Finite Group Databasebeta

← Group #100285

Character table — Group #100285

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444444444444444444888888888888888888888888888824
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-11-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111
χ811111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ911111111-1-111-1-1-1-111-1-111-1-1-1-11111-1-11-1-1ii−i−iii−i−iiiii−i−i−i−iii−i−i11-1-1ii−i−i1-1
χ1011111111-1-111-1-1-1-111-1-111-1-1-1-11111-1-11-1-1ii−i−iii−i−i−i−i−i−iiiii−i−iii-1-111ii−i−i-11
χ1111111111-1-111-1-1-1-111-1-111-1-1-1-11111-1-11-1-1−i−iii−i−iiiiiii−i−i−i−iii−i−i-1-111−i−iii-11
χ1211111111-1-111-1-1-1-111-1-111-1-1-1-11111-1-11-1-1−i−iii−i−iii−i−i−i−iiiii−i−iii11-1-1−i−iii1-1
χ1311111111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111ii−i−iii−i−iiiii−i−i−i−i−i−iii11-1-1−i−iii-11
χ1411111111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111ii−i−iii−i−i−i−i−i−iiiiiii−i−i-1-111−i−iii1-1
χ1511111111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111−i−iii−i−iiiiiii−i−i−i−i−i−iii-1-111ii−i−i1-1
χ1611111111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111−i−iii−i−iii−i−i−i−iiiiiii−i−i11-1-1ii−i−i-11
χ17222222222222-2-22222-2-2-2-2-2-22222-2-222-2-2-2000000000000000000000000000000
χ18222222222222-2-22222-2-2-2-2-2-222-2-222-2-2-222000000000000000000000000000000
χ192222222222-2-22222-2-22222-2-2-2-2000000-2002222-2-2-2-20000000000000000000000
χ202222222222-2-22222-2-22222-2-2-2-2000000-200-2-2-2-222220000000000000000000000
χ212222222222-2-2-2-222-2-2-2-2-2-222-2-20000002000000000000000000000000002i−2i2i−2i00
χ222222222222-2-2-2-222-2-2-2-2-2-222-2-2000000200000000000000000000000000−2i2i−2i2i00
χ2322222222-2-22222-2-22222-2-222-2-222-2-2-2-2-222000000000000000000000000000000
χ2422222222-2-22222-2-22222-2-222-2-2-2-22222-2-2-2000000000000000000000000000000
χ2522222222-2-2-2-222-2-2-2-222-2-2-2-2220000002000000000000000000000000002-2-2200
χ2622222222-2-2-2-222-2-2-2-222-2-2-2-222000000200000000000000000000000000-222-200
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000-2002i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000-200−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ2922-2-222-2-2002-22i−2i002-22i−2i002i−2i00002i−2i2-2000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i−1−i1−i−1+i0000000000
χ3022-2-222-2-2002-22i−2i002-22i−2i002i−2i00002i−2i2-200000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i1+i−1+i1−i0000000000
χ3122-2-222-2-2002-22i−2i002-22i−2i002i−2i0000−2i2i-22000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i1+i−1+i1−i0000000000
χ3222-2-222-2-2002-22i−2i002-22i−2i002i−2i0000−2i2i-2200000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i−1−i1−i−1+i0000000000
χ3322-2-222-2-2002-2−2i2i002-2−2i2i00−2i2i00002i−2i-22000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i1−i−1−i1+i0000000000
χ3422-2-222-2-2002-2−2i2i002-2−2i2i00−2i2i00002i−2i-2200000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i−1+i1+i−1−i0000000000
χ3522-2-222-2-2002-2−2i2i002-2−2i2i00−2i2i0000−2i2i2-2000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i−1+i1+i−1−i0000000000
χ3622-2-222-2-2002-2−2i2i002-2−2i2i00−2i2i0000−2i2i2-200000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i1−i−1−i1+i0000000000
χ372-22-22-22-22i−2i002i−2i2i−2i00−2i2i2-200000000000002ζ−2ζ2ζ3−2ζ300001+i−1−i1+i−1−i1−i−1+i1−i−1+i00002−2i2−i2000000
χ382-22-22-22-22i−2i002i−2i2i−2i00−2i2i2-200000000000002ζ−2ζ2ζ3−2ζ30000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000−22−i2i2000000
χ392-22-22-22-22i−2i002i−2i2i−2i00−2i2i2-20000000000000−2ζ2ζ−2ζ32ζ300001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000−22−i2i2000000
χ402-22-22-22-22i−2i002i−2i2i−2i00−2i2i2-20000000000000−2ζ2ζ−2ζ32ζ30000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00002−2i2−i2000000
χ412-22-22-22-2−2i2i00−2i2i−2i2i002i−2i2-200000000000002ζ3−2ζ32ζ−2ζ00001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000−22i2−i2000000
χ422-22-22-22-2−2i2i00−2i2i−2i2i002i−2i2-200000000000002ζ3−2ζ32ζ−2ζ0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00002−2−i2i2000000
χ432-22-22-22-2−2i2i00−2i2i−2i2i002i−2i2-20000000000000−2ζ32ζ3−2ζ2ζ00001−i−1+i1−i−1+i1+i−1−i1+i−1−i00002−2−i2i2000000
χ442-22-22-22-2−2i2i00−2i2i−2i2i002i−2i2-20000000000000−2ζ32ζ3−2ζ2ζ0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000−22i2−i2000000
χ4544-4-444-4-400-444i−4i00-444i−4i00−4i4i00000000000000000000000000000000000000000
χ4644-4-444-4-400-44−4i4i00-44−4i4i004i−4i00000000000000000000000000000000000000000
χ4744-4-4-4-444440000-4-4000000000000000000000002i2−2i22i2−2i20000000000000000000000
χ4844-4-4-4-444440000-4-400000000000000000000000−2i22i2−2i22i20000000000000000000000
χ4944-4-4-4-444-4-40000440000000000000000000000022−22−22220000000000000000000000
χ5044-4-4-4-444-4-400004400000000000000000000000−222222−220000000000000000000000
χ514-44-44-44-44i−4i00−4i4i4i−4i004i−4i-440000000000000000000000000000000000000000000
χ524-44-44-44-4−4i4i004i−4i−4i4i00−4i4i-440000000000000000000000000000000000000000000
χ534-44-4-44-4400440000-4-4000000004i−4i0000000000000000000000000000000000000
χ544-44-4-44-4400440000-4-400000000−4i4i0000000000000000000000000000000000000
χ554-44-4-44-4400-4-40000440000000000000004-4000000000000000000000000000000
χ564-44-4-44-4400-4-4000044000000000000000-44000000000000000000000000000000
χ574-4-444-4-440000440000-4-4000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ584-4-444-4-440000440000-4-400000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ594-4-444-4-440000-4-4000044000000000000000000000002-2-222-2-2200000000000000
χ604-4-444-4-440000-4-400004400000000000000000000000-222-2-222-200000000000000
χ614-4-44-444-44i−4i4-400−4i4i-440000004i−4i000000000000000000000000000000000000000
χ624-4-44-444-44i−4i-4400−4i4i4-4000000−4i4i000000000000000000000000000000000000000
χ634-4-44-444-4−4i4i4-4004i−4i-44000000−4i4i000000000000000000000000000000000000000
χ644-4-44-444-4−4i4i-44004i−4i4-40000004i−4i000000000000000000000000000000000000000
χ658888-8-8-8-8000000000000000000000000000000000000000000000000000000000

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