Finite Group Databasebeta

← Group #8352

Character table — Group #8352

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46
size11112222222222444444444444448888888888888816161616
order1222222222444444444488888888222444444488884444
χ11111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ411111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-111-1-111111111-111-111-1-1-1-1-1-1-1-111-1-1
χ611111111111111-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111
χ711111111111111-1-111-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-11111-1-111
χ811111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ9111111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i11-1-11-11-11-1ii−i−ii−ii−i
χ10111111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i1-11-1-11-11-11ii−i−i−ii−ii
χ11111111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii11-1-11-11-11-1−i−iii−ii−ii
χ12111111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii1-11-1-11-11-11−i−iiii−ii−i
χ13111111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i-11-111-1-11-11−i−iiii−i−ii
χ14111111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i-1-111-111-11-1−i−iii−iii−i
χ15111111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii-11-111-1-11-11ii−i−i−iii−i
χ16111111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii-1-111-111-11-1ii−i−ii−i−ii
χ172222222222-2-2-2-222-2-22200000000-200-200000000000000
χ182222222222-2-2-2-2-2-2-2-2-2-200000000200200000000000000
χ19222222-2-2-2-2222222-2-2-2-200000000-200200000000000000
χ20222222-2-2-2-22222-2-2-2-22200000000200-200000000000000
χ212222-2-22-22-22-2-22002-2000000000000000022-2-200000000
χ222222-2-22-22-22-2-22002-20000000000000000-2-22200000000
χ232222-2-22-22-2-222-200-22000000000002-20-22000000000000
χ242222-2-22-22-2-222-200-2200000000000-2202-2000000000000
χ252222-2-2-22-222-2-2200-2200000000000220-2-2000000000000
χ262222-2-2-22-222-2-2200-2200000000000-2-2022000000000000
χ272222-2-2-22-22-222-2002-200000000000000002-2-2200000000
χ282222-2-2-22-22-222-2002-20000000000000000-222-200000000
χ2922-2-22-22-2-2200002i−2i002i−2i22−2−222−2−20000000000i2−i2i2−i20000
χ3022-2-22-22-2-2200002i−2i002i−2i−2−222−2−2220000000000−i2i2−i2i20000
χ3122-2-22-22-2-220000−2i2i00−2i2i22−2−222−2−20000000000−i2i2−i2i20000
χ3222-2-22-22-2-220000−2i2i00−2i2i−2−222−2−2220000000000i2−i2i2−i20000
χ3322-2-22-2-222-200002i−2i00−2i2ii2i2−i2−i2−i2−i2i2i20000000000−222−20000
χ3422-2-22-2-222-200002i−2i00−2i2i−i2−i2i2i2i2i2−i2−i200000000002−2−220000
χ3522-2-22-2-222-20000−2i2i002i−2ii2i2−i2−i2−i2−i2i2i200000000002−2−220000
χ3622-2-22-2-222-20000−2i2i002i−2i−i2−i2i2i2i2i2−i2−i20000000000−222−20000
χ3744-4-4-4444-4-4000000000000000000000000000000000000
χ3844-4-4-44-4-444000000000000000000000000000000000000
χ394-44-400000004i−4i00000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000
χ404-44-400000004i−4i0000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000
χ414-44-40000000−4i4i00000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000
χ424-44-40000000−4i4i0000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000
χ434-4-44000000400-40000002i−2i−2i2i2i−2i−2i2i000000000000000000
χ444-4-44000000400-4000000−2i2i2i−2i−2i2i2i−2i000000000000000000
χ454-4-44000000-40040000002-2-22-222-2000000000000000000
χ464-4-44000000-4004000000-222-22-2-22000000000000000000

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