Finite Group Databasebeta

← Group #8348

Character table — Group #8348

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46
size11112222222222444444444444448888888888888816161616
order1222224444444422444488888888224444444488888888
χ11111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ411111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-111-1-1111111111-1-1-1111-1-1-1-1-1-1-111-1-1
χ611111111111111-1-111-1-111111111-11-1-1-1-1-1111-1-1-1-1-1-111
χ711111111111111-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1111-1-1-11111-1-111
χ811111111111111-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1111111111-1-1
χ9111111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i111-11-1-11-1-1ii−i−ii−ii−i
χ10111111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i-1-11-1-111-111ii−i−i−ii−ii
χ11111111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii111-11-1-11-1-1−i−iii−ii−ii
χ12111111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii-1-11-1-111-111−i−iiii−ii−i
χ13111111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i1-1-111-1-1-111−i−iiii−i−ii
χ14111111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i-11-11-1111-1-1−i−iii−iii−i
χ15111111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii1-1-111-1-1-111ii−i−i−iii−i
χ16111111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii-11-11-1111-1-1ii−i−ii−i−ii
χ172222222222-2-2-2-222-2-2220000000000-2-200000000000000
χ182222222222-2-2-2-2-2-2-2-2-2-200000000002200000000000000
χ19222222-2-2-2-2222222-2-2-2-20000000000-2200000000000000
χ20222222-2-2-2-22222-2-2-2-22200000000002-200000000000000
χ212222-2-222-2-222-2-2002-200000000000200000-22-200000000
χ222222-2-222-2-222-2-2002-200000000000-2000002-2200000000
χ232222-2-222-2-2-2-22200-2200000000002000-22-200000000000
χ242222-2-222-2-2-2-22200-220000000000-20002-2200000000000
χ252222-2-2-2-22222-2-200-2200000000002000-2-2200000000000
χ262222-2-2-2-22222-2-200-220000000000-200022-200000000000
χ272222-2-2-2-222-2-222002-200000000000200000-2-2200000000
χ282222-2-2-2-222-2-222002-200000000000-20000022-200000000
χ2922-2-22-22i−2i2i−2i00002-2002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000001+i−1−i1−i−1+i0000
χ3022-2-22-22i−2i2i−2i00002-2002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000−1−i1+i−1+i1−i0000
χ3122-2-22-22i−2i2i−2i0000-2200−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000−1−i1+i−1+i1−i0000
χ3222-2-22-22i−2i2i−2i0000-2200−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000001+i−1−i1−i−1+i0000
χ3322-2-22-2−2i2i−2i2i00002-200−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000001−i−1+i1+i−1−i0000
χ3422-2-22-2−2i2i−2i2i00002-200−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000−1+i1−i−1−i1+i0000
χ3522-2-22-2−2i2i−2i2i0000-22002i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000−1+i1−i−1−i1+i0000
χ3622-2-22-2−2i2i−2i2i0000-22002i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000001−i−1+i1+i−1−i0000
χ3744-4-4-444i−4i−4i4i000000000000000000000000000000000000
χ3844-4-4-44−4i4i4i−4i000000000000000000000000000000000000
χ394-44-4000000004i−4i0000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000
χ404-44-4000000004i−4i000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000
χ414-44-400000000−4i4i0000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000
χ424-44-400000000−4i4i000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000
χ434-4-440000004i−4i000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000
χ444-4-440000004i−4i00000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000
χ454-4-44000000−4i4i000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000000000000
χ464-4-44000000−4i4i00000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000000000000

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