Finite Group Databasebeta

← Group #8667

Character table — Group #8667

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size11111111222222222222222244444444444444444444448888888816161616
order1222444422444444888888882244444444888888888888444444448888
χ11111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-1-1-1-1-111-1-1111111-1-1-1-1111-111-1-1-1-111-1-11111-1-1-1-1ii−i−iii−i−ii−ii−i
χ101111-1-1-1-1-1-111-1-1111111-1-1-1-1111-111-1-1-1-111-1-11111-1-1-1-1−i−iii−i−iii−ii−ii
χ111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11-1-1-1111111-1-1-1-1-1-11111ii−i−iii−i−i−ii−ii
χ121111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11-1-1-1111111-1-1-1-1-1-11111−i−iii−i−iiii−ii−i
χ131111-1-1-1-1-1-111-1-111-1-1-1-11111111-111-1-1-1-1-1-111-1-1-1-11111ii−i−i−i−iiii−i−ii
χ141111-1-1-1-1-1-111-1-111-1-1-1-11111111-111-1-1-1-1-1-111-1-1-1-11111−i−iiiii−i−i−iii−i
χ151111-1-1-1-1-1-111-1-111-1-1-1-11111-1-11-1-1-11111-1-1111111-1-1-1-1ii−i−i−i−iii−iii−i
χ161111-1-1-1-1-1-111-1-111-1-1-1-11111-1-11-1-1-11111-1-1111111-1-1-1-1−i−iiiii−i−ii−i−ii
χ17222222222222-2-2-2-20000000022-2-2-2-222-2-2000000000000000000000000
χ18222222222222-2-2-2-200000000-2-2-2-222-2-222000000000000000000000000
χ1922222222-2-2-2-222222222222200-2-2000000-2-2-2-200000000000000000000
χ2022222222-2-2-2-22222-2-2-2-2-2-2-2-200-2-2000000222200000000000000000000
χ2122222222-2-2-2-2-2-2-2-200000000002200000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2222222222-2-2-2-2-2-2-2-20000000000220000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ232222-2-2-2-222-2-222-2-200000000002-200000000002i2i−2i−2i−2i−2i2i2i000000000000
χ242222-2-2-2-222-2-222-2-200000000002-20000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ252222-2-2-2-222-2-2-2-2222222-2-2-2-200-22000000-2-22200000000000000000000
χ262222-2-2-2-222-2-2-2-222-2-2-2-2222200-2200000022-2-200000000000000000000
χ272222-2-2-2-2-2-22222-2-20000000022-22-2-2-2-222000000000000000000000000
χ282222-2-2-2-2-2-22222-2-200000000-2-2-222222-2-2000000000000000000000000
χ2922-2-222-2-22-22-2000022−2−222−2−22-200002-2002−22−22−22−22−22−2000000000000
χ3022-2-222-2-22-22-2000022−2−222−2−2-220000-22002−22−2−22−22−22−22000000000000
χ3122-2-222-2-22-22-20000−2−222−2−2222-200002-200−22−22−22−22−22−22000000000000
χ3222-2-222-2-22-22-20000−2−222−2−222-220000-2200−22−222−22−22−22−2000000000000
χ3322-2-222-2-2-22-22000022−2−222−2−200002i−2i002i−2i−22−22i2−i2−i2i2i2−i2−i2i2000000000000
χ3422-2-222-2-2-22-22000022−2−222−2−20000−2i2i00−2i2i−22−22−i2i2i2−i2−i2i2i2−i2000000000000
χ3522-2-222-2-2-22-220000−2−222−2−22200002i−2i002i−2i2−22−2−i2i2i2−i2−i2i2i2−i2000000000000
χ3622-2-222-2-2-22-220000−2−222−2−2220000−2i2i00−2i2i2−22−2i2−i2−i2i2i2−i2−i2i2000000000000
χ3722-2-2-2-2222-2-22000022−2−2−2−22200002i−2i00−2i2i−222−2i2−i2−i2i2−i2i2i2−i2000000000000
χ3822-2-2-2-2222-2-22000022−2−2−2−2220000−2i2i002i−2i−222−2−i2i2i2−i2i2−i2−i2i2000000000000
χ3922-2-2-2-2222-2-220000−2−22222−2−200002i−2i00−2i2i2−2−22−i2i2i2−i2i2−i2−i2i2000000000000
χ4022-2-2-2-2222-2-220000−2−22222−2−20000−2i2i002i−2i2−2−22i2−i2−i2i2−i2i2i2−i2000000000000
χ4122-2-2-2-222-222-2000022−2−2−2−2222-20000-22002−2−222−22−2−22−22000000000000
χ4222-2-2-2-222-222-2000022−2−2−2−222-2200002-2002−2−22−22−222−22−2000000000000
χ4322-2-2-2-222-222-20000−2−22222−2−22-20000-2200−222−2−22−222−22−2000000000000
χ4422-2-2-2-222-222-20000−2−22222−2−2-2200002-200−222−22−22−2−22−22000000000000
χ452-22-22i−2i2i−2i00002i−2i2-22-22-22i−2i2i−2i00000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000
χ462-22-22i−2i2i−2i00002i−2i2-22-22-22i−2i2i−2i0000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000
χ472-22-22i−2i2i−2i00002i−2i2-2-22-22−2i2i−2i2i00000000000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i0000
χ482-22-22i−2i2i−2i00002i−2i2-2-22-22−2i2i−2i2i0000000000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i0000
χ492-22-2−2i2i−2i2i0000−2i2i2-22-22-2−2i2i−2i2i00000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000
χ502-22-2−2i2i−2i2i0000−2i2i2-22-22-2−2i2i−2i2i0000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000
χ512-22-2−2i2i−2i2i0000−2i2i2-2-22-222i−2i2i−2i00000000000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i0000
χ522-22-2−2i2i−2i2i0000−2i2i2-2-22-222i−2i2i−2i0000000000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i0000
χ534-44-44i−4i4i−4i0000−4i4i-44000000000000000000000000000000000000000000
χ544-44-4−4i4i−4i4i00004i−4i-44000000000000000000000000000000000000000000
χ554-4-444i−4i−4i4i0000000022−22−22222i2−2i2−2i22i20000000000000000000000000000000000
χ564-4-444i−4i−4i4i00000000−222222−22−2i22i22i2−2i20000000000000000000000000000000000
χ574-4-44−4i4i4i−4i0000000022−22−2222−2i22i22i2−2i20000000000000000000000000000000000
χ584-4-44−4i4i4i−4i00000000−222222−222i2−2i2−2i22i20000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).