Finite Group Databasebeta

← Group #1985

Character table — Group #1985

Order 128.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size11111111111111114444444444444444444444444444
order12222222444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222-2-22-2-22222-2-2-2-200000000000000002-22-200000000
χ18222-2-22-2-22222-2-2-2-20000000000000000-22-2200000000
χ19222-2-22-2-2-2-2-2-2222200000000000000002i−2i−2i2i00000000
χ20222-2-22-2-2-2-2-2-222220000000000000000−2i2i2i−2i00000000
χ2122-22-2-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000002ζ3−2ζ32ζ−2ζ
χ2222-22-2-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ2322-22-2-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ2422-22-2-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ2522-2-22-2-222i−2i2i−2i−2i2i−2i2i00002i−2i2-200000000000000000000
χ2622-2-22-2-222i−2i2i−2i−2i2i−2i2i0000−2i2i-2200000000000000000000
χ2722-2-22-2-22−2i2i−2i2i2i−2i2i−2i00002i−2i-2200000000000000000000
χ2822-2-22-2-22−2i2i−2i2i2i−2i2i−2i0000−2i2i2-200000000000000000000
χ292-222-2-2-222i−2i−2i2i2i−2i−2i2i000000002-22i−2i0000000000000000
χ302-222-2-2-222i−2i−2i2i2i−2i−2i2i00000000-22−2i2i0000000000000000
χ312-222-2-2-22−2i2i2i−2i−2i2i2i−2i000000002-2−2i2i0000000000000000
χ322-222-2-2-22−2i2i2i−2i−2i2i2i−2i00000000-222i−2i0000000000000000
χ332-22-22-22-22i−2i−2i2i−2i2i2i−2i000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ342-22-22-22-22i−2i−2i2i−2i2i2i−2i00000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ352-22-22-22-2−2i2i2i−2i2i−2i−2i2i000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ362-22-22-22-2−2i2i2i−2i2i−2i−2i2i00000000000000000000−2ζ2ζ−2ζ32ζ30000
χ372-2-2222-2-222-2-222-2-20000000000002-22-2000000000000
χ382-2-2222-2-222-2-222-2-2000000000000-22-22000000000000
χ392-2-2222-2-2-2-222-2-2220000000000002i−2i−2i2i000000000000
χ402-2-2222-2-2-2-222-2-222000000000000−2i2i2i−2i000000000000
χ412-2-2-2-222222-2-2-2-2222-22-2000000000000000000000000
χ422-2-2-2-222222-2-2-2-222-22-22000000000000000000000000
χ432-2-2-2-2222-2-22222-2-22-2-22000000000000000000000000
χ442-2-2-2-2222-2-22222-2-2-222-2000000000000000000000000

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