Finite Group Databasebeta

← Group #8671

Character table — Group #8671

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size11111111222222222222222244444444444444444444448888888816161616
order1222444444444444888888882224444444888888888888888888888888
χ11111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
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
χ71111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-1-1-111-1-111-1-11111-1-1-1-1-111111-1-1-1-111-1-11111-1-1-1-1ii−i−iii−i−ii−ii−i
χ101111-1-1-1-111-1-111-1-11111-1-1-1-1-111111-1-1-1-111-1-11111-1-1-1-1−i−iii−i−iii−ii−ii
χ111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-11-1-1111111-1-1-1-1-1-11111ii−i−iii−i−i−ii−ii
χ121111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-11-1-1111111-1-1-1-1-1-11111−i−iii−i−iiii−ii−i
χ131111-1-1-1-111-1-111-1-1-1-1-1-11111-111111-1-1-1-1-1-111-1-1-1-11111ii−i−i−i−iiii−i−ii
χ141111-1-1-1-111-1-111-1-1-1-1-1-11111-111111-1-1-1-1-1-111-1-1-1-11111−i−iiiii−i−i−iii−i
χ151111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-11-1-11111-1-1111111-1-1-1-1ii−i−i−i−iii−iii−i
χ161111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-11-1-11111-1-1111111-1-1-1-1−i−iiiii−i−ii−i−ii
χ172222222222-2-2-2-22200000000-222-2-2-222-2-2000000000000000000000000
χ182222222222-2-2-2-22200000000-2-2-2-222-2-222000000000000000000000000
χ1922222222-2-22222-2-222222222-200-2000000-2-2-2-200000000000000000000
χ2022222222-2-22222-2-2-2-2-2-2-2-2-2-2-200-2000000222200000000000000000000
χ2122222222-2-2-2-2-2-2-2-200000000200200000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2222222222-2-2-2-2-2-2-2-20000000020020000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ232222-2-2-2-22222-2-2-2-200000000222-2-2-2-2-222000000000000000000000000
χ242222-2-2-2-22222-2-2-2-2000000002-2-2-22222-2-2000000000000000000000000
χ252222-2-2-2-2-2-222-2-22200000000-200200000000002i2i−2i−2i−2i−2i2i2i000000000000
χ262222-2-2-2-2-2-222-2-22200000000-20020000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ272222-2-2-2-2-2-2-2-222222222-2-2-2-2200-2000000-2-22200000000000000000000
χ282222-2-2-2-2-2-2-2-22222-2-2-2-22222200-200000022-2-200000000000000000000
χ2922-2-22i−2i2i−2i002i−2i2-20022-2-22i2i−2i−2i00000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000
χ3022-2-22i−2i2i−2i002i−2i2-20022-2-22i2i−2i−2i0000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000
χ3122-2-22i−2i2i−2i002i−2i2-200-2-222−2i−2i2i2i00000000000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i0000
χ3222-2-22i−2i2i−2i002i−2i2-200-2-222−2i−2i2i2i0000000000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i0000
χ3322-2-2−2i2i−2i2i00−2i2i2-20022-2-2−2i−2i2i2i00000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000
χ3422-2-2−2i2i−2i2i00−2i2i2-20022-2-2−2i−2i2i2i0000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000
χ3522-2-2−2i2i−2i2i00−2i2i2-200-2-2222i2i−2i−2i00000000000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i0000
χ3622-2-2−2i2i−2i2i00−2i2i2-200-2-2222i2i−2i−2i0000000000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i0000
χ372-22-22i−2i−2i2i2-200002i−2i2−22−2i2−i2i2−i200002i−2i002-22−2i2−i2i2−i2i2−i22−22−2000000000000
χ382-22-22i−2i−2i2i2-200002i−2i2−22−2i2−i2i2−i20000−2i2i00-222−2i2−i2−i2i2−i2i2−22−22000000000000
χ392-22-22i−2i−2i2i2-200002i−2i−22−22−i2i2−i2i200002i−2i002-2−22−i2i2−i2i2−i2i2−22−22000000000000
χ402-22-22i−2i−2i2i2-200002i−2i−22−22−i2i2−i2i20000−2i2i00-22−22−i2i2i2−i2i2−i22−22−2000000000000
χ412-22-22i−2i−2i2i-220000−2i2i2−22−2i2−i2i2−i202-20002i−2i00−22−i2i22−2−22−i2i2i2−i2000000000000
χ422-22-22i−2i−2i2i-220000−2i2i2−22−2i2−i2i2−i20-22000−2i2i00−22−i2i2−222−2i2−i2−i2i2000000000000
χ432-22-22i−2i−2i2i-220000−2i2i−22−22−i2i2−i2i202-20002i−2i002−2i2−i2−222−2i2−i2−i2i2000000000000
χ442-22-22i−2i−2i2i-220000−2i2i−22−22−i2i2−i2i20-22000−2i2i002−2i2−i22−2−22−i2i2i2−i2000000000000
χ452-22-2−2i2i2i−2i2-20000−2i2i2−22−2−i2i2−i2i200002i−2i00-222−2−i2i2i2−i2i2−i2−22−22000000000000
χ462-22-2−2i2i2i−2i2-20000−2i2i2−22−2−i2i2−i2i20000−2i2i002-22−2−i2i2−i2i2−i2i22−22−2000000000000
χ472-22-2−2i2i2i−2i2-20000−2i2i−22−22i2−i2i2−i200002i−2i00-22−22i2−i2−i2i2−i2i22−22−2000000000000
χ482-22-2−2i2i2i−2i2-20000−2i2i−22−22i2−i2i2−i20000−2i2i002-2−22i2−i2i2−i2i2−i2−22−22000000000000
χ492-22-2−2i2i2i−2i-2200002i−2i2−22−2−i2i2−i2i202-2000−2i2i00−22i2−i22−2−22i2−i2−i2i2000000000000
χ502-22-2−2i2i2i−2i-2200002i−2i2−22−2−i2i2−i2i20-220002i−2i00−22i2−i2−222−2−i2i2i2−i2000000000000
χ512-22-2−2i2i2i−2i-2200002i−2i−22−22i2−i2i2−i202-2000−2i2i002−2−i2i2−222−2−i2i2i2−i2000000000000
χ522-22-2−2i2i2i−2i-2200002i−2i−22−22i2−i2i2−i20-220002i−2i002−2−i2i22−2−22i2−i2−i2i2000000000000
χ5344-4-44i−4i4i−4i00−4i4i-4400000000000000000000000000000000000000000000
χ5444-4-4−4i4i−4i4i004i−4i-4400000000000000000000000000000000000000000000
χ554-4-4444-4-40000000022−22−222222−22−22220000000000000000000000000000000000
χ564-4-4444-4-400000000−222222−22−222222−220000000000000000000000000000000000
χ574-4-44-4-4440000000022−22−2222−222222−220000000000000000000000000000000000
χ584-4-44-4-44400000000−222222−2222−22−22220000000000000000000000000000000000

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