Finite Group Databasebeta

← Group #13173418

Character table — Group #13173418

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222244444444444444444444444444444444888888888888888888888888888888888888999918181818181836363636363636365454545454545454108108108108
order122234466622333333666666666666666666666612126666666666666666666666661212121212121212121212124444441212121244121212121212888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−i
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii
χ51111111111-1-1111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-111-1-1-1-111111111-1-1-1-1
χ61111111111-1-1111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111-1-1111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-11111ii−i−iii−i−i−i−iii
χ81111111111-1-1111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-11111−i−iii−i−iiiii−i−i
χ911111-1-11111-111111111-1-1111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-1-1-111-1-11111-1-1-1-11-11-1
χ1011111-1-11111-111111111-1-1111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-1-1-111-1-1-1-1-1-11111-11-11
χ1111111-1-11111-111111111-1-1111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111-1-111ii−i−i−i−iiii−i−ii
χ1211111-1-11111-111111111-1-1111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111-1-111−i−iiiii−i−i−iii−i
χ1311111-1-1111-11111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-11-1-1-1-1111111-1-1-1-1-11-11
χ1411111-1-1111-11111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-11-1-1-1-111-1-1-1-111111-11-1
χ1511111-1-1111-11111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-11111-1-1ii−i−i−i−iii−iii−i
χ1611111-1-1111-11111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-11111-1-1−i−iiiii−i−ii−i−ii
χ172222-122-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222-1-1-1-122-1-1-1-1-1-1000000000000
χ182222-122-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-21111-2-2111111000000000000
χ192222-122-1-1-1-2-222-1-1-1-111112222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-211111111-2-2-2-2111111112222-1-1-1-1-1-1-1-1222222-1-1-1-1-2-2-1-11111000000000000
χ202222-122-1-1-1-2-222-1-1-1-111112222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-211111111-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2-2-2-2-211112211-1-1-1-1000000000000
χ212222-1-2-2-1-1-12-222-1-1-1-1-1-1112222-1-1-1-1-1-1-1-122-1-1-1-1112222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-2111111112222-2-2-1-1-1-12-211-1-111000000000000
χ222222-1-2-2-1-1-12-222-1-1-1-1-1-1112222-1-1-1-1-1-1-1-122-1-1-1-1112222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2-2-2221111-22-1-111-1-1000000000000
χ232222-1-2-2-1-1-1-2222-1-1-1-111-1-12222-1-1-1-1-1-1-1-122-1-1-1-111-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2-2-2111111112222-2-2-1-1-1-1-221111-1-1000000000000
χ242222-1-2-2-1-1-1-2222-1-1-1-111-1-12222-1-1-1-1-1-1-1-122-1-1-1-111-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-22211112-2-1-1-1-111000000000000
χ2522-2-222-22-2-2002222220000-2-2-2-2-2-2-2-2-2-2-2-22222222-200000000000000000000000022-2-22222-2-2-2-22i−2i2i−2i2i−2i2i2i−2i−2i002i−2i0000000000000000
χ2622-2-222-22-2-2002222220000-2-2-2-2-2-2-2-2-2-2-2-22222222-200000000000000000000000022-2-22222-2-2-2-2−2i2i−2i2i−2i2i−2i−2i2i2i00−2i2i0000000000000000
χ2722-2-22-222-2-2002222220000-2-2-2-2-2-2-2-2-2-2-2-2222222-22000000000000000000000000-2-222-2-2-2-222222i−2i2i−2i−2i2i2i2i−2i−2i00−2i2i0000000000000000
χ2822-2-22-222-2-2002222220000-2-2-2-2-2-2-2-2-2-2-2-2222222-22000000000000000000000000-2-222-2-2-2-22222−2i2i−2i2i2i−2i−2i−2i2i2i002i−2i0000000000000000
χ2922-2-2-12-2-1110022-1-1-1-1−i3i3−i3i3-2-2-2-21111111122-1-1-1-1-110000−i3−i3−i3−i3i3i3i3i30000−i3−i3−i3−i3i3i3i3i322-2-2-1-1-1-111112i−2i2i−2i2i−2i−i−iii00−ii3−33−3000000000000
χ3022-2-2-12-2-1110022-1-1-1-1−i3i3−i3i3-2-2-2-21111111122-1-1-1-1-110000−i3−i3−i3−i3i3i3i3i30000−i3−i3−i3−i3i3i3i3i322-2-2-1-1-1-11111−2i2i−2i2i−2i2iii−i−i00i−i−33−33000000000000
χ3122-2-2-12-2-1110022-1-1-1-1i3−i3i3−i3-2-2-2-21111111122-1-1-1-1-110000i3i3i3i3−i3−i3−i3−i30000i3i3i3i3−i3−i3−i3−i322-2-2-1-1-1-111112i−2i2i−2i2i−2i−i−iii00−ii−33−33000000000000
χ3222-2-2-12-2-1110022-1-1-1-1i3−i3i3−i3-2-2-2-21111111122-1-1-1-1-110000i3i3i3i3−i3−i3−i3−i30000i3i3i3i3−i3−i3−i3−i322-2-2-1-1-1-11111−2i2i−2i2i−2i2iii−i−i00i−i3−33−3000000000000
χ3322-2-2-1-22-1110022-1-1-1-1−i3i3i3−i3-2-2-2-21111111122-1-1-1-11-10000−i3−i3−i3−i3i3i3i3i30000i3i3i3i3−i3−i3−i3−i3-2-2221111-1-1-1-12i−2i2i−2i−2i2i−i−iii00i−i3−3−33000000000000
χ3422-2-2-1-22-1110022-1-1-1-1−i3i3i3−i3-2-2-2-21111111122-1-1-1-11-10000−i3−i3−i3−i3i3i3i3i30000i3i3i3i3−i3−i3−i3−i3-2-2221111-1-1-1-1−2i2i−2i2i2i−2iii−i−i00−ii−333−3000000000000
χ3522-2-2-1-22-1110022-1-1-1-1i3−i3−i3i3-2-2-2-21111111122-1-1-1-11-10000i3i3i3i3−i3−i3−i3−i30000−i3−i3−i3−i3i3i3i3i3-2-2221111-1-1-1-12i−2i2i−2i−2i2i−i−iii00i−i−333−3000000000000
χ3622-2-2-1-22-1110022-1-1-1-1i3−i3−i3i3-2-2-2-21111111122-1-1-1-11-10000i3i3i3i3−i3−i3−i3−i30000−i3−i3−i3−i3i3i3i3i3-2-2221111-1-1-1-1−2i2i−2i2i2i−2iii−i−i00−ii3−3−33000000000000
χ372-22-2200-22-200222222000022-2-22222-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000002i−2i−2i2i002i−2i2i−2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000
χ382-22-2200-22-200222222000022-2-22222-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000002i−2i−2i2i002i−2i2i−2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000
χ392-22-2200-22-200222222000022-2-22222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000−2i2i2i−2i00−2i2i−2i2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000
χ402-22-2200-22-200222222000022-2-22222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000−2i2i2i−2i00−2i2i−2i2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000
χ412-2-22200-2-22002222220000-2-222-2-2-2-22222-2-2-2-2-2-20000000000000000000000000000000000000022-2-2002-2-220000000000002i−2i2i−2i0000
χ422-2-22200-2-22002222220000-2-222-2-2-2-22222-2-2-2-2-2-20000000000000000000000000000000000000022-2-2002-2-22000000000000−2i2i−2i2i0000
χ432-2-22200-2-22002222220000-2-222-2-2-2-22222-2-2-2-2-2-200000000000000000000000000000000000000-2-22200-222-20000000000002-2-220000
χ442-2-22200-2-22002222220000-2-222-2-2-2-22222-2-2-2-2-2-200000000000000000000000000000000000000-2-22200-222-2000000000000-222-20000
χ454444444444441-211-2-244441-21-211-2-211-2-21-211-2-24411-2-211-2-211-2-211-2-211-2-211-2-21-21-211-2-211-2-2000000000000000000000000000000
χ46444444444444-21-2-2114444-21-21-2-211-2-211-21-2-21144-2-211-2-211-2-211-2-211-2-211-2-211-21-21-2-211-2-211000000000000000000000000000000
χ474444444444-4-41-211-2-2-4-4-4-41-21-211-2-211-2-21-211-2-244-1-122-1-122-1-122-1-122-1-122-1-1221-21-211-2-211-2-2000000000000000000000000000000
χ484444444444-4-4-21-2-211-4-4-4-4-21-21-2-211-2-211-21-2-2114422-1-122-1-122-1-122-1-122-1-122-1-1-21-21-2-211-2-211000000000000000000000000000000
χ4944444-4-44444-41-211-2-244-4-41-21-211-2-211-2-21-211-2-2-4-411-2-211-2-211-2-2-1-122-1-122-1-122-12-12-1-122-1-122000000000000000000000000000000
χ5044444-4-44444-4-21-2-21144-4-4-21-21-2-211-2-211-21-2-211-4-4-2-211-2-211-2-21122-1-122-1-122-1-12-12-122-1-122-1-1000000000000000000000000000000
χ5144444-4-4444-441-211-2-2-4-4441-21-211-2-211-2-21-211-2-2-4-4-1-122-1-122-1-12211-2-211-2-211-2-2-12-12-1-122-1-122000000000000000000000000000000
χ5244444-4-4444-44-21-2-211-4-444-21-21-2-211-2-211-21-2-211-4-422-1-122-1-122-1-1-2-211-2-211-2-2112-12-122-1-122-1-1000000000000000000000000000000
χ534444-244-2-2-2441-2−1−3i32−1+3i3211-2-2-2-21-21-2−1−3i32−1+3i3211−1−3i32−1+3i32111-2−1−3i32−1+3i3211-2-211-2-2−1−3i32−1+3i3211−1−3i32−1+3i321111-2-2−1−3i32−1+3i3211−1−3i32−1+3i32111-21-2−1−3i32−1+3i3211−1−3i32−1+3i3211000000000000000000000000000000
χ544444-244-2-2-2441-2−1+3i32−1−3i3211-2-2-2-21-21-2−1+3i32−1−3i3211−1+3i32−1−3i32111-2−1+3i32−1−3i3211-2-211-2-2−1+3i32−1−3i3211−1+3i32−1−3i321111-2-2−1+3i32−1−3i3211−1+3i32−1−3i32111-21-2−1+3i32−1−3i3211−1+3i32−1−3i3211000000000000000000000000000000
χ554444-244-2-2-244-2111−1−3i32−1+3i32-2-2-2-2-21-2111−1−3i32−1+3i3211−1−3i32−1+3i32-2111−1−3i32−1+3i32-2-2-2-21111−1−3i32−1+3i3211−1−3i32−1+3i32-2-21111−1−3i32−1+3i3211−1−3i32−1+3i32-21-2111−1−3i32−1+3i3211−1−3i32−1+3i32000000000000000000000000000000
χ564444-244-2-2-244-2111−1+3i32−1−3i32-2-2-2-2-21-2111−1+3i32−1−3i3211−1+3i32−1−3i32-2111−1+3i32−1−3i32-2-2-2-21111−1+3i32−1−3i3211−1+3i32−1−3i32-2-21111−1+3i32−1−3i3211−1+3i32−1−3i32-21-2111−1+3i32−1−3i3211−1+3i32−1−3i32000000000000000000000000000000
χ574444-244-2-2-2-4-41-2−1−3i32−1+3i321122221-21-2−1−3i32−1+3i3211−1−3i32−1+3i32111-2−1−3i32−1+3i3211-2-2-1-1221+3i321−3i32-1-11+3i321−3i32-1-1-1-1221+3i321−3i32-1-11+3i321−3i32-1-11-21-2−1−3i32−1+3i3211−1−3i32−1+3i3211000000000000000000000000000000
χ584444-244-2-2-2-4-41-2−1+3i32−1−3i321122221-21-2−1+3i32−1−3i3211−1+3i32−1−3i32111-2−1+3i32−1−3i3211-2-2-1-1221−3i321+3i32-1-11−3i321+3i32-1-1-1-1221−3i321+3i32-1-11−3i321+3i32-1-11-21-2−1+3i32−1−3i3211−1+3i32−1−3i3211000000000000000000000000000000
χ594444-244-2-2-2-4-4-2111−1−3i32−1+3i322222-21-2111−1−3i32−1+3i3211−1−3i32−1+3i32-2111−1−3i32−1+3i32-2-222-1-1-1-11+3i321−3i32-1-11+3i321−3i3222-1-1-1-11+3i321−3i32-1-11+3i321−3i32-21-2111−1−3i32−1+3i3211−1−3i32−1+3i32000000000000000000000000000000
χ604444-244-2-2-2-4-4-2111−1+3i32−1−3i322222-21-2111−1+3i32−1−3i3211−1+3i32−1−3i32-2111−1+3i32−1−3i32-2-222-1-1-1-11−3i321+3i32-1-11−3i321+3i3222-1-1-1-11−3i321+3i32-1-11−3i321+3i32-21-2111−1+3i32−1−3i3211−1+3i32−1−3i32000000000000000000000000000000
χ614444-2-4-4-2-2-24-41-2−1−3i32−1+3i3211-2-2221-21-2−1−3i32−1+3i3211−1−3i32−1+3i32111-2−1−3i32−1+3i32112211-2-2−1−3i32−1+3i3211−1−3i32−1+3i3211-1-1221+3i321−3i32-1-11+3i321−3i32-1-1-12-121+3i321−3i32-1-11+3i321−3i32-1-1000000000000000000000000000000
χ624444-2-4-4-2-2-24-41-2−1+3i32−1−3i3211-2-2221-21-2−1+3i32−1−3i3211−1+3i32−1−3i32111-2−1+3i32−1−3i32112211-2-2−1+3i32−1−3i3211−1+3i32−1−3i3211-1-1221−3i321+3i32-1-11−3i321+3i32-1-1-12-121−3i321+3i32-1-11−3i321+3i32-1-1000000000000000000000000000000
χ634444-2-4-4-2-2-24-4-2111−1−3i32−1+3i32-2-222-21-2111−1−3i32−1+3i3211−1−3i32−1+3i32-2111−1−3i32−1+3i3222-2-21111−1−3i32−1+3i3211−1−3i32−1+3i3222-1-1-1-11+3i321−3i32-1-11+3i321−3i322-12-1-1-11+3i321−3i32-1-11+3i321−3i32000000000000000000000000000000
χ644444-2-4-4-2-2-24-4-2111−1+3i32−1−3i32-2-222-21-2111−1+3i32−1−3i3211−1+3i32−1−3i32-2111−1+3i32−1−3i3222-2-21111−1+3i32−1−3i3211−1+3i32−1−3i3222-1-1-1-11−3i321+3i32-1-11−3i321+3i322-12-1-1-11−3i321+3i32-1-11−3i321+3i32000000000000000000000000000000
χ654444-2-4-4-2-2-2-441-2−1−3i32−1+3i321122-2-21-21-2−1−3i32−1+3i3211−1−3i32−1+3i32111-2−1−3i32−1+3i321122-1-1221+3i321−3i32-1-11+3i321−3i32-1-111-2-2−1−3i32−1+3i3211−1−3i32−1+3i3211-12-121+3i321−3i32-1-11+3i321−3i32-1-1000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.