Finite Group Databasebeta

← Group #1945

Character table — Group #1945

Order 128.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size11111111222222222222222222222222222288888888
order12224444224444444444888888888888888844448888
χ111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ511111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ611111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ711111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ811111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ91111-1-1-1-1-1-11iiii−i−i−i−i1iiii−i−i−i−i1111-1-1-1-11-11-1i−ii−i
χ101111-1-1-1-1-1-11iiii−i−i−i−i1iiii−i−i−i−i1111-1-1-1-1-11-11−ii−ii
χ111111-1-1-1-1-1-11iiii−i−i−i−i1−i−i−i−iiiii-1-1-1-111111-1-11i−i−ii
χ121111-1-1-1-1-1-11iiii−i−i−i−i1−i−i−i−iiiii-1-1-1-11111-111-1−iii−i
χ131111-1-1-1-1-1-11−i−i−i−iiiii1iiii−i−i−i−i-1-1-1-111111-1-11−iii−i
χ141111-1-1-1-1-1-11−i−i−i−iiiii1iiii−i−i−i−i-1-1-1-11111-111-1i−i−ii
χ151111-1-1-1-1-1-11−i−i−i−iiiii1−i−i−i−iiiii1111-1-1-1-11-11-1−ii−ii
χ161111-1-1-1-1-1-11−i−i−i−iiiii1−i−i−i−iiiii1111-1-1-1-1-11-11i−ii−i
χ1722222222-2-2-200000000-222-2-222-2-20000000000000000
χ1822222222-2-2-200000000-2-2-222-2-2220000000000000000
χ192222-2-2-2-222-200000000-22i2i−2i−2i−2i−2i2i2i0000000000000000
χ202222-2-2-2-222-200000000-2−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2122-2-222-2-22-2-20000000020000000022-2-222-2-200000000
χ2222-2-222-2-22-2-200000000200000000-2-222-2-22200000000
χ2322-2-222-2-2-22222-2-222-2-2-2000000000000000000000000
χ2422-2-222-2-2-222-2-222-2-222-2000000000000000000000000
χ2522-2-2-2-2222-222i2i−2i−2i−2i−2i2i2i-2000000000000000000000000
χ2622-2-2-2-2222-22−2i−2i2i2i2i2i−2i−2i-2000000000000000000000000
χ2722-2-2-2-222-22-20000000020000000022-2-2-2-22200000000
χ2822-2-2-2-222-22-200000000200000000-2-22222-2-200000000
χ292-22-22i−2i2i−2i0001+i−1−i1+i−1−i1−i−1+i1−i−1+i0002ζ3−2ζ3002ζ−2ζi2−i2i2−i22−22−200000000
χ302-22-22i−2i2i−2i0001+i−1−i1+i−1−i1−i−1+i1−i−1+i000−2ζ32ζ300−2ζ2ζ−i2i2−i2i2−22−2200000000
χ312-22-22i−2i2i−2i000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0002ζ3−2ζ3002ζ−2ζ−i2i2−i2i2−22−2200000000
χ322-22-22i−2i2i−2i000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000−2ζ32ζ300−2ζ2ζi2−i2i2−i22−22−200000000
χ332-22-2−2i2i−2i2i0001−i−1+i1−i−1+i1+i−1−i1+i−1−i0002ζ−2ζ002ζ3−2ζ3i2−i2i2−i2−22−2200000000
χ342-22-2−2i2i−2i2i0001−i−1+i1−i−1+i1+i−1−i1+i−1−i000−2ζ2ζ00−2ζ32ζ3−i2i2−i2i22−22−200000000
χ352-22-2−2i2i−2i2i000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0002ζ−2ζ002ζ3−2ζ3−i2i2−i2i22−22−200000000
χ362-22-2−2i2i−2i2i000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000−2ζ2ζ00−2ζ32ζ3i2−i2i2−i2−22−2200000000
χ372-2-222i−2i−2i2i0001+i−1−i−1−i1+i1−i−1+i−1+i1−i02ζ3−2ζ3002ζ−2ζ00i2−i2−i2i22−2−2200000000
χ382-2-222i−2i−2i2i0001+i−1−i−1−i1+i1−i−1+i−1+i1−i0−2ζ32ζ300−2ζ2ζ00−i2i2i2−i2−222−200000000
χ392-2-222i−2i−2i2i000−1−i1+i1+i−1−i−1+i1−i1−i−1+i02ζ3−2ζ3002ζ−2ζ00−i2i2i2−i2−222−200000000
χ402-2-222i−2i−2i2i000−1−i1+i1+i−1−i−1+i1−i1−i−1+i0−2ζ32ζ300−2ζ2ζ00i2−i2−i2i22−2−2200000000
χ412-2-22−2i2i2i−2i0001−i−1+i−1+i1−i1+i−1−i−1−i1+i02ζ−2ζ002ζ3−2ζ300i2−i2−i2i2−222−200000000
χ422-2-22−2i2i2i−2i0001−i−1+i−1+i1−i1+i−1−i−1−i1+i0−2ζ2ζ00−2ζ32ζ300−i2i2i2−i22−2−2200000000
χ432-2-22−2i2i2i−2i000−1+i1−i1−i−1+i−1−i1+i1+i−1−i02ζ−2ζ002ζ3−2ζ300−i2i2i2−i22−2−2200000000
χ442-2-22−2i2i2i−2i000−1+i1−i1−i−1+i−1−i1+i1+i−1−i0−2ζ2ζ00−2ζ32ζ300i2−i2−i2i2−222−200000000

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