Finite Group Databasebeta

← Group #7699

Character table — Group #7699

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46
size11111111222222224444444444888888888888888816161616
order1222222244444444444444444488888888888888882244
χ11111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-11-1
χ6111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11-11
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-11
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1
χ911111111-1-1-1-1-1-1-1-1111111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i1-1-11
χ1011111111-1-1-1-1-1-1-1-1111111-1-1-1-1ii−i−iii−i−i−i−iii−i−iii-111-1
χ1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1−i−iii−i−iiiii−i−iii−i−i-111-1
χ1211111111-1-1-1-1-1-1-1-1111111-1-1-1-1−i−iii−i−iii−i−iii−i−iii1-1-11
χ1311111111-1-1-1-1-1-1-1-111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii11-1-1
χ1411111111-1-1-1-1-1-1-1-111-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i-1-111
χ1511111111-1-1-1-1-1-1-1-111-1-1-1-11111−i−iiiii−i−iii−i−i−i−iii-1-111
χ1611111111-1-1-1-1-1-1-1-111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i11-1-1
χ17222222222222-2-2-2-2-2-222-2-222-2-200000000000000000000
χ18222222222222-2-2-2-2-2-2-2-222-2-22200000000000000000000
χ1922222222-2-2-2-22222-2-222-2-2-2-22200000000000000000000
χ2022222222-2-2-2-22222-2-2-2-22222-2-200000000000000000000
χ212222-2-2-2-200002i2i−2i−2i00002i−2i2-2001+i−1−i1−i−1+i1−i−1+i1+i−1−i000000000000
χ222222-2-2-2-200002i2i−2i−2i00002i−2i2-200−1−i1+i−1+i1−i−1+i1−i−1−i1+i000000000000
χ232222-2-2-2-200002i2i−2i−2i0000−2i2i-22001+i−1−i1−i−1+i−1+i1−i−1−i1+i000000000000
χ242222-2-2-2-200002i2i−2i−2i0000−2i2i-2200−1−i1+i−1+i1−i1−i−1+i1+i−1−i000000000000
χ252222-2-2-2-20000−2i−2i2i2i00002i−2i-22001−i−1+i1+i−1−i−1−i1+i−1+i1−i000000000000
χ262222-2-2-2-20000−2i−2i2i2i00002i−2i-2200−1+i1−i−1−i1+i1+i−1−i1−i−1+i000000000000
χ272222-2-2-2-20000−2i−2i2i2i0000−2i2i2-2001−i−1+i1+i−1−i1+i−1−i1−i−1+i000000000000
χ282222-2-2-2-20000−2i−2i2i2i0000−2i2i2-200−1+i1−i−1−i1+i−1−i1+i−1+i1−i000000000000
χ2922-2-222-2-22i2i−2i−2i2i−2i2i−2i2-2000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ3022-2-222-2-22i2i−2i−2i2i−2i2i−2i2-200000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ3122-2-222-2-22i2i−2i−2i−2i2i−2i2i-2200000000000000002ζ−2ζ2ζ3−2ζ300000000
χ3222-2-222-2-22i2i−2i−2i−2i2i−2i2i-220000000000000000−2ζ2ζ−2ζ32ζ300000000
χ3322-2-222-2-2−2i−2i2i2i2i−2i2i−2i-2200000000000000002ζ3−2ζ32ζ−2ζ00000000
χ3422-2-222-2-2−2i−2i2i2i2i−2i2i−2i-220000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ3522-2-222-2-2−2i−2i2i2i−2i2i−2i2i2-2000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ3622-2-222-2-2−2i−2i2i2i−2i2i−2i2i2-200000000000000000000−2ζ2ζ−2ζ32ζ30000
χ3744-4-4-4-44400004-4-44000000000000000000000000000000
χ3844-4-4-4-4440000-444-4000000000000000000000000000000
χ394-44-44-44-400000000004i−4i00000000000000000000000000
χ404-44-44-44-40000000000−4i4i00000000000000000000000000
χ414-44-4-44-444-44-40000000000000000000000000000000000
χ424-44-4-44-44-44-440000000000000000000000000000000000
χ434-4-444-4-4400000000000000004-400000000000000000000
χ444-4-444-4-440000000000000000-4400000000000000000000
χ454-4-44-444-44i−4i−4i4i0000000000000000000000000000000000
χ464-4-44-444-4−4i4i4i−4i0000000000000000000000000000000000

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