Finite Group Databasebeta

← Group #1585

Character table — Group #1585

Order 128.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38
size11111111222222224444444444444444448888
order12224444444488882244888888888888884488
χ111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1
χ41111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ91111-1-1-1-111-1-1ii−i−i11-1-1i−iii−i−i11-1-1ii−i−i1-1i−i
χ101111-1-1-1-111-1-1ii−i−i11-1-1i−iii−i−i-1-111−i−iii-11−ii
χ111111-1-1-1-111-1-1ii−i−i-1-111i−i−i−iii11-1-1ii−i−i-11−ii
χ121111-1-1-1-111-1-1ii−i−i-1-111i−i−i−iii-1-111−i−iii1-1i−i
χ131111-1-1-1-111-1-1−i−iii11-1-1−ii−i−iii11-1-1−i−iii1-1−ii
χ141111-1-1-1-111-1-1−i−iii11-1-1−ii−i−iii-1-111ii−i−i-11i−i
χ151111-1-1-1-111-1-1−i−iii-1-111−iiii−i−i11-1-1−i−iii-11i−i
χ161111-1-1-1-111-1-1−i−iii-1-111−iiii−i−i-1-111ii−i−i1-1−ii
χ1722222222-2-2-2-222220000-2-20000000000000000
χ1822222222-2-2-2-2-2-2-2-20000220000000000000000
χ192222-2-2-2-2-2-2222i2i−2i−2i0000−2i2i0000000000000000
χ202222-2-2-2-2-2-222−2i−2i2i2i00002i−2i0000000000000000
χ2122-2-22i−2i2i−2i00002ζ−2ζ2ζ3−2ζ30000000000i2−i22−21−i−1+i1+i−1−i0000
χ2222-2-22i−2i2i−2i00002ζ−2ζ2ζ3−2ζ30000000000−i2i2−22−1+i1−i−1−i1+i0000
χ2322-2-22i−2i2i−2i0000−2ζ2ζ−2ζ32ζ30000000000i2−i22−2−1+i1−i−1−i1+i0000
χ2422-2-22i−2i2i−2i0000−2ζ2ζ−2ζ32ζ30000000000−i2i2−221−i−1+i1+i−1−i0000
χ2522-2-2−2i2i−2i2i00002ζ3−2ζ32ζ−2ζ0000000000i2−i2−221+i−1−i1−i−1+i0000
χ2622-2-2−2i2i−2i2i00002ζ3−2ζ32ζ−2ζ0000000000−i2i22−2−1−i1+i−1+i1−i0000
χ2722-2-2−2i2i−2i2i0000−2ζ32ζ3−2ζ2ζ0000000000i2−i2−22−1−i1+i−1+i1−i0000
χ2822-2-2−2i2i−2i2i0000−2ζ32ζ3−2ζ2ζ0000000000−i2i22−21+i−1−i1−i−1+i0000
χ292-22-22i−2i−2i2i2-22i−2i00000000002ζ3−2ζ32ζ−2ζ000000000000
χ302-22-22i−2i−2i2i2-22i−2i0000000000−2ζ32ζ3−2ζ2ζ000000000000
χ312-22-22i−2i−2i2i-22−2i2i00002-22i−2i000000000000000000
χ322-22-22i−2i−2i2i-22−2i2i0000-22−2i2i000000000000000000
χ332-22-2−2i2i2i−2i2-2−2i2i00000000002ζ−2ζ2ζ3−2ζ3000000000000
χ342-22-2−2i2i2i−2i2-2−2i2i0000000000−2ζ2ζ−2ζ32ζ3000000000000
χ352-22-2−2i2i2i−2i-222i−2i00002-2−2i2i000000000000000000
χ362-22-2−2i2i2i−2i-222i−2i0000-222i−2i000000000000000000
χ374-4-4444-4-4000000000000000000000000000000
χ384-4-44-4-444000000000000000000000000000000

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