Finite Group Databasebeta

← Group #8308

Character table — Group #8308

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size1111111122222222222244444444888888888888888888888888
order1222222222224444444422224444444444448888888888888888
χ11111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111ii−i−iii−i−iii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111−i−iii−i−iii−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1ii−i−iii−i−i−i−iii−i−iii
χ12111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1−i−iii−i−iiiii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iiiii−i−iii−i−i−i−iii
χ1722222222-2-2-2-22222-2-2-2-222-2-222-2-2000000000000000000000000
χ1822222222-2-2-2-22222-2-2-2-2-2-222-2-222000000000000000000000000
χ1922222222-2-2-2-2-2-2-2-2222222-2-2-2-222000000000000000000000000
χ2022222222-2-2-2-2-2-2-2-22222-2-22222-2-2000000000000000000000000
χ21222-2-2-22-222-2-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ22222-2-2-22-222-2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ23222-2-2-22-222-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ24222-2-2-22-222-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ25222-2-2-22-2-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ26222-2-2-22-2-2-2222i2i−2i−2i−2i−2i2i2i000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ27222-2-2-22-2-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ28222-2-2-22-2-2-222−2i−2i2i2i2i2i−2i−2i000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ292-2-222-22-22-22-22i−2i2i−2i2i−2i2i−2i000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ302-2-222-22-22-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ312-2-222-22-22-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ322-2-222-22-22-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ332-2-222-22-2-22-222i−2i2i−2i−2i2i−2i2i00000000000000002ζ−2ζ2ζ3−2ζ3000000000000
χ342-2-222-22-2-22-222i−2i2i−2i−2i2i−2i2i0000000000000000−2ζ2ζ−2ζ32ζ3000000000000
χ352-2-222-22-2-22-22−2i2i−2i2i2i−2i2i−2i00000000000000002ζ3−2ζ32ζ−2ζ000000000000
χ362-2-222-22-2-22-22−2i2i−2i2i2i−2i2i−2i0000000000000000−2ζ32ζ3−2ζ2ζ000000000000
χ372-2-2-2-22222-2-222-2-222-2-22000000002-2002-2000000000000000000
χ382-2-2-2-22222-2-222-2-222-2-2200000000-2200-22000000000000000000
χ392-2-2-2-22222-2-22-222-2-222-2000000002-200-22000000000000000000
χ402-2-2-2-22222-2-22-222-2-222-200000000-22002-2000000000000000000
χ412-2-2-2-2222-222-22-2-22-222-200000000002-2002-20000000000000000
χ422-2-2-2-2222-222-22-2-22-222-20000000000-2200-220000000000000000
χ432-2-2-2-2222-222-2-222-22-2-2200000000002-200-220000000000000000
χ442-2-2-2-2222-222-2-222-22-2-220000000000-22002-20000000000000000
χ4544-44-44-4-4000000000000004-40000000000000000000000000000
χ4644-44-44-4-400000000000000-440000000000000000000000000000
χ4744-4-44-4-4400000000000000004-400000000000000000000000000
χ4844-4-44-4-440000000000000000-4400000000000000000000000000
χ494-444-4-4-440000000000000000004-4000000000000000000000000
χ504-444-4-4-44000000000000000000-44000000000000000000000000
χ514-44-444-4-40000000000004-4000000000000000000000000000000
χ524-44-444-4-4000000000000-44000000000000000000000000000000

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