Finite Group Databasebeta

← Group #8358

Character table — Group #8358

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46
size11112222222222444444444444448888888888888816161616
order1222224444444444444488888888222244444488888888
χ11111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ411111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111-1-1
χ61111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111
χ71111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ81111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ9111111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i1-11-11-11-11-1ii−i−ii−ii−i
χ10111111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i1-1-11-11-11-11ii−i−i−ii−ii
χ11111111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii1-11-11-11-11-1−i−iii−ii−ii
χ12111111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii1-1-11-11-11-11−i−iiii−ii−i
χ13111111-1-1-1-1-1-1-1-111-1-111iiii−i−i−i−i-111-11-1-11-11−i−iiii−i−ii
χ14111111-1-1-1-1-1-1-1-111-1-111iiii−i−i−i−i-11-11-111-11-1−i−iii−iii−i
χ15111111-1-1-1-1-1-1-1-111-1-111−i−i−i−iiiii-111-11-1-11-11ii−i−i−iii−i
χ16111111-1-1-1-1-1-1-1-111-1-111−i−i−i−iiiii-11-11-111-11-1ii−i−ii−i−ii
χ1722222222-2-2-222-2-2-2222200000000-2-20000000000000000
χ1822222222-2-2-222-2-2-2-2-2-2-200000000220000000000000000
χ19222222-2-2222-2-22-2-222-2-200000000-220000000000000000
χ20222222-2-2222-2-22-2-2-2-222000000002-20000000000000000
χ212222-2-22-22-2-22-222-200000000000000000022-2-200000000
χ222222-2-22-22-2-22-222-2000000000000000000-2-22200000000
χ232222-2-22-2-2222-2-2-22000000000000002-2-22000000000000
χ242222-2-22-2-2222-2-2-2200000000000000-222-2000000000000
χ252222-2-2-222-2-2-222-220000000000000022-2-2000000000000
χ262222-2-2-222-2-2-222-2200000000000000-2-222000000000000
χ272222-2-2-22-222-22-22-20000000000000000002-2-2200000000
χ282222-2-2-22-222-22-22-2000000000000000000-222-200000000
χ2922-2-22-22-2000-220002i−2i2i−2ii2i2−i2−i2i2i2−i2−i200000000002−22−20000
χ3022-2-22-22-2000-220002i−2i2i−2i−i2−i2i2i2−i2−i2i2i20000000000−22−220000
χ3122-2-22-22-2000-22000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i20000000000−22−220000
χ3222-2-22-22-2000-22000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i200000000002−22−20000
χ3322-2-22-2-220002-20002i−2i−2i2i22−2−2−2−2220000000000−i2i2i2−i20000
χ3422-2-22-2-220002-20002i−2i−2i2i−2−22222−2−20000000000i2−i2−i2i20000
χ3522-2-22-2-220002-2000−2i2i2i−2i22−2−2−2−2220000000000i2−i2−i2i20000
χ3622-2-22-2-220002-2000−2i2i2i−2i−2−22222−2−20000000000−i2i2i2−i20000
χ3744-4-4-4444000-4-4000000000000000000000000000000000
χ3844-4-4-44-4-400044000000000000000000000000000000000
χ394-44-4000004i−4i0000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000
χ404-44-4000004i−4i000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000
χ414-44-400000−4i4i0000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000
χ424-44-400000−4i4i000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000
χ434-4-44000040000-40000002i−2i−2i2i−2i2i2i−2i000000000000000000
χ444-4-44000040000-4000000−2i2i2i−2i2i−2i−2i2i000000000000000000
χ454-4-440000-4000040000002-2-222-2-22000000000000000000
χ464-4-440000-400004000000-222-2-222-2000000000000000000

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