Finite Group Databasebeta

← Group #1485

Character table — Group #1485

Order 128.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38
size11111111222222224444444444444444448888
order12224444444444442488888888888888884444
χ111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ71111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111
χ81111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ91111-1-1-1-11111-1-1-1-11-1ii−i−iii−i−iii−i−iii−i−i1-11-1
χ101111-1-1-1-11111-1-1-1-11-1ii−i−iii−i−i−i−iii−i−iii-11-11
χ111111-1-1-1-11111-1-1-1-11-1−i−iii−i−iiiii−i−iii−i−i-11-11
χ121111-1-1-1-11111-1-1-1-11-1−i−iii−i−iii−i−iii−i−iii1-11-1
χ131111-1-1-1-111-1-111-1-1-11ii−i−i−i−iiiii−i−i−i−iii1-1-11
χ141111-1-1-1-111-1-111-1-1-11ii−i−i−i−iii−i−iiiii−i−i-111-1
χ151111-1-1-1-111-1-111-1-1-11−i−iiiii−i−iii−i−i−i−iii-111-1
χ161111-1-1-1-111-1-111-1-1-11−i−iiiii−i−i−i−iiiii−i−i1-1-11
χ1722222222-2-22222-2-2-2-200000000000000000000
χ1822222222-2-2-2-2-2-2-2-22200000000000000000000
χ192222-2-2-2-2-2-222-2-222-2200000000000000000000
χ202222-2-2-2-2-2-2-2-222222-200000000000000000000
χ212-22-22i2i−2i−2i002i−2i2-20000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000
χ222-22-22i2i−2i−2i002i−2i2-2000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000
χ232-22-22i2i−2i−2i00−2i2i-220000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i0000
χ242-22-22i2i−2i−2i00−2i2i-22000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i0000
χ252-22-2−2i−2i2i2i002i−2i-220000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i0000
χ262-22-2−2i−2i2i2i002i−2i-22000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i0000
χ272-22-2−2i−2i2i2i00−2i2i2-20000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000
χ282-22-2−2i−2i2i2i00−2i2i2-2000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000
χ292-2-222i−2i2i−2i2-200002i−2i0000002ζ−2ζ2ζ3−2ζ3000000000000
χ302-2-222i−2i2i−2i2-200002i−2i000000−2ζ2ζ−2ζ32ζ3000000000000
χ312-2-222i−2i2i−2i-220000−2i2i002ζ−2ζ2ζ3−2ζ30000000000000000
χ322-2-222i−2i2i−2i-220000−2i2i00−2ζ2ζ−2ζ32ζ30000000000000000
χ332-2-22−2i2i−2i2i2-20000−2i2i0000002ζ3−2ζ32ζ−2ζ000000000000
χ342-2-22−2i2i−2i2i2-20000−2i2i000000−2ζ32ζ3−2ζ2ζ000000000000
χ352-2-22−2i2i−2i2i-2200002i−2i002ζ3−2ζ32ζ−2ζ0000000000000000
χ362-2-22−2i2i−2i2i-2200002i−2i00−2ζ32ζ3−2ζ2ζ0000000000000000
χ3744-4-44-4-44000000000000000000000000000000
χ3844-4-4-444-4000000000000000000000000000000

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