ζ00−i2i2−i2i2−22−2200000000−1−i1+i−1+i1−i00
χ3922-2-22-22-2002i−2i2i−2i002i−2i2i−2i002-20000000000000−2ζ32ζ3−2ζ2ζ00i2−i2i2−i22−22−200000000−1−i1+i−1+i1−i00
χ4022-2-22-22-2002i−2i2i−2i002i−2i2i−2i002-20000000000000−2ζ32ζ3−2ζ2ζ00−i2i2−i2i2−22−22000000001+i−1−i1−i−1+i00
χ4122-2-22-22-200−2i2i−2i2i00−2i2i−2i2i002-200000000000002ζ−2ζ2ζ3−2ζ300i2−i2i2−i2−22−22000000001−i−1+i1+i−1−i00
χ4222-2-22-22-200−2i2i−2i2i00−2i2i−2i2i002-200000000000002ζ−2ζ2ζ3−2ζ300−i2i2−i2i22−22−200000000−1+i1−i−1−i1+i00
χ4322-2-22-22-200−2i2i−2i2i00−2i2i−2i2i002-20000000000000−2ζ2ζ−2ζ32ζ300i2−i2i2−i2−22−2200000000−1+i1−i−1−i1+i00
χ4422-2-22-22-200−2i2i−2i2i00−2i2i−2i2i002-20000000000000−2ζ2ζ−2ζ32ζ300−i2i2−i2i22−22−2000000001−i−1+i1+i−1−i00
χ454444-4-4-4-44400-4-4-4-40044-440000000000000000000000000000000000000000000
χ464444-4-4-4-4-4-400444400-4-4-440000000000000000000000000000000000000000000
χ4744-4-44-44-4004i−4i−4i4i004i−4i−4i4i00-4400000000000000000000000000000000000000000
χ4844-4-44-44-400−4i4i4i−4i00−4i4i4i−4i00-4400000000000000000000000000000000000000000
χ4944-4-4-44-4400004i−4i0000−4i4i000000000000000000000002i−2i−2i2i2-2-2200000000000000
χ5044-4-4-44-4400004i−4i0000−4i4i00000000000000000000000−2i2i2i−2i-222-200000000000000
χ5144-4-4-44-440000−4i4i00004i−4i000000000000000000000002i−2i−2i2i-222-200000000000000
χ5244-4-4-44-440000−4i4i00004i−4i00000000000000000000000−2i2i2i−2i2-2-2200000000000000
χ534-44-444-4-400440000-4-40000000000000000022−22000022−220000000000000000000000
χ544-44-444-4-400440000-4-400000000000000000−22220000−22220000000000000000000000
χ554-44-444-4-400-4-4000044000000000000000002i2−2i20000−2i22i20000000000000000000000
χ564-44-444-4-400-4-400004400000000000000000−2i22i200002i2−2i20000000000000000000000
χ574-4-444-4-444i−4i4i−4i004i−4i−4i4i0000004-4000000000000000000000000000000000000000
χ584-4-444-4-444i−4i−4i4i004i−4i4i−4i000000-44000000000000000000000000000000000000000
χ594-4-444-4-44−4i4i4i−4i00−4i4i−4i4i000000-44000000000000000000000000000000000000000
χ604-4-444-4-44−4i4i−4i4i00−4i4i4i−4i0000004-4000000000000000000000000000000000000000
χ614-4-44-444-44i−4i0000−4i4i0000000000000002−2i−2+2i2+2i−2−2i000000000000000000000000000000
χ624-4-44-444-44i−4i0000−4i4i000000000000000−2+2i2−2i−2−2i2+2i000000000000000000000000000000
χ634-4-44-444-4−4i4i00004i−4i0000000000000002+2i−2−2i2−2i−2+2i000000000000000000000000000000
χ644-4-44-444-4−4i4i00004i−4i000000000000000−2−2i2+2i−2+2i2−2i000000000000000000000000000000
χ658-88-8-8-888000000000000000000000000000000000000000000000000000000000

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