Finite Group Databasebeta

← Group #9719

Character table — Group #9719

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size11111111222222222222222244444444444444444444448888888816161616
order1222444422444444888888884488888888888888888888444444442244
χ11111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ61111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ71111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ81111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1
χ91111-1-1-1-1-1-11111-1-11111-1-1-1-11-1iiii−i−i−i−i11-1-1iiii−i−i−i−iii−i−iii−i−i11-1-1
χ101111-1-1-1-1-1-11111-1-11111-1-1-1-11-1iiii−i−i−i−i11-1-1iiii−i−i−i−i−i−iii−i−iii-1-111
χ111111-1-1-1-1-1-11111-1-11111-1-1-1-11-1−i−i−i−iiiii11-1-1−i−i−i−iiiiiii−i−iii−i−i-1-111
χ121111-1-1-1-1-1-11111-1-11111-1-1-1-11-1−i−i−i−iiiii11-1-1−i−i−i−iiiii−i−iii−i−iii11-1-1
χ131111-1-1-1-1-1-11111-1-1-1-1-1-111111-1iiii−i−i−i−i-1-111−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141111-1-1-1-1-1-11111-1-1-1-1-1-111111-1iiii−i−i−i−i-1-111−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151111-1-1-1-1-1-11111-1-1-1-1-1-111111-1−i−i−i−iiiii-1-111iiii−i−i−i−iii−i−i−i−iii-111-1
χ161111-1-1-1-1-1-11111-1-1-1-1-1-111111-1−i−i−i−iiiii-1-111iiii−i−i−i−i−i−iiiii−i−i1-1-11
χ17222222222222-2-2-2-200000000-2-222-2-222-2-2000000000000000000000000
χ18222222222222-2-2-2-200000000-2-2-2-222-2-222000000000000000000000000
χ1922222222-2-2-2-2222222222222-2-200000000-2-2-2-200000000000000000000
χ2022222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-200000000222200000000000000000000
χ2122222222-2-2-2-2-2-2-2-200000000220000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2222222222-2-2-2-2-2-2-2-20000000022000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ232222-2-2-2-222-2-222-2-22222-2-2-2-2-2200000000-2-22200000000000000000000
χ242222-2-2-2-222-2-222-2-2-2-2-2-22222-220000000022-2-200000000000000000000
χ252222-2-2-2-222-2-2-2-222000000002-200000000000022-2-2-2-222000000000000
χ262222-2-2-2-222-2-2-2-222000000002-2000000000000-2-22222-2-2000000000000
χ272222-2-2-2-2-2-222-2-22200000000-222i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ282222-2-2-2-2-2-222-2-22200000000-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ2922-2-22i2i−2i−2i00002-22i−2i22-2-22i2i−2i−2i00000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000
χ3022-2-22i2i−2i−2i00002-22i−2i22-2-22i2i−2i−2i0000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000
χ3122-2-22i2i−2i−2i00002-22i−2i-2-222−2i−2i2i2i00000000000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i0000
χ3222-2-22i2i−2i−2i00002-22i−2i-2-222−2i−2i2i2i0000000000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i0000
χ3322-2-2−2i−2i2i2i00002-2−2i2i22-2-2−2i−2i2i2i00000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000
χ3422-2-2−2i−2i2i2i00002-2−2i2i22-2-2−2i−2i2i2i0000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000
χ3522-2-2−2i−2i2i2i00002-2−2i2i-2-2222i2i−2i−2i00000000000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i0000
χ3622-2-2−2i−2i2i2i00002-2−2i2i-2-2222i2i−2i−2i0000000000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i0000
χ372-2-222-22-22-22-200002−22−22−22−200002i−2i002i−2i2−22−2i2−i2i2−i2i2−i2i2−i2000000000000
χ382-2-222-22-22-22-200002−22−22−22−20000−2i2i00−2i2i2−22−2−i2i2−i2i2−i2i2−i2i2000000000000
χ392-2-222-22-22-22-20000−22−22−22−2200002i−2i002i−2i−22−22−i2i2−i2i2−i2i2−i2i2000000000000
χ402-2-222-22-22-22-20000−22−22−22−220000−2i2i00−2i2i−22−22i2−i2i2−i2i2−i2i2−i2000000000000
χ412-2-222-22-2-22-2200002−22−22−22−2002-2002-200−22−222−2−222−2−22000000000000
χ422-2-222-22-2-22-2200002−22−22−22−200-2200-2200−22−22−222−2−222−2000000000000
χ432-2-222-22-2-22-220000−22−22−22−22002-2002-2002−22−2−222−2−222−2000000000000
χ442-2-222-22-2-22-220000−22−22−22−2200-2200-22002−22−22−2−222−2−22000000000000
χ452-2-22-22-222-2-2200002−22−2−22−22002i−2i00−2i2i00−222−2i2−i2−i2i2−i2i2i2−i2000000000000
χ462-2-22-22-222-2-2200002−22−2−22−2200−2i2i002i−2i00−222−2−i2i2i2−i2i2−i2−i2i2000000000000
χ472-2-22-22-222-2-220000−22−222−22−2002i−2i00−2i2i002−2−22−i2i2i2−i2i2−i2−i2i2000000000000
χ482-2-22-22-222-2-220000−22−222−22−200−2i2i002i−2i002−2−22i2−i2−i2i2−i2i2i2−i2000000000000
χ492-2-22-22-22-222-200002−22−2−22−2200002-200-222−2−222−22−2−22−22000000000000
χ502-2-22-22-22-222-200002−22−2−22−220000-22002-22−2−22−22−222−22−2000000000000
χ512-2-22-22-22-222-20000−22−222−22−200002-200-22−222−2−22−222−22−2000000000000
χ522-2-22-22-22-222-20000−22−222−22−20000-22002-2−222−22−22−2−22−22000000000000
χ5344-4-44i4i−4i−4i0000-44−4i4i000000000000000000000000000000000000000000
χ5444-4-4−4i−4i4i4i0000-444i−4i000000000000000000000000000000000000000000
χ554-44-44i−4i−4i4i0000000022−22−22222i2−2i2−2i22i20000000000000000000000000000000000
χ564-44-44i−4i−4i4i00000000−222222−22−2i22i22i2−2i20000000000000000000000000000000000
χ574-44-4−4i4i4i−4i0000000022−22−2222−2i22i22i2−2i20000000000000000000000000000000000
χ584-44-4−4i4i4i−4i00000000−222222−222i2−2i2−2i22i20000000000000000000000000000000000

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