Finite Group Databasebeta

← Group #97990

Character table — Group #97990

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444422224444488888888888888882444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1111-1-11111111111111111-1-1-11-1-11-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-111111111
χ5111111111111111111111111-1-1111-1-11111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-111111111-111-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-111-11-1-1-1-11111
χ8111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-111-111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-11-11-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-11-11-1−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11-1-111iiii−i−i−i−iiiii−i−i−i−i-1-11-1-1111−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11-1-111−i−i−i−iiiii−i−i−i−iiiii-1-11-1-1111ii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111-1-1iiii−i−i−i−i−i−i−i−iiiii-11-11-11-11ii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111-1-1−i−i−i−iiiiiiiii−i−i−i−i-11-11-11-11−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111iiii−i−i−i−i−i−i−i−iiiii1-1111-1-1-1−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111−i−i−i−iiiiiiiii−i−i−i−i1-1111-1-1-1ii−i−i−i−iii
χ172222222222222222-2-222-2-2-2-20022-2002200000000000000000-2-20000000000000
χ182222222222222222-2-222-2-2-2-200-2-2-200-2-200000000000000000220000000000000
χ192222222222-2-222-2-222-2-2-2-2222200-2-2-2000000000000000000000200-2000000000
χ202222222222-2-222-2-222-2-2-2-222-2-200-222000000000000000000000-2002000000000
χ212222222222-2-222-2-2-2-2-2-222-2-200002000000000000000000002000-2-20200000000
χ222222222222-2-222-2-2-2-2-2-222-2-20000200000000000000000000-2000220-200000000
χ2322222222-2-222-2-22222-2-222-2-22200-222000000000000000000000-200-2000000000
χ2422222222-2-222-2-22222-2-222-2-2-2-200-2-2-20000000000000000000002002000000000
χ2522222222-2-222-2-222-2-2-2-2-2-22200002000000000000000000002000-220-200000000
χ2622222222-2-222-2-222-2-2-2-2-2-2220000200000000000000000000-20002-20200000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222220022-200-2-200000000000000000-220000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222222200-2-2-20022000000000000000002-20000000000000
χ2922-22-22-2-2002i−2i002i−2i2-2002i−2i002-20002i−2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000
χ3022-22-22-2-2002i−2i002i−2i2-2002i−2i002-20002i−2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000
χ3122-22-22-2-2002i−2i002i−2i2-2002i−2i00-22000−2i2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000
χ3222-22-22-2-2002i−2i002i−2i2-2002i−2i00-22000−2i2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000
χ3322-22-22-2-200−2i2i00−2i2i2-200−2i2i002-2000−2i2i001−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000
χ3422-22-22-2-200−2i2i00−2i2i2-200−2i2i002-2000−2i2i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000
χ3522-22-22-2-200−2i2i00−2i2i2-200−2i2i00-220002i−2i001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000
χ3622-22-22-2-200−2i2i00−2i2i2-200−2i2i00-220002i−2i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000
χ372-2-2-2-22222222-2-2-2-2002-20000002-20002-200000000i2−i2i2−i2i2−i2i2−i2000000000000i2−i2i2−i2
χ382-2-2-2-22222222-2-2-2-2002-20000002-20002-200000000−i2i2−i2i2−i2i2−i2i2000000000000−i2i2−i2i2
χ392-2-2-2-22222222-2-2-2-2002-2000000-22000-2200000000i2−i2i2−i2i2−i2i2−i2000000000000−i2i2−i2i2
χ402-2-2-2-22222222-2-2-2-2002-2000000-22000-2200000000−i2i2−i2i2−i2i2−i2i2000000000000i2−i2i2−i2
χ412-2-2-2-2222-2-2-2-22222002-20000002-2000-22000000002−22−2−22−220000000000002−2−22
χ422-2-2-2-2222-2-2-2-22222002-20000002-2000-2200000000−22−222−22−2000000000000−222−2
χ432-2-2-2-2222-2-2-2-22222002-2000000-220002-2000000002−22−2−22−22000000000000−222−2
χ442-2-2-2-2222-2-2-2-22222002-2000000-220002-200000000−22−222−22−20000000000002−2−22
χ45444-4-4-4-44000000000000004i−4i0000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ46444-4-4-4-44000000000000004i−4i000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000
χ47444-4-4-4-4400000000000000−4i4i0000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000
χ48444-4-4-4-4400000000000000−4i4i000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000
χ4944-44-44-4-4004i−4i004i−4i-4400−4i4i0000000000000000000000000000000000000000000
χ5044-44-44-4-400−4i4i00−4i4i-44004i−4i0000000000000000000000000000000000000000000
χ5144-4-44-44-44i−4i004i−4i00000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000
χ5244-4-44-44-44i−4i004i−4i0000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000
χ5344-4-44-44-4−4i4i00−4i4i00000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000000000000000000
χ5444-4-44-44-4−4i4i00−4i4i0000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000
χ554-444-4-44-44i−4i00−4i4i00000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ564-444-4-44-44i−4i00−4i4i0000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ574-444-4-44-4−4i4i004i−4i00000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ584-444-4-44-4−4i4i004i−4i0000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ594-44-444-4-4004i−4i00−4i4i00000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ0000000000000000
χ604-44-444-4-4004i−4i00−4i4i0000000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ0000000000000000
χ614-44-444-4-400−4i4i004i−4i00000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000
χ624-44-444-4-400−4i4i004i−4i0000000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ30000000000000000
χ634-4-4-4-444444-4-4-4-44400-44000000000000000000000000000000000000000000000
χ644-4-4-4-4444-4-44444-4-400-44000000000000000000000000000000000000000000000
χ658-8-888-8-88000000000000000000000000000000000000000000000000000000000

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