Finite Group Databasebeta

← Group #97992

Character table — Group #97992

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444444444444488888888888888882244444488888888
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
χ311111111111111111111111111111-1-1-1-11111111111111111-1-11-1-11-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111111111
χ5111111111111111111111111-1-11-1-1111111111111-1-1-1-1-1-1-1-11-1-1-1-1-11-11111-1-1-1-1
χ6111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1-11-1-1-1-1-11111
χ7111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-111-1-11-1-1-1-11111
χ8111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-111-1-111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i-1-11-11-111−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii-1-11-11-111ii−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−iiiii1-1-1-111-11ii−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−i1-1-1-111-11−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-111iiii−i−i−i−i−i−i−i−iiiii-11-11-111-1−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-111−i−i−i−iiiiiiiii−i−i−i−i-11-11-111-1ii−i−i−i−iii
χ17222222222222222222-2-2-2-2-2-200-20022220000000000000000-200000-2000000000
χ18222222222222222222-2-2-2-2-2-200-200-2-2-2-200000000000000002000002000000000
χ192222222222-2-222-2-2-2-222-2-22222-2-2-20000000000000000000000-20020000000000
χ202222222222-2-222-2-2-2-222-2-222-2-2-2220000000000000000000000200-20000000000
χ212222222222-2-222-2-2-2-2-2-222-2-20020000000000000000000000020-2-200200000000
χ222222222222-2-222-2-2-2-2-2-222-2-200200000000000000000000000-202200-200000000
χ2322222222-2-222-2-222-2-22222-2-222-2220000000000000000000000-200-20000000000
χ2422222222-2-222-2-222-2-22222-2-2-2-2-2-2-2000000000000000000000020020000000000
χ2522222222-2-222-2-222-2-2-2-2-2-2220020000000000000000000000020-2200-200000000
χ2622222222-2-222-2-222-2-2-2-2-2-22200200000000000000000000000-202-200200000000
χ2722222222-2-2-2-2-2-2-2-222-2-2222200-20022-2-20000000000000000-2000002000000000
χ2822222222-2-2-2-2-2-2-2-222-2-2222200-200-2-2220000000000000000200000-2000000000
χ29222-2-22-2-2002i−2i002i−2i002-22i−2i002-202i−2i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000
χ30222-2-22-2-2002i−2i002i−2i002-22i−2i002-202i−2i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000
χ31222-2-22-2-2002i−2i002i−2i002-22i−2i00-220−2i2i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000
χ32222-2-22-2-2002i−2i002i−2i002-22i−2i00-220−2i2i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000
χ33222-2-22-2-200−2i2i00−2i2i002-2−2i2i002-20−2i2i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000
χ34222-2-22-2-200−2i2i00−2i2i002-2−2i2i002-20−2i2i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000
χ35222-2-22-2-200−2i2i00−2i2i002-2−2i2i00-2202i−2i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000
χ36222-2-22-2-200−2i2i00−2i2i002-2−2i2i00-2202i−2i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000
χ3722-22-2-22-222-2-2-2-2222-2000000000002i−2i2i−2i000000002−22−22−22−2000000000000i2−i2i2−i2
χ3822-22-2-22-222-2-2-2-2222-2000000000002i−2i2i−2i00000000−22−22−22−22000000000000−i2i2−i2i2
χ3922-22-2-22-222-2-2-2-2222-200000000000−2i2i−2i2i000000002−22−22−22−2000000000000−i2i2−i2i2
χ4022-22-2-22-222-2-2-2-2222-200000000000−2i2i−2i2i00000000−22−22−22−22000000000000i2−i2i2−i2
χ4122-22-2-22-2-2-22222-2-22-2000000000002i−2i−2i2i00000000i2−i2i2−i2−i2i2−i2i2000000000000−222−2
χ4222-22-2-22-2-2-22222-2-22-2000000000002i−2i−2i2i00000000−i2i2−i2i2i2−i2i2−i20000000000002−2−22
χ4322-22-2-22-2-2-22222-2-22-200000000000−2i2i2i−2i00000000i2−i2i2−i2−i2i2−i2i20000000000002−2−22
χ4422-22-2-22-2-2-22222-2-22-200000000000−2i2i2i−2i00000000−i2i2−i2i2i2−i2i2−i2000000000000−222−2
χ45444-4-44-4-4004i−4i004i−4i00-44−4i4i0000000000000000000000000000000000000000000
χ46444-4-44-4-400−4i4i00−4i4i00-444i−4i0000000000000000000000000000000000000000000
χ4744-44-4-44-44444-4-4-4-4-4400000000000000000000000000000000000000000000000
χ4844-44-4-44-4-4-4-4-44444-4400000000000000000000000000000000000000000000000
χ4944-4-44-4-44004i−4i00−4i4i00000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000000000
χ5044-4-44-4-44004i−4i00−4i4i0000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000000000000000
χ5144-4-44-4-4400−4i4i004i−4i00000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000000000000000
χ5244-4-44-4-4400−4i4i004i−4i0000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000
χ534-444-4-4-444i−4i004i−4i00000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ544-444-4-4-444i−4i004i−4i0000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000
χ554-444-4-4-44−4i4i00−4i4i00000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000
χ564-444-4-4-44−4i4i00−4i4i0000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000
χ574-44-44-44-4000000000000004i−4i0000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000
χ584-44-44-44-4000000000000004i−4i000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000
χ594-44-44-44-400000000000000−4i4i0000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000000000000000000
χ604-44-44-44-400000000000000−4i4i000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000
χ614-4-4444-4-44i−4i00−4i4i00000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ624-4-4444-4-44i−4i00−4i4i0000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ634-4-4444-4-4−4i4i004i−4i00000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ644-4-4444-4-4−4i4i004i−4i0000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ658-8-8-8-8888000000000000000000000000000000000000000000000000000000000

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