Finite Group Databasebeta

← Group #98211

Character table — Group #98211

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222222244444444444444444444444444444888888888888888844444444448888
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
χ3111111111111111111111111111111111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1
χ5111111111111111111111-1-1-1-1111111-1-111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ7111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ8111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111
χ911111111-1-1-1-11111-1-1-1-1-1111111-1-1-11-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-1-111ii−i−iii−i−i
χ1011111111-1-1-1-11111-1-1-1-1-1111111-1-1-11-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-1-111−i−iii−i−iii
χ1111111111-1-1-1-11111-1-1-1-1-1111111-1-1-11-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii1-111-1-1−i−iiiii−i−i
χ1211111111-1-1-1-11111-1-1-1-1-1111111-1-1-11-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i1-111-1-1ii−i−i−i−iii
χ1311111111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-111111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1111-1-1−i−iii−i−iii
χ1411111111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-111111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1111-1-1ii−i−iii−i−i
χ1511111111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1-1-1-111ii−i−i−i−iii
χ1611111111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-1-1-111−i−iiiii−i−i
χ172222222222222222-2-2-2-222222-2-2-2-22-22200-2-2-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-22-2-2-2-2-2-2-2-22-2-2-200222200000000000000000000000000000000
χ19222222222222-2-2-2-22222-2000022-2-2-2-200220000220000000000000000-2-2000000000000
χ20222222222222-2-2-2-22222-2000022-2-2-2-200-2-20000-2-2000000000000000022000000000000
χ21222222222222-2-2-2-2-2-2-2-2-20000-2-222-2200000000000000000000000000002-22-200000000
χ22222222222222-2-2-2-2-2-2-2-2-20000-2-222-220000000000000000000000000000-22-2200000000
χ2322222222-2-2-2-222222222-22222-2-222-2-2-2-200-2-22200000000000000000000000000000000
χ2422222222-2-2-2-222222222-2-2-2-2-2-2-222-2-2220022-2-200000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2222220000-2-2-2-22200000000000000000000000000002-2-2200000000
χ2622222222-2-2-2-2-2-2-2-2222220000-2-2-2-2220000000000000000000000000000-222-200000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22000022222-200220000-2-200000000000000002-2000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22000022222-200-2-20000220000000000000000-22000000000000
χ29222-22-2-2-222-2-222-2-20000222-2-20000-202-20000000022−2−222−2−20000000000000000002−22−2
χ30222-22-2-2-222-2-222-2-20000222-2-20000-202-200000000−2−222−2−222000000000000000000−22−22
χ31222-22-2-2-222-2-222-2-200002-2-2220000-20-220000000022−2−222−2−2000000000000000000−22−22
χ32222-22-2-2-222-2-222-2-200002-2-2220000-20-2200000000−2−222−2−2220000000000000000002−22−2
χ33222-22-2-2-2-2-22222-2-20000-222-2-2000020-2200000000i2i2−i2−i2−i2−i2i2i2000000000000000000i2−i2−i2i2
χ34222-22-2-2-2-2-22222-2-20000-222-2-2000020-2200000000−i2−i2i2i2i2i2−i2−i2000000000000000000−i2i2i2−i2
χ35222-22-2-2-2-2-22222-2-20000-2-2-2220000202-200000000i2i2−i2−i2−i2−i2i2i2000000000000000000−i2i2i2−i2
χ36222-22-2-2-2-2-22222-2-20000-2-2-2220000202-200000000−i2−i2i2i2i2i2−i2−i2000000000000000000i2−i2−i2i2
χ372-222-2-2-2200002-22-22i−2i2i−2i02i−2i2i−2i002i−2i000000002-200000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000001+i−1−i1−i−1+i0000
χ382-222-2-2-2200002-22-22i−2i2i−2i02i−2i2i−2i002i−2i000000002-20000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000−1−i1+i−1+i1−i0000
χ392-222-2-2-2200002-22-22i−2i2i−2i0−2i2i−2i2i002i−2i00000000-2200000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000−1−i1+i−1+i1−i0000
χ402-222-2-2-2200002-22-22i−2i2i−2i0−2i2i−2i2i002i−2i00000000-220000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000001+i−1−i1−i−1+i0000
χ412-222-2-2-2200002-22-2−2i2i−2i2i02i−2i2i−2i00−2i2i00000000-2200000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000−1+i1−i−1−i1+i0000
χ422-222-2-2-2200002-22-2−2i2i−2i2i02i−2i2i−2i00−2i2i00000000-220000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000001−i−1+i1+i−1−i0000
χ432-222-2-2-2200002-22-2−2i2i−2i2i0−2i2i−2i2i00−2i2i000000002-200000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000001−i−1+i1+i−1−i0000
χ442-222-2-2-2200002-22-2−2i2i−2i2i0−2i2i−2i2i00−2i2i000000002-20000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000−1+i1−i−1−i1+i0000
χ452-2-2-22-2222-22-2000022-2-2000002-20000002-200002-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000000000
χ462-2-2-22-2222-22-2000022-2-2000002-20000002-200002-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000000000
χ472-2-2-22-2222-22-2000022-2-2000002-2000000-220000-22i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000000000
χ482-2-2-22-2222-22-2000022-2-2000002-2000000-220000-22−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000000000
χ492-2-2-22-222-22-220000-2-222000002-20000002-20000-222−22−2−22−222−22−2−22−2200000000000000
χ502-2-2-22-222-22-220000-2-222000002-20000002-20000-22−22−222−22−2−22−222−22−200000000000000
χ512-2-2-22-222-22-220000-2-222000002-2000000-2200002-22−22−2−22−22−22−222−22−200000000000000
χ522-2-2-22-222-22-220000-2-222000002-2000000-2200002-2−22−222−22−22−22−2−22−2200000000000000
χ53444-44-4-4-444-4-4-4-4440000-400000000400000000000000000000000000000000000000000
χ54444-44-4-4-4-4-444-4-4440000400000000-400000000000000000000000000000000000000000
χ5544-4-4-44-44000000004i−4i−4i4i000000000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000
χ5644-4-4-44-44000000004i−4i−4i4i00000000000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000
χ5744-4-4-44-4400000000−4i4i4i−4i000000000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000
χ5844-4-4-44-4400000000−4i4i4i−4i00000000000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000
χ594-444-4-4-440000-44-444i−4i4i−4i0000000−4i4i000000000000000000000000000000000000000000
χ604-444-4-4-440000-44-44−4i4i−4i4i00000004i−4i000000000000000000000000000000000000000000
χ614-44-4-444-400004-4-44000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ624-44-4-444-400004-4-4400000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ634-44-4-444-40000-444-400000000000000000004i−4i0000000000000000000000000000000000
χ644-44-4-444-40000-444-40000000000000000000−4i4i0000000000000000000000000000000000
χ654-4-4444-4-44-4-44000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ664-4-4444-4-44-4-4400000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000
χ674-4-4444-4-4-444-4000000000000000000000000000002-2-22-222-20000000000000000000000
χ684-4-4444-4-4-444-400000000000000000000000000000-222-22-2-220000000000000000000000
χ694-4-4-44-4444-44-40000-4-44400000-4400000000000000000000000000000000000000000000
χ704-4-4-44-444-44-44000044-4-400000-4400000000000000000000000000000000000000000000
χ7188-88-8-88-8000000000000000000000000000000000000000000000000000000000000000

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