Finite Group Databasebeta

← Group #98188

Character table — Group #98188

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222222244444444444444444444444444444888888888888888822444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1
χ511111111111111111111111-1-1-1-111111-1-1-1-11-1-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111-1-1-1-111111-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111
χ711111111111111111111111-1-1-1-1111-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1
χ811111111111111111111111-1-1-1-1111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11111
χ911111111-1-1-1-1-1-11111-1-111-11111-1-1-11111-1-11-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-11-111ii−i−iii−i−i
χ1011111111-1-1-1-1-1-11111-1-111-11111-1-1-11111-1-11-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-11-111−i−iii−i−iii
χ1111111111-1-1-1-1-1-11111-1-111-11111-1-1-1-1-111-1-11-1-111iiii−i−i−i−i−i−i−i−iiiii11-11-1-1−i−iiiii−i−i
χ1211111111-1-1-1-1-1-11111-1-111-11111-1-1-1-1-111-1-11-1-111−i−i−i−iiiiiiiii−i−i−i−i11-11-1-1ii−i−i−i−iii
χ1311111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-111111-1-1iiii−i−i−i−iiiii−i−i−i−i111-1-1-1−i−iii−i−iii
χ1411111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-111111-1-1−i−i−i−iiiii−i−i−i−iiiii111-1-1-1ii−i−iii−i−i
χ1511111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111iiii−i−i−i−i−i−i−i−iiiii-1-1-1111ii−i−i−i−iii
χ1611111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1111−i−iiiii−i−i
χ1722222222222222-2-2-2-22222-20000-2-2-2220000-20022000000000000000000-2-20000000000
χ1822222222222222-2-2-2-22222-20000-2-2-2-2-20000-200-2-2000000000000000000220000000000
χ19222222222222-2-22222-2-2-2-222222-2-2200-2-2-2-2-22200000000000000000000000000000000
χ20222222222222-2-22222-2-2-2-22-2-2-2-2-2-22002222-2-2-200000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2000022-20000002000000000000000000002-2002-200000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2000022-2000000200000000000000000000-2200-2200000000
χ2322222222-2-2-2-222222222-2-2-2222222-200-2-222-2-2-200000000000000000000000000000000
χ2422222222-2-2-2-222222222-2-2-2-2-2-2-222-20022-2-2-22200000000000000000000000000000000
χ2522222222-2-2-2-222-2-2-2-222-2-220000-2-220000002000000000000000000002-200-2200000000
χ2622222222-2-2-2-222-2-2-2-222-2-220000-2-22000000200000000000000000000-22002-200000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22220000222220000-200-2-2000000000000000000-220000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22220000222-2-20000-200220000000000000000002-20000000000
χ2922-2-22-22-222-2-20022-2-20000-22i2i−2i−2i00200000002i−2i00i2i2−i2−i2i2i2−i2−i20000000000000000002−22−2
χ3022-2-22-22-222-2-20022-2-20000-22i2i−2i−2i00200000002i−2i00−i2−i2i2i2−i2−i2i2i2000000000000000000−22−22
χ3122-2-22-22-222-2-20022-2-20000-2−2i−2i2i2i0020000000−2i2i00i2i2−i2−i2i2i2−i2−i2000000000000000000−22−22
χ3222-2-22-22-222-2-20022-2-20000-2−2i−2i2i2i0020000000−2i2i00−i2−i2i2i2−i2−i2i2i20000000000000000002−22−2
χ3322-2-22-22-2-2-2220022-2-2000022i2i−2i−2i00-20000000−2i2i0022−2−2−2−222000000000000000000−i2i2i2−i2
χ3422-2-22-22-2-2-2220022-2-2000022i2i−2i−2i00-20000000−2i2i00−2−22222−2−2000000000000000000i2−i2−i2i2
χ3522-2-22-22-2-2-2220022-2-200002−2i−2i2i2i00-200000002i−2i0022−2−2−2−222000000000000000000i2−i2−i2i2
χ3622-2-22-22-2-2-2220022-2-200002−2i−2i2i2i00-200000002i−2i00−2−22222−2−2000000000000000000−i2i2i2−i2
χ372-222-2-22-200002i−2i2-22-22i−2i0002i−2i2i−2i2i−2i000002-200000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000001−i−1+i1+i−1−i0000
χ382-222-2-22-200002i−2i2-22-22i−2i0002i−2i2i−2i2i−2i000002-20000000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000−1+i1−i−1−i1+i0000
χ392-222-2-22-200002i−2i2-22-22i−2i000−2i2i−2i2i2i−2i00000-2200000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000−1+i1−i−1−i1+i0000
χ402-222-2-22-200002i−2i2-22-22i−2i000−2i2i−2i2i2i−2i00000-220000000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000001−i−1+i1+i−1−i0000
χ412-222-2-22-20000−2i2i2-22-2−2i2i0002i−2i2i−2i−2i2i00000-2200000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000−1−i1+i−1+i1−i0000
χ422-222-2-22-20000−2i2i2-22-2−2i2i0002i−2i2i−2i−2i2i00000-220000000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000001+i−1−i1−i−1+i0000
χ432-222-2-22-20000−2i2i2-22-2−2i2i000−2i2i−2i2i−2i2i000002-200000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000001+i−1−i1−i−1+i0000
χ442-222-2-22-20000−2i2i2-22-2−2i2i000−2i2i−2i2i−2i2i000002-20000000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000−1−i1+i−1+i1−i0000
χ452-22-222-2-22-22-2-2-20000222-2000000002i−2i00000002i−2ii2−i2i2−i2i2−i2i2−i22−22−22−22−200000000000000
χ462-22-222-2-22-22-2-2-20000222-2000000002i−2i00000002i−2i−i2i2−i2i2−i2i2−i2i2−22−22−22−2200000000000000
χ472-22-222-2-22-22-2-2-20000222-200000000−2i2i0000000−2i2ii2−i2i2−i2i2−i2i2−i2−22−22−22−2200000000000000
χ482-22-222-2-22-22-2-2-20000222-200000000−2i2i0000000−2i2i−i2i2−i2i2−i2i2−i2i22−22−22−22−200000000000000
χ492-22-222-2-2-22-22220000-2-22-2000000002i−2i0000000−2i2i2−22−2−22−22−i2i2−i2i2i2−i2i2−i200000000000000
χ502-22-222-2-2-22-22220000-2-22-2000000002i−2i0000000−2i2i−22−222−22−2i2−i2i2−i2−i2i2−i2i200000000000000
χ512-22-222-2-2-22-22220000-2-22-200000000−2i2i00000002i−2i2−22−2−22−22i2−i2i2−i2−i2i2−i2i200000000000000
χ522-22-222-2-2-22-22220000-2-22-200000000−2i2i00000002i−2i−22−222−22−2−i2i2−i2i2i2−i2i2−i200000000000000
χ53444-4-4-4-4400004i−4i0000−4i4i000000000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ00000000000000
χ54444-4-4-4-4400004i−4i0000−4i4i00000000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ00000000000000
χ55444-4-4-4-440000−4i4i00004i−4i000000000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ300000000000000
χ56444-4-4-4-440000−4i4i00004i−4i00000000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ300000000000000
χ5744-4-44-44-444-4-400-4-44400004000000-400000000000000000000000000000000000000000
χ5844-4-44-44-4-4-44400-4-4440000-4000000400000000000000000000000000000000000000000
χ594-444-4-44-400004i−4i-44-444i−4i0000000−4i4i000000000000000000000000000000000000000000
χ604-444-4-44-40000−4i4i-44-44−4i4i00000004i−4i000000000000000000000000000000000000000000
χ614-44-444-4-44-44-4440000-4-4-440000000000000000000000000000000000000000000000000
χ624-44-444-4-4-44-44-4-4000044-440000000000000000000000000000000000000000000000000
χ634-4-444-4-444-4-44000000000000000000000000000002-2-222-2-220000000000000000000000
χ644-4-444-4-444-4-4400000000000000000000000000000-222-2-222-20000000000000000000000
χ654-4-444-4-44-444-4000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ664-4-444-4-44-444-400000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ674-4-4-4-44440000004-4-44000004-4-4400000000000000000000000000000000000000000000
χ684-4-4-4-44440000004-4-4400000-444-400000000000000000000000000000000000000000000
χ694-4-4-4-4444000000-444-4000000000000004-40000000000000000000000000000000000000
χ704-4-4-4-4444000000-444-400000000000000-440000000000000000000000000000000000000
χ7188-88-88-8-8000000000000000000000000000000000000000000000000000000000000000

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