Finite Group Databasebeta

← Group #11670

Character table — Group #11670

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46
size11112222222222444444444444448888888888888816161616
order12442444448888248888888888882244488888888816161616
χ11111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1
χ311111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-11111
χ511111111111111-1-1-1-111111111111-11-1-111-1-1-1-1-1-1-111-1-1
χ611111111111111-1-1-1-11111111111-11-11-1-1-111-1-1-1-1-1-1-111
χ711111111111111-1-1-1-111-1-1-1-1-1-1-1-11-11-1-111-1-1-11111-1-111
χ811111111111111-1-1-1-111-1-1-1-1-1-1-1-1-11-11-1-1-111-1111111-1-1
χ9111111-1-1-1-1-1-1-1-111-1-111iiii−i−i−i−i1111-1-1-1-1-11ii−i−ii−ii−i
χ10111111-1-1-1-1-1-1-1-111-1-111iiii−i−i−i−i-1-1-1-1-111111ii−i−i−ii−ii
χ11111111-1-1-1-1-1-1-1-111-1-111−i−i−i−iiiii1111-1-1-1-1-11−i−iii−ii−ii
χ12111111-1-1-1-1-1-1-1-111-1-111−i−i−i−iiiii-1-1-1-1-111111−i−iiii−ii−i
χ13111111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i1-11-11-1-111-1−i−iiii−i−ii
χ14111111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i-11-11111-1-1-1−i−iii−iii−i
χ15111111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii1-11-11-1-111-1ii−i−i−iii−i
χ16111111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii-11-11111-1-1-1ii−i−ii−i−ii
χ172222222222-2-2-2-222-2-2-2-200000000000020000-200000000
χ182222222222-2-2-2-2-2-222-2-2000000000000-20000200000000
χ19222222-2-2-2-222222222-2-2000000000000-20000-200000000
χ20222222-2-2-2-22222-2-2-2-2-2-200000000000020000200000000
χ2122-2-22-200002i2i−2i−2i2-22i−2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000001+i−1−i1−i−1+i0000
χ2222-2-22-200002i2i−2i−2i2-22i−2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000−1−i1+i−1+i1−i0000
χ2322-2-22-200002i2i−2i−2i-22−2i2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000−1−i1+i−1+i1−i0000
χ2422-2-22-200002i2i−2i−2i-22−2i2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000001+i−1−i1−i−1+i0000
χ2522-2-22-20000−2i−2i2i2i2-2−2i2i001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000001−i−1+i1+i−1−i0000
χ2622-2-22-20000−2i−2i2i2i2-2−2i2i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000−1+i1−i−1−i1+i0000
χ2722-2-22-20000−2i−2i2i2i-222i−2i001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000−1+i1−i−1−i1+i0000
χ2822-2-22-20000−2i−2i2i2i-222i−2i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000001−i−1+i1+i−1−i0000
χ2922-2-2-222i2i−2i−2i2i−2i2i−2i00002-200000000020-20002i−2i000000000
χ3022-2-2-222i2i−2i−2i2i−2i2i−2i00002-2000000000-202000−2i2i000000000
χ3122-2-2-222i2i−2i−2i−2i2i−2i2i0000-220000000020-2002i−2i00000000000
χ3222-2-2-222i2i−2i−2i−2i2i−2i2i0000-2200000000-20200−2i2i00000000000
χ3322-2-2-22−2i−2i2i2i2i−2i2i−2i0000-220000000020-200−2i2i00000000000
χ3422-2-2-22−2i−2i2i2i2i−2i2i−2i0000-2200000000-202002i−2i00000000000
χ3522-2-2-22−2i−2i2i2i−2i2i−2i2i00002-200000000020-2000−2i2i000000000
χ3622-2-2-22−2i−2i2i2i−2i2i−2i2i00002-2000000000-2020002i−2i000000000
χ374444-4-400004-4-4400000000000000000000000000000000
χ384444-4-40000-444-400000000000000000000000000000000
χ394-44i−4i002+2i−2−2i2−2i−2+2i00000000002ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ000000000000000000
χ404-44i−4i002+2i−2−2i2−2i−2+2i0000000000−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ000000000000000000
χ414-44i−4i00−2−2i2+2i−2+2i2−2i00000000002ζ3−2ζ3−2ζ2ζ2ζ−2ζ−2ζ32ζ3000000000000000000
χ424-44i−4i00−2−2i2+2i−2+2i2−2i0000000000−2ζ32ζ32ζ−2ζ−2ζ2ζ2ζ3−2ζ3000000000000000000
χ434-4−4i4i002−2i−2+2i2+2i−2−2i00000000002ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ3000000000000000000
χ444-4−4i4i002−2i−2+2i2+2i−2−2i0000000000−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ3000000000000000000
χ454-4−4i4i00−2+2i2−2i−2−2i2+2i00000000002ζ−2ζ−2ζ32ζ32ζ3−2ζ3−2ζ2ζ000000000000000000
χ464-4−4i4i00−2+2i2−2i−2−2i2+2i0000000000−2ζ2ζ2ζ3−2ζ3−2ζ32ζ32ζ−2ζ000000000000000000

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