Finite Group Databasebeta

← Group #1493

Character table — Group #1493

Order 128.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size11111111222222222222222222222222222288888888
order12224444224444444444888888888888888844448888
χ111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ611111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ711111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ811111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ91111-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−i
χ101111-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11−ii−ii
χ111111-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii
χ121111-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−i
χ131111-1-1-1-1-1-11111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii1-1-11i−i−ii
χ141111-1-1-1-1-1-11111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii-111-1−iii−i
χ151111-1-1-1-1-1-11111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1-11−iii−i
χ161111-1-1-1-1-1-11111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i-111-1i−i−ii
χ17222222222222-2-2-2-2-2-2-2-2000000000000000000000000
χ1822222222-2-2-2-2-2-22222-2-2000000000000000000000000
χ192222-2-2-2-222-2-2-2-2-2-22222000000000000000000000000
χ202222-2-2-2-2-2-222-2-222-2-222000000000000000000000000
χ2122-2-222-2-22-22-20000000022−2−222−2−222−2−222−2−200000000
χ2222-2-222-2-22-22-200000000−2−222−2−222−2−222−2−22200000000
χ2322-2-222-2-2-22-220000000022−2−222−2−2−2−222−2−22200000000
χ2422-2-222-2-2-22-2200000000−2−222−2−22222−2−222−2−200000000
χ2522-2-2-2-2222-2-2200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000
χ2622-2-2-2-2222-2-2200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000
χ2722-2-2-2-222-222-200000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000
χ2822-2-2-2-222-222-200000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000
χ292-22-22i−2i2i−2i0000002i−2i2-2001+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ302-22-22i−2i2i−2i0000002i−2i2-200−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ312-22-22i−2i2i−2i000000−2i2i-22001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ322-22-22i−2i2i−2i000000−2i2i-2200−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ332-22-2−2i2i−2i2i0000002i−2i-22001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ342-22-2−2i2i−2i2i0000002i−2i-2200−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ352-22-2−2i2i−2i2i000000−2i2i2-2001−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ362-22-2−2i2i−2i2i000000−2i2i2-200−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ372-2-222i−2i−2i2i00002-200002i−2i000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ00000000
χ382-2-222i−2i−2i2i00002-200002i−2i00000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ00000000
χ392-2-222i−2i−2i2i0000-220000−2i2i2ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000000000000000
χ402-2-222i−2i−2i2i0000-220000−2i2i−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000
χ412-2-22−2i2i2i−2i00002-20000−2i2i000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ300000000
χ422-2-22−2i2i2i−2i00002-20000−2i2i00000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ300000000
χ432-2-22−2i2i2i−2i0000-2200002i−2i2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000000000
χ442-2-22−2i2i2i−2i0000-2200002i−2i−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000000000000000

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