Finite Group Databasebeta

← Group #1482

Character table — Group #1482

Order 128.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38
size11111111222222224444444444444444448888
order12224444444444442488888888888888882444
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
χ2122-2-222-2-2002i−2i2i−2i0000000000002−22−2i2−i2i2−i20000
χ2222-2-222-2-2002i−2i2i−2i000000000000−22−22−i2i2−i2i20000
χ2322-2-222-2-200−2i2i−2i2i0000000000002−22−2−i2i2−i2i20000
χ2422-2-222-2-200−2i2i−2i2i000000000000−22−22i2−i2i2−i20000
χ2522-2-2-2-222002i−2i−2i2i000000000000i2−i2−i2i2−222−20000
χ2622-2-2-2-222002i−2i−2i2i000000000000−i2i2i2−i22−2−220000
χ2722-2-2-2-22200−2i2i2i−2i000000000000i2−i2−i2i22−2−220000
χ2822-2-2-2-22200−2i2i2i−2i000000000000−i2i2i2−i2−222−20000
χ292-22-22i−2i2i−2i2-200002i−2i0000002ζ−2ζ2ζ3−2ζ3000000000000
χ302-22-22i−2i2i−2i2-200002i−2i000000−2ζ2ζ−2ζ32ζ3000000000000
χ312-22-22i−2i2i−2i-220000−2i2i002ζ−2ζ2ζ3−2ζ30000000000000000
χ322-22-22i−2i2i−2i-220000−2i2i00−2ζ2ζ−2ζ32ζ30000000000000000
χ332-22-2−2i2i−2i2i2-20000−2i2i0000002ζ3−2ζ32ζ−2ζ000000000000
χ342-22-2−2i2i−2i2i2-20000−2i2i000000−2ζ32ζ3−2ζ2ζ000000000000
χ352-22-2−2i2i−2i2i-2200002i−2i002ζ3−2ζ32ζ−2ζ0000000000000000
χ362-22-2−2i2i−2i2i-2200002i−2i00−2ζ32ζ3−2ζ2ζ0000000000000000
χ374-4-444i−4i−4i4i000000000000000000000000000000
χ384-4-44−4i4i4i−4i000000000000000000000000000000

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