Finite Group Databasebeta

← Group #13157177

Character table — Group #13157177

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222244444444444444444444444444444444888888888888888888888888888888888888999918181818181836363636363636365454545454545454108108108108
order122234466633333344666666666666666666121212121212121212121212121212121212121212121212121212121212121212121212121212121212444444121212122266661212888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ51111111111111111-1-111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111111111-1-1-1-1
χ61111111111111111-1-111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ71111111111111111-1-111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiii−i−i−i−i−i−iii
χ81111111111111111-1-111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−iiiiiii−i−i
χ911-1-111-11-1-1111111i−i-1-1-1-1-1-1111111-1-1-1-1-1-11-1ii−i−i111111-1-1-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−ii−ii−ii−iii−i−i1-111-1-1i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ1011-1-111-11-1-1111111i−i-1-1-1-1-1-1111111-1-1-1-1-1-11-1ii−i−i111111-1-1-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−ii−ii−ii−iii−i−i1-111-1-1i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ1111-1-111-11-1-1111111i−i-1-1-1-1-1-1111111-1-1-1-1-1-11-1ii−i−i111111-1-1-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−ii−ii−ii−i−iii-11-1-111−ii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ1211-1-111-11-1-1111111i−i-1-1-1-1-1-1111111-1-1-1-1-1-11-1ii−i−i111111-1-1-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−ii−ii−ii−i−iii-11-1-111−iiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ1311-1-111-11-1-1111111−ii-1-1-1-1-1-1111111-1-1-1-1-1-11-1−i−iii111111-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiii−ii−ii−iii−i−i-11-1-111i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ1411-1-111-11-1-1111111−ii-1-1-1-1-1-1111111-1-1-1-1-1-11-1−i−iii111111-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiii−ii−ii−iii−i−i-11-1-111i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ1511-1-111-11-1-1111111−ii-1-1-1-1-1-1111111-1-1-1-1-1-11-1−i−iii111111-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−ii−ii−ii−i−iii1-111-1-1−ii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ1611-1-111-11-1-1111111−ii-1-1-1-1-1-1111111-1-1-1-1-1-11-1−i−iii111111-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−ii−ii−ii−i−iii1-111-1-1−iiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ1722222-2-222222222200222222222222222222-2-20000-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000002222-2-22222000000-2-2000000000000
χ1822222-2-222222222200222222222222222222-2-20000-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000-2-2-2-222-2-2-2-200000022000000000000
χ192222-122-1-1-122-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222-1-1-1-122-1-1-1-1-1-1000000000000
χ202222-122-1-1-122-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-21111-2-2111111000000000000
χ212222-122-1-1-122-1-1-1-1-2-222-1-1-1-122-1-1-1-122-1-1-1-1-1-1111122-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-211111111222222-1-1-1-1-2-21111-1-1000000000000
χ222222-122-1-1-122-1-1-1-1-2-222-1-1-1-122-1-1-1-122-1-1-1-1-1-1111122-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2-2-2-2-2111122-1-1-1-111000000000000
χ232222-1-2-2-1-1-122-1-1-1-10022-1-1-1-122-1-1-1-122-1-1-1-111−i3i3−i3i3-2-21111-2-211110000−i3−i3−i3−i3i3i3i3i30000−i3−i3−i3−i3i3i3i3i32222-2-2-1-1-1-100−i3i3−i3i311000000000000
χ242222-1-2-2-1-1-122-1-1-1-10022-1-1-1-122-1-1-1-122-1-1-1-111−i3i3−i3i3-2-21111-2-211110000−i3−i3−i3−i3i3i3i3i30000−i3−i3−i3−i3i3i3i3i3-2-2-2-222111100i3−i3i3−i3-1-1000000000000
χ252222-1-2-2-1-1-122-1-1-1-10022-1-1-1-122-1-1-1-122-1-1-1-111i3−i3i3−i3-2-21111-2-211110000i3i3i3i3−i3−i3−i3−i30000i3i3i3i3−i3−i3−i3−i32222-2-2-1-1-1-100i3−i3i3−i311000000000000
χ262222-1-2-2-1-1-122-1-1-1-10022-1-1-1-122-1-1-1-122-1-1-1-111i3−i3i3−i3-2-21111-2-211110000i3i3i3i3−i3−i3−i3−i30000i3i3i3i3−i3−i3−i3−i3-2-2-2-222111100−i3i3−i3i3-1-1000000000000
χ2722-2-22-222-2-222222200-2-2-2-2-2-2222222-2-2-2-2-2-2-220000-2-2-2-2-2-22222220000000000000000000000002i−2i2i−2i−2i2i2i2i−2i−2i000000−2i2i000000000000
χ2822-2-22-222-2-222222200-2-2-2-2-2-2222222-2-2-2-2-2-2-220000-2-2-2-2-2-2222222000000000000000000000000−2i2i−2i2i2i−2i−2i−2i2i2i0000002i−2i000000000000
χ2922-2-2-12-2-11122-1-1-1-12i−2i-2-2111122-1-1-1-1-2-21111-11−i−iii22-1-1-1-1-2-211112i2i2i2i−i−i−i−i−i−i−i−i−2i−2i−2i−2iiiiiiiii2i−2i2i−2i2i−2i−i−iii2-2-1-111−ii000000000000
χ3022-2-2-12-2-11122-1-1-1-12i−2i-2-2111122-1-1-1-1-2-21111-11−i−iii22-1-1-1-1-2-211112i2i2i2i−i−i−i−i−i−i−i−i−2i−2i−2i−2iiiiiiiii−2i2i−2i2i−2i2iii−i−i-2211-1-1i−i000000000000
χ3122-2-2-12-2-11122-1-1-1-1−2i2i-2-2111122-1-1-1-1-2-21111-11ii−i−i22-1-1-1-1-2-21111−2i−2i−2i−2iiiiiiiii2i2i2i2i−i−i−i−i−i−i−i−i2i−2i2i−2i2i−2i−i−iii-2211-1-1−ii000000000000
χ3222-2-2-12-2-11122-1-1-1-1−2i2i-2-2111122-1-1-1-1-2-21111-11ii−i−i22-1-1-1-1-2-21111−2i−2i−2i−2iiiiiiiii2i2i2i2i−i−i−i−i−i−i−i−i−2i2i−2i2i−2i2iii−i−i2-2-1-111i−i000000000000
χ3322-2-2-1-22-11122-1-1-1-100-2-2111122-1-1-1-1-2-211111-13−3−33-2-2111122-1-1-1-100003333−3−3−3−30000−3−3−3−333332i−2i2i−2i−2i2i−i−iii00−i3i3i3−i3i−i000000000000
χ3422-2-2-1-22-11122-1-1-1-100-2-2111122-1-1-1-1-2-211111-13−3−33-2-2111122-1-1-1-100003333−3−3−3−30000−3−3−3−33333−2i2i−2i2i2i−2iii−i−i00i3−i3−i3i3−ii000000000000
χ3522-2-2-1-22-11122-1-1-1-100-2-2111122-1-1-1-1-2-211111-1−333−3-2-2111122-1-1-1-10000−3−3−3−3333300003333−3−3−3−32i−2i2i−2i−2i2i−i−iii00i3−i3−i3i3i−i000000000000
χ3622-2-2-1-22-11122-1-1-1-100-2-2111122-1-1-1-1-2-211111-1−333−3-2-2111122-1-1-1-10000−3−3−3−3333300003333−3−3−3−3−2i2i−2i2i2i−2iii−i−i00−i3i3i3−i3−ii000000000000
χ372-22-2200-22-222222200222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000002i−2i−2i2i002i−2i2i−2i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ382-22-2200-22-222222200222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000002i−2i−2i2i002i−2i2i−2i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ392-22-2200-22-222222200222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000−2i2i2i−2i00−2i2i−2i2i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ402-22-2200-22-222222200222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000−2i2i2i−2i00−2i2i−2i2i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ412-2-22200-2-2222222200-2-2-2-2-2-2-2-2-2-2-2-222222200000000000000000000000000000000000000000022-2-2002-2-2200000000−i2i2i2−i2i2−i2−i2i20000
χ422-2-22200-2-2222222200-2-2-2-2-2-2-2-2-2-2-2-222222200000000000000000000000000000000000000000022-2-2002-2-2200000000i2−i2−i2i2−i2i2i2−i20000
χ432-2-22200-2-2222222200-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000000000000000000000-2-22200-222-2000000002−2−222−2−220000
χ442-2-22200-2-2222222200-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000000000000000000000-2-22200-222-200000000−222−2−222−20000
χ4544444444441-211-2-2441-211-2-21-211-2-21-211-2-24444441-211-2-21-211-2-211-2-211-2-211-2-211-2-211-2-211-2-2000000000000000000000000000000
χ4644444444441-211-2-2-4-41-211-2-21-211-2-21-211-2-244-4-4-4-41-211-2-21-211-2-2-1-122-1-122-1-122-1-122-1-122-1-122000000000000000000000000000000
χ474444444444-21-2-21144-21-2-211-21-2-211-21-2-211444444-21-2-211-21-2-211-2-211-2-211-2-211-2-211-2-211-2-211000000000000000000000000000000
χ484444444444-21-2-211-4-4-21-2-211-21-2-211-21-2-21144-4-4-4-4-21-2-211-21-2-21122-1-122-1-122-1-122-1-122-1-122-1-1000000000000000000000000000000
χ4944444-4-44441-211-2-2001-211-2-21-211-2-21-211-2-2-4-40000-12-1-122-12-1-1223-3003-3003-3003-3003-3003-300000000000000000000000000000000
χ5044444-4-44441-211-2-2001-211-2-21-211-2-21-211-2-2-4-40000-12-1-122-12-1-122-3300-3300-3300-3300-3300-3300000000000000000000000000000000
χ5144444-4-4444-21-2-21100-21-2-211-21-2-211-21-2-211-4-400002-122-1-12-122-1-1003-3003-3003-3003-3003-3003-3000000000000000000000000000000
χ5244444-4-4444-21-2-21100-21-2-211-21-2-211-21-2-211-4-400002-122-1-12-122-1-100-3300-3300-3300-3300-3300-33000000000000000000000000000000
χ534444-244-2-2-21-2−1−3i32−1+3i3211441-2−1−3i32−1+3i32111-2−1−3i32−1+3i32111-2−1−3i32−1+3i3211-2-2-2-2-2-21-2−1−3i32−1+3i32111-2−1−3i32−1+3i321111-2-2−1−3i32−1+3i3211−1+3i32−1−3i321111-2-2−1−3i32−1+3i3211−1+3i32−1−3i3211000000000000000000000000000000
χ544444-244-2-2-21-2−1−3i32−1+3i3211-4-41-2−1−3i32−1+3i32111-2−1−3i32−1+3i32111-2−1−3i32−1+3i3211-2-222221-2−1−3i32−1+3i32111-2−1−3i32−1+3i3211-1-1221+3i321−3i32-1-11−3i321+3i32-1-1-1-1221+3i321−3i32-1-11−3i321+3i32-1-1000000000000000000000000000000
χ554444-244-2-2-21-2−1+3i32−1−3i3211441-2−1+3i32−1−3i32111-2−1+3i32−1−3i32111-2−1+3i32−1−3i3211-2-2-2-2-2-21-2−1+3i32−1−3i32111-2−1+3i32−1−3i321111-2-2−1+3i32−1−3i3211−1−3i32−1+3i321111-2-2−1+3i32−1−3i3211−1−3i32−1+3i3211000000000000000000000000000000
χ564444-244-2-2-21-2−1+3i32−1−3i3211-4-41-2−1+3i32−1−3i32111-2−1+3i32−1−3i32111-2−1+3i32−1−3i3211-2-222221-2−1+3i32−1−3i32111-2−1+3i32−1−3i3211-1-1221−3i321+3i32-1-11+3i321−3i32-1-1-1-1221−3i321+3i32-1-11+3i321−3i32-1-1000000000000000000000000000000
χ574444-244-2-2-2-2111−1−3i32−1+3i3244-2111−1−3i32−1+3i32-2111−1−3i32−1+3i32-2111−1−3i32−1+3i32-2-2-2-2-2-2-2111−1−3i32−1+3i32-2111−1−3i32−1+3i32-2-21111−1−3i32−1+3i3211−1+3i32−1−3i32-2-21111−1−3i32−1+3i3211−1+3i32−1−3i32000000000000000000000000000000
χ584444-244-2-2-2-2111−1−3i32−1+3i32-4-4-2111−1−3i32−1+3i32-2111−1−3i32−1+3i32-2111−1−3i32−1+3i32-2-22222-2111−1−3i32−1+3i32-2111−1−3i32−1+3i3222-1-1-1-11+3i321−3i32-1-11−3i321+3i3222-1-1-1-11+3i321−3i32-1-11−3i321+3i32000000000000000000000000000000
χ594444-244-2-2-2-2111−1+3i32−1−3i3244-2111−1+3i32−1−3i32-2111−1+3i32−1−3i32-2111−1+3i32−1−3i32-2-2-2-2-2-2-2111−1+3i32−1−3i32-2111−1+3i32−1−3i32-2-21111−1+3i32−1−3i3211−1−3i32−1+3i32-2-21111−1+3i32−1−3i3211−1−3i32−1+3i32000000000000000000000000000000
χ604444-244-2-2-2-2111−1+3i32−1−3i32-4-4-2111−1+3i32−1−3i32-2111−1+3i32−1−3i32-2111−1+3i32−1−3i32-2-22222-2111−1+3i32−1−3i32-2111−1+3i32−1−3i3222-1-1-1-11−3i321+3i32-1-11+3i321−3i3222-1-1-1-11−3i321+3i32-1-11+3i321−3i32000000000000000000000000000000
χ614444-2-4-4-2-2-21-2−1−3i32−1+3i3211001-2−1−3i32−1+3i32111-2−1−3i32−1+3i32111-2−1−3i32−1+3i321122−2i32i3−2i32i3-121+3i321−3i32-1-1-121+3i321−3i32-1-13-300−3−i323−i32i3i3−3+i323+i32−i3−i33-300−3−i323−i32i3i3−3+i323+i32−i3−i3000000000000000000000000000000
χ624444-2-4-4-2-2-21-2−1−3i32−1+3i3211001-2−1−3i32−1+3i32111-2−1−3i32−1+3i32111-2−1−3i32−1+3i3211222i3−2i32i3−2i3-121+3i321−3i32-1-1-121+3i321−3i32-1-1-33003+i32−3+i32−i3−i33−i32−3−i32i3i3-33003+i32−3+i32−i3−i33−i32−3−i32i3i3000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.