Finite Group Databasebeta

← Group #98151

Character table — Group #98151

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444224444444444444444444444444448888888844444488888888
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
χ311111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-111-1-11-1-11111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ7111111111111111111111111-1-1-1-111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ8111111111111111111111111-1-1-1-111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1
χ911111111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i1-111-1-1ii−i−iii−i−i
χ1011111111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii1-111-1-1−i−iii−i−iii
χ1111111111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-11-1-111ii−i−i−i−iii
χ1211111111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-11-1-111−i−iiiii−i−i
χ1311111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-1-1-111−i−iii−i−iii
χ1411111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-1-1-111ii−i−iii−i−i
χ1511111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii-1111-1-1−i−iiiii−i−i
χ1611111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1111-1-1ii−i−i−i−iii
χ1722222222222222-2-222-2-2-2-2-2-222222222-2-2-20000-2-2000000000000000000000000000000
χ1822222222222222-2-222-2-2-2-2-2-2-2-2-2-222-2-2-222000022000000000000000000000000000000
χ192222222222-2-2-2-2222222-2-2220000-2-200-2002222000000000000000000-2-2000000000000
χ202222222222-2-2-2-2222222-2-2220000-2-200-200-2-2-2-200000000000000000022000000000000
χ212222222222-2-2-2-2-2-222-2-222-2-20000-2-2002000000000000000000000000002-22-200000000
χ222222222222-2-2-2-2-2-222-2-222-2-20000-2-200200000000000000000000000000-22-2200000000
χ2322222222-2-2222222-2-22222-2-22222-2-2-2-2-2220000-2-2000000000000000000000000000000
χ2422222222-2-2222222-2-22222-2-2-2-2-2-2-2-222-2-2-2000022000000000000000000000000000000
χ2522222222-2-2-2-2-2-222-2-222-2-2-2-2000022002000000000000000000000000002-2-2200000000
χ2622222222-2-2-2-2-2-222-2-222-2-2-2-200002200200000000000000000000000000-222-200000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222200002200-20022-2-2000000000000000000-22000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222200002200-200-2-2220000000000000000002-2000000000000
χ2922-2-2-2-2220022-2-22200-2-2-22002i2i−2i−2i000002i−2i00000000000000i2i2−i2−i2i2i2−i2−i200000000002−22−2
χ3022-2-2-2-2220022-2-22200-2-2-22002i2i−2i−2i000002i−2i00000000000000−i2−i2i2i2−i2−i2i2i20000000000−22−22
χ3122-2-2-2-2220022-2-22200-2-2-2200−2i−2i2i2i00000−2i2i00000000000000i2i2−i2−i2i2i2−i2−i20000000000−22−22
χ3222-2-2-2-2220022-2-22200-2-2-2200−2i−2i2i2i00000−2i2i00000000000000−i2−i2i2i2−i2−i2i2i200000000002−22−2
χ3322-2-2-2-2220022-2-2-2-200222-2002i2i−2i−2i00000−2i2i0000000000000022−2−2−2−2220000000000−i2i2i2−i2
χ3422-2-2-2-2220022-2-2-2-200222-2002i2i−2i−2i00000−2i2i00000000000000−2−22222−2−20000000000i2−i2−i2i2
χ3522-2-2-2-2220022-2-2-2-200222-200−2i−2i2i2i000002i−2i0000000000000022−2−2−2−2220000000000i2−i2−i2i2
χ3622-2-2-2-2220022-2-2-2-200222-200−2i−2i2i2i000002i−2i00000000000000−2−22222−2−20000000000−i2i2i2−i2
χ372-222-2-22-22i−2i00002i−2i2i−2i2i−2i002-2000000000002-22i−2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ382-222-2-22-22i−2i00002i−2i2i−2i2i−2i002-2000000000002-22i−2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ392-222-2-22-22i−2i00002i−2i2i−2i2i−2i002-200000000000-22−2i2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ402-222-2-22-22i−2i00002i−2i2i−2i2i−2i002-200000000000-22−2i2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ412-222-2-22-2−2i2i0000−2i2i−2i2i−2i2i002-2000000000002-2−2i2i001−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ422-222-2-22-2−2i2i0000−2i2i−2i2i−2i2i002-2000000000002-2−2i2i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ432-222-2-22-2−2i2i0000−2i2i−2i2i−2i2i002-200000000000-222i−2i001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ442-222-2-22-2−2i2i0000−2i2i−2i2i−2i2i002-200000000000-222i−2i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ452-22-22-2-222i−2i2-22-200−2i2i0000002-22-22i−2i2i−2i0000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000001+i−1−i1−i−1+i0000
χ462-22-22-2-222i−2i2-22-200−2i2i0000002-22-22i−2i2i−2i000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000−1−i1+i−1+i1−i0000
χ472-22-22-2-222i−2i2-22-200−2i2i000000-22-222i−2i−2i2i0000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000−1−i1+i−1+i1−i0000
χ482-22-22-2-222i−2i2-22-200−2i2i000000-22-222i−2i−2i2i000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000001+i−1−i1−i−1+i0000
χ492-22-22-2-22−2i2i2-22-2002i−2i0000002-22-2−2i2i−2i2i0000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000001−i−1+i1+i−1−i0000
χ502-22-22-2-22−2i2i2-22-2002i−2i0000002-22-2−2i2i−2i2i000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000−1+i1−i−1−i1+i0000
χ512-22-22-2-22−2i2i2-22-2002i−2i000000-22-22−2i2i2i−2i0000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000−1+i1−i−1−i1+i0000
χ522-22-22-2-22−2i2i2-22-2002i−2i000000-22-22−2i2i2i−2i000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000001−i−1+i1+i−1−i0000
χ53444-4-44-4-444000000-4-4000000000000000000000002-2-222-2-220000000000000000000000
χ54444-4-44-4-444000000-4-400000000000000000000000-222-2-222-20000000000000000000000
χ55444-4-44-4-4-4-400000044000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ56444-4-44-4-4-4-40000004400000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ5744-4-4-4-44400-4-4444400-4-44-40000000000000000000000000000000000000000000000000
χ5844-4-4-4-44400-4-444-4-40044-440000000000000000000000000000000000000000000000000
χ594-444-4-44-44i−4i0000−4i4i4i−4i−4i4i00-4400000000000000000000000000000000000000000000000
χ604-444-4-44-4−4i4i00004i−4i−4i4i4i−4i00-4400000000000000000000000000000000000000000000000
χ614-44-44-4-444i−4i-44-4400−4i4i0000000000−4i4i00000000000000000000000000000000000000000
χ624-44-44-4-44−4i4i-44-44004i−4i00000000004i−4i00000000000000000000000000000000000000000
χ634-4-44-44-44004-4-4400000000004i−4i−4i4i0000000000000000000000000000000000000000000
χ644-4-44-44-44004-4-440000000000−4i4i4i−4i0000000000000000000000000000000000000000000
χ654-4-44-44-4400-444-400000000000000000000000004i−4i000000000000000000000000000000
χ664-4-44-44-4400-444-40000000000000000000000000−4i4i000000000000000000000000000000
χ674-4-4-4444-40000004i−4i00−4i4i000000000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000
χ684-4-4-4444-40000004i−4i00−4i4i00000000000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000
χ694-4-4-4444-4000000−4i4i004i−4i000000000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000
χ704-4-4-4444-4000000−4i4i004i−4i00000000000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000
χ7188-888-8-8-8000000000000000000000000000000000000000000000000000000000000000

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