Finite Group Databasebeta

← Group #12902

Character table — Group #12902

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size1111111122222222222244444444888888888888888888888888
order124488882224448888881616161616161616444444888888161616161616161616161616
χ11111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111
χ711111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1
χ91111-1-1-1-1111111-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1-1-111ii−i−iii−i−iii−i−i
χ101111-1-1-1-1111111-1-1-1-1-1-1iiii−i−i−i−i11-1-111-1-111-1-1ii−i−i−i−iii−i−iii
χ111111-1-1-1-1111111-1-1-1-1-1-1iiii−i−i−i−i-1-1111111-1-1-1-1−i−iiiii−i−i−i−iii
χ121111-1-1-1-1111111-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1-1-1111111−i−iii−i−iiiii−i−i
χ131111-1-1-1-1111111-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1-1-111−i−iii−i−iii−i−iii
χ141111-1-1-1-1111111-1-1-1-1-1-1−i−i−i−iiiii11-1-111-1-111-1-1−i−iiiii−i−iii−i−i
χ151111-1-1-1-1111111-1-1-1-1-1-1−i−i−i−iiiii-1-1111111-1-1-1-1ii−i−i−i−iiiii−i−i
χ161111-1-1-1-1111111-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-1-1-1111111ii−i−iii−i−i−i−iii
χ17222222222-2-22-2-222-2-2-2-20000000000002-200002-2000000000000
χ18222222222-2-22-2-222-2-2-2-2000000000000-220000-22000000000000
χ1922222222-22-2-22-2-2-222-2-200000000002-200002-200000000000000
χ2022222222-22-2-22-2-2-222-2-20000000000-220000-2200000000000000
χ2122222222-2-22-2-22-2-2-2-222000000002-200002-20000000000000000
χ2222222222-2-22-2-22-2-2-2-22200000000-220000-220000000000000000
χ232222-2-2-2-22-2-22-2-2-2-222220000000000002-20000-22000000000000
χ242222-2-2-2-22-2-22-2-2-2-22222000000000000-2200002-2000000000000
χ252222-2-2-2-2-22-2-22-222-2-22200000000002-20000-2200000000000000
χ262222-2-2-2-2-22-2-22-222-2-2220000000000-2200002-200000000000000
χ272222-2-2-2-2-2-22-2-222222-2-2000000002-20000-220000000000000000
χ282222-2-2-2-2-2-22-2-222222-2-200000000-2200002-20000000000000000
χ2922-2-22i2i−2i−2i222-2-2-22i−2i2i−2i2i−2i2ζ22ζ2−2ζ2−2ζ22ζ62ζ6−2ζ6−2ζ6000000000000000000000000
χ3022-2-22i2i−2i−2i222-2-2-22i−2i2i−2i2i−2i−2ζ2−2ζ22ζ22ζ2−2ζ6−2ζ62ζ62ζ6000000000000000000000000
χ3122-2-22i2i−2i−2i2-2-2-2222i−2i−2i2i−2i2i00000000000000000000000000002ζ6−2ζ62ζ2−2ζ2
χ3222-2-22i2i−2i−2i2-2-2-2222i−2i−2i2i−2i2i0000000000000000000000000000−2ζ62ζ6−2ζ22ζ2
χ3322-2-22i2i−2i−2i-22-22-22−2i2i2i−2i−2i2i0000000000000000000000002ζ2−2ζ22ζ6−2ζ60000
χ3422-2-22i2i−2i−2i-22-22-22−2i2i2i−2i−2i2i000000000000000000000000−2ζ22ζ2−2ζ62ζ60000
χ3522-2-22i2i−2i−2i-2-2222-2−2i2i−2i2i2i−2i000000000000000000002ζ2−2ζ22ζ6−2ζ600000000
χ3622-2-22i2i−2i−2i-2-2222-2−2i2i−2i2i2i−2i00000000000000000000−2ζ22ζ2−2ζ62ζ600000000
χ3722-2-2−2i−2i2i2i222-2-2-2−2i2i−2i2i−2i2i2ζ62ζ6−2ζ6−2ζ62ζ22ζ2−2ζ2−2ζ2000000000000000000000000
χ3822-2-2−2i−2i2i2i222-2-2-2−2i2i−2i2i−2i2i−2ζ6−2ζ62ζ62ζ6−2ζ2−2ζ22ζ22ζ2000000000000000000000000
χ3922-2-2−2i−2i2i2i2-2-2-222−2i2i2i−2i2i−2i00000000000000000000000000002ζ2−2ζ22ζ6−2ζ6
χ4022-2-2−2i−2i2i2i2-2-2-222−2i2i2i−2i2i−2i0000000000000000000000000000−2ζ22ζ2−2ζ62ζ6
χ4122-2-2−2i−2i2i2i-22-22-222i−2i−2i2i2i−2i0000000000000000000000002ζ6−2ζ62ζ2−2ζ20000
χ4222-2-2−2i−2i2i2i-22-22-222i−2i−2i2i2i−2i000000000000000000000000−2ζ62ζ6−2ζ22ζ20000
χ4322-2-2−2i−2i2i2i-2-2222-22i−2i2i−2i−2i2i000000000000000000002ζ6−2ζ62ζ2−2ζ200000000
χ4422-2-2−2i−2i2i2i-2-2222-22i−2i2i−2i−2i2i00000000000000000000−2ζ62ζ6−2ζ22ζ200000000
χ454-44i−4i4ζ2−4ζ24ζ6−4ζ60000000000002ζ−2ζ2ζ5−2ζ52ζ3−2ζ32ζ7−2ζ7000000000000000000000000
χ464-44i−4i4ζ2−4ζ24ζ6−4ζ6000000000000−2ζ2ζ−2ζ52ζ5−2ζ32ζ3−2ζ72ζ7000000000000000000000000
χ474-44i−4i−4ζ24ζ2−4ζ64ζ60000000000002ζ5−2ζ5−2ζ2ζ−2ζ72ζ72ζ3−2ζ3000000000000000000000000
χ484-44i−4i−4ζ24ζ2−4ζ64ζ6000000000000−2ζ52ζ52ζ−2ζ2ζ7−2ζ7−2ζ32ζ3000000000000000000000000
χ494-4−4i4i4ζ6−4ζ64ζ2−4ζ20000000000002ζ3−2ζ3−2ζ72ζ7−2ζ2ζ2ζ5−2ζ5000000000000000000000000
χ504-4−4i4i4ζ6−4ζ64ζ2−4ζ2000000000000−2ζ32ζ32ζ7−2ζ72ζ−2ζ−2ζ52ζ5000000000000000000000000
χ514-4−4i4i−4ζ64ζ6−4ζ24ζ20000000000002ζ7−2ζ72ζ3−2ζ32ζ5−2ζ52ζ−2ζ000000000000000000000000
χ524-4−4i4i−4ζ64ζ6−4ζ24ζ2000000000000−2ζ72ζ7−2ζ32ζ3−2ζ52ζ5−2ζ2ζ000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.