Finite Group Databasebeta

← Group #8430

Character table — Group #8430

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43
size111122222222444444488888888888888888888881616
order1222224444444444444222244444488888888888844
χ11111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ4111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111-1-1-1-11-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
χ611111111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ711111111111111-1-1-1-11-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ811111111111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ91111-1-111-1-1-1-11111-1-1-11-11-11-111-1-1ii−i−iii−i−iii−i−ii−i
χ101111-1-111-1-1-1-11111-1-1-11-11-11-111-1-1−i−iii−i−iii−i−iii−ii
χ111111-1-111-1-1-1-11111-1-1-11-1-11-11-1-111ii−i−i−i−iiiii−i−i−ii
χ121111-1-111-1-1-1-11111-1-1-11-1-11-11-1-111−i−iiiii−i−i−i−iiii−i
χ131111-1-111-1-1-1-111-1-111-1-111-11-1-1-111ii−i−i−i−iii−i−iiii−i
χ141111-1-111-1-1-1-111-1-111-1-111-11-1-1-111−i−iiiii−i−iii−i−i−ii
χ151111-1-111-1-1-1-111-1-111-1-11-11-1111-1-1ii−i−iii−i−i−i−iii−ii
χ161111-1-111-1-1-1-111-1-111-1-11-11-1111-1-1−i−iii−i−iiiii−i−ii−i
χ17222222222-2-22-2-22222-2-2-20000000000000000000000
χ18222222222-2-22-2-2-2-2-2-2-2220000000000000000000000
χ19222222-2-2-222-2-220000-2002-2-22000000000000000000
χ20222222-2-2-222-2-220000-200-222-2000000000000000000
χ21222222-2-2-2-2-2-22-2000020000002-22-200000000000000
χ22222222-2-2-2-2-2-22-200002000000-22-2200000000000000
χ232222-2-222-222-2-2-222-2-22-220000000000000000000000
χ242222-2-222-222-2-2-2-2-22222-20000000000000000000000
χ252222-2-2-2-222222-20000-20000002-2-2200000000000000
χ262222-2-2-2-222222-20000-2000000-222-200000000000000
χ272222-2-2-2-22-2-22-22000020022-2-2000000000000000000
χ282222-2-2-2-22-2-22-220000200-2-222000000000000000000
χ2922-2-22-22-2-2002002i−2i2i−2i00000000000i2−i2i2−i200002−22−200
χ3022-2-22-22-2-2002002i−2i2i−2i00000000000−i2i2−i2i20000−22−2200
χ3122-2-22-22-2-200200−2i2i−2i2i00000000000i2−i2i2−i20000−22−2200
χ3222-2-22-22-2-200200−2i2i−2i2i00000000000−i2i2−i2i200002−22−200
χ3322-2-2-222-2200-2002i−2i−2i2i000000000002−2−220000−i2i2i2−i200
χ3422-2-2-222-2200-2002i−2i−2i2i00000000000−222−20000i2−i2−i2i200
χ3522-2-2-222-2200-200−2i2i2i−2i000000000002−2−220000i2−i2−i2i200
χ3622-2-2-222-2200-200−2i2i2i−2i00000000000−222−20000−i2i2i2−i200
χ3744-4-44-4-44400-40000000000000000000000000000000
χ3844-4-4-44-44-40040000000000000000000000000000000
χ394-44-4000004i−4i00000000000000000000002ζ−2ζ2ζ3−2ζ3000000
χ404-44-4000004i−4i0000000000000000000000−2ζ2ζ−2ζ32ζ3000000
χ414-44-400000−4i4i00000000000000000000002ζ3−2ζ32ζ−2ζ000000
χ424-44-400000−4i4i0000000000000000000000−2ζ32ζ3−2ζ2ζ000000
χ438-8-88000000000000000000000000000000000000000

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