Finite Group Databasebeta

← Group #13157206

Character table — Group #13157206

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222244444444444444444444444444444444888888888888888888888888888888888888999918181818181836363636363636365454545454545454108108108108
order12442346121233333366666668812121212121212121212121212242424246666661212121212122424242424242424242424242424242424242424242424242244246612126881224242424444444444444
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
χ511111111111111111111111-1-11111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11-1-1-1-111111111-1-1-1-1
χ611111111111111111111111-1-11111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111-1-11111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111iiii−i−i−i−i−i−iii
χ811111111111111111111111-1-11111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111−i−i−i−iiiiiii−i−i
χ911-1-1-1111-1-1111111-1111111i−i1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1-1-1-1-1111111iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i11-1-1-1111-1-1-1i−i1ii−i−iii−i−iii−i−i1-11-1
χ1011-1-1-1111-1-1111111-1111111i−i1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1-1-1-1-1111111iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i11-1-1-1111-1-1-1i−i1ii−i−i−i−iii−i−iii-11-11
χ1111-1-1-1111-1-1111111-1111111i−i1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1-1-1-1-1111111iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i-1-1111-1-1-1111−ii-1−i−iii11-1-1-1-111−iii−i
χ1211-1-1-1111-1-1111111-1111111i−i1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1-1-1-1-1111111iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i-1-1111-1-1-1111−ii-1−i−iii-1-11111-1-1i−i−ii
χ1311-1-1-1111-1-1111111-1111111−ii1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1-1-1-1-1111111−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii11-1-1-1111-1-1-1−ii1−i−iiiii−i−iii−i−i-11-11
χ1411-1-1-1111-1-1111111-1111111−ii1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1-1-1-1-1111111−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii11-1-1-1111-1-1-1−ii1−i−iii−i−iii−i−iii1-11-1
χ1511-1-1-1111-1-1111111-1111111−ii1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1-1-1-1-1111111−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii-1-1111-1-1-1111i−i-1ii−i−i11-1-1-1-111i−i−ii
χ1611-1-1-1111-1-1111111-1111111−ii1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1-1-1-1-1111111−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii-1-1111-1-1-1111i−i-1ii−i−i-1-11111-1-1−iii−i
χ1722222-12-1-1-122-1-1-1-1-122-1-1-1-122-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222-1-1-1-1-122-1-1-1-1-1000000000000
χ1822222-12-1-1-122-1-1-1-1-122-1-1-1-122-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-211111-2-211111000000000000
χ1922222-12-1-1-122-1-1-1-1-122-1-1-1-1-2-2-12222-1-1-1-1-1-1-1-1111122-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-211111111222222-1-1-1-1-1-2-2-11111000000000000
χ2022222-12-1-1-122-1-1-1-1-122-1-1-1-1-2-2-12222-1-1-1-1-1-1-1-1111122-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2-2-2-2-211111221-1-1-1-1000000000000
χ212222-22-2222222222-222222200-22222222222220000-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000002222-2-22222-200-20000000000000000
χ222222-22-2222222222-222222200-22222222222220000-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000-2-2-2-222-2-2-2-220020000000000000000
χ232222-2-1-2-1-1-122-1-1-1-1122-1-1-1-10012222-1-1-1-1-1-1-1-1−i3i3−i3i3-2-21111-2-211110000−i3−i3−i3−i3i3i3i3i30000−i3−i3−i3−i3i3i3i3i32222-2-2-1-1-1-11001−i3i3−i3i3000000000000
χ242222-2-1-2-1-1-122-1-1-1-1122-1-1-1-10012222-1-1-1-1-1-1-1-1−i3i3−i3i3-2-21111-2-211110000−i3−i3−i3−i3i3i3i3i30000−i3−i3−i3−i3i3i3i3i3-2-2-2-2221111-100-1i3−i3i3−i3000000000000
χ252222-2-1-2-1-1-122-1-1-1-1122-1-1-1-10012222-1-1-1-1-1-1-1-1i3−i3i3−i3-2-21111-2-211110000i3i3i3i3−i3−i3−i3−i30000i3i3i3i3−i3−i3−i3−i32222-2-2-1-1-1-11001i3−i3i3−i3000000000000
χ262222-2-1-2-1-1-122-1-1-1-1122-1-1-1-10012222-1-1-1-1-1-1-1-1i3−i3i3−i3-2-21111-2-211110000i3i3i3i3−i3−i3−i3−i30000i3i3i3i3−i3−i3−i3−i3-2-2-2-2221111-100-1−i3i3−i3i3000000000000
χ2722-2-222-22-2-2222222222222200-2-2-2-2-2-2-2-2-2-2-2-2-20000222222-2-2-2-2-2-200000000000000000000000022-2-22-222-2-2200-20000000000000000
χ2822-2-222-22-2-2222222222222200-2-2-2-2-2-2-2-2-2-2-2-2-20000222222-2-2-2-2-2-2000000000000000000000000-2-222-22-2-222-20020000000000000000
χ2922-2-22-1-2-11122-1-1-1-1-122-1-1-1-1001-2-2-2-2111111113−3−3322-1-1-1-1-2-2111100003333−3−3−3−30000−3−3−3−3333322-2-22-2-1-111-10013−3−33000000000000
χ3022-2-22-1-2-11122-1-1-1-1-122-1-1-1-1001-2-2-2-2111111113−3−3322-1-1-1-1-2-2111100003333−3−3−3−30000−3−3−3−33333-2-222-2211-1-1100-1−333−3000000000000
χ3122-2-22-1-2-11122-1-1-1-1-122-1-1-1-1001-2-2-2-211111111−333−322-1-1-1-1-2-211110000−3−3−3−3333300003333−3−3−3−322-2-22-2-1-111-1001−333−3000000000000
χ3222-2-22-1-2-11122-1-1-1-1-122-1-1-1-1001-2-2-2-211111111−333−322-1-1-1-1-2-211110000−3−3−3−3333300003333−3−3−3−3-2-222-2211-1-1100-13−3−33000000000000
χ3322-2-2-2-12-11122-1-1-1-1122-1-1-1-12i−2i-1-2-2-2-211111111−i−iii-2-2111122-1-1-1-12i2i2i2i−i−i−i−i−i−i−i−i−2i−2i−2i−2iiiiiiiii22-2-2-22-1-11112i−2i-1−i−iii000000000000
χ3422-2-2-2-12-11122-1-1-1-1122-1-1-1-12i−2i-1-2-2-2-211111111−i−iii-2-2111122-1-1-1-12i2i2i2i−i−i−i−i−i−i−i−i−2i−2i−2i−2iiiiiiiii-2-2222-211-1-1-1−2i2i1ii−i−i000000000000
χ3522-2-2-2-12-11122-1-1-1-1122-1-1-1-1−2i2i-1-2-2-2-211111111ii−i−i-2-2111122-1-1-1-1−2i−2i−2i−2iiiiiiiii2i2i2i2i−i−i−i−i−i−i−i−i22-2-2-22-1-1111−2i2i-1ii−i−i000000000000
χ3622-2-2-2-12-11122-1-1-1-1122-1-1-1-1−2i2i-1-2-2-2-211111111ii−i−i-2-2111122-1-1-1-1−2i−2i−2i−2iiiiiiiii2i2i2i2i−i−i−i−i−i−i−i−i-2-2222-211-1-1-12i−2i1−i−iii000000000000
χ372-22i−2i020-22i−2i2222220-2-2-2-2-2-20002i2i−2i−2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000000000002-22i−2i002-22i−2i000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000
χ382-22i−2i020-22i−2i2222220-2-2-2-2-2-20002i2i−2i−2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000000000002-22i−2i002-22i−2i00000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000
χ392-22i−2i020-22i−2i2222220-2-2-2-2-2-20002i2i−2i−2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000-22−2i2i00-22−2i2i000000001−i−1+i−1−i1+i−1+i1−i1+i−1−i0000
χ402-22i−2i020-22i−2i2222220-2-2-2-2-2-20002i2i−2i−2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000-22−2i2i00-22−2i2i00000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i0000
χ412-2−2i2i020-2−2i2i2222220-2-2-2-2-2-2000−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000000000002-2−2i2i002-2−2i2i000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000
χ422-2−2i2i020-2−2i2i2222220-2-2-2-2-2-2000−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000000000002-2−2i2i002-2−2i2i00000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000
χ432-2−2i2i020-2−2i2i2222220-2-2-2-2-2-2000−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000-222i−2i00-222i−2i000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i0000
χ442-2−2i2i020-2−2i2i2222220-2-2-2-2-2-2000−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000-222i−2i00-222i−2i00000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i0000
χ4544444444441-211-2-241-211-2-24441-21-211-2-211-2-244441-211-2-21-211-2-211-2-211-2-211-2-211-2-211-2-211-2-2000000000000000000000000000000
χ4644444444441-211-2-241-211-2-2-4-441-21-211-2-211-2-2-4-4-4-41-211-2-21-211-2-2-1-122-1-122-1-122-1-122-1-122-1-122000000000000000000000000000000
χ474444444444-21-2-2114-21-2-211444-21-21-2-211-2-2114444-21-2-211-21-2-211-2-211-2-211-2-211-2-211-2-211-2-211000000000000000000000000000000
χ484444444444-21-2-2114-21-2-211-4-44-21-21-2-211-2-211-4-4-4-4-21-2-211-21-2-21122-1-122-1-122-1-122-1-122-1-122-1-1000000000000000000000000000000
χ4944444-24-2-2-21-2−1−3i32−1+3i3211-21-2−1−3i32−1+3i321144-21-21-2−1−3i32−1+3i3211−1−3i32−1+3i3211-2-2-2-21-2−1−3i32−1+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
χ5044444-24-2-2-21-2−1−3i32−1+3i3211-21-2−1−3i32−1+3i3211-4-4-21-21-2−1−3i32−1+3i3211−1−3i32−1+3i321122221-2−1−3i32−1+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
χ5144444-24-2-2-21-2−1+3i32−1−3i3211-21-2−1+3i32−1−3i321144-21-21-2−1+3i32−1−3i3211−1+3i32−1−3i3211-2-2-2-21-2−1+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
χ5244444-24-2-2-21-2−1+3i32−1−3i3211-21-2−1+3i32−1−3i3211-4-4-21-21-2−1+3i32−1−3i3211−1+3i32−1−3i321122221-2−1+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
χ5344444-24-2-2-2-2111−1−3i32−1+3i32-2-2111−1−3i32−1+3i3244-2-21-2111−1−3i32−1+3i3211−1−3i32−1+3i32-2-2-2-2-2111−1−3i32−1+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
χ5444444-24-2-2-2-2111−1−3i32−1+3i32-2-2111−1−3i32−1+3i32-4-4-2-21-2111−1−3i32−1+3i3211−1−3i32−1+3i322222-2111−1−3i32−1+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
χ5544444-24-2-2-2-2111−1+3i32−1−3i32-2-2111−1+3i32−1−3i3244-2-21-2111−1+3i32−1−3i3211−1+3i32−1−3i32-2-2-2-2-2111−1+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
χ5644444-24-2-2-2-2111−1+3i32−1−3i32-2-2111−1+3i32−1−3i32-4-4-2-21-2111−1+3i32−1−3i3211−1+3i32−1−3i322222-2111−1+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
χ574444-44-44441-211-2-2-41-211-2-200-41-21-211-2-211-2-20000-12-1-122-12-1-1223-3003-300-33003-3003-300-3300000000000000000000000000000000
χ584444-44-44441-211-2-2-41-211-2-200-41-21-211-2-211-2-20000-12-1-122-12-1-122-3300-33003-300-3300-33003-300000000000000000000000000000000
χ594444-44-4444-21-2-211-4-21-2-21100-4-21-21-2-211-2-21100002-122-1-12-122-1-1003-3003-300-33003-3003-300-33000000000000000000000000000000
χ604444-44-4444-21-2-211-4-21-2-21100-4-21-21-2-211-2-21100002-122-1-12-122-1-100-3300-33003-300-3300-33003-3000000000000000000000000000000
χ614444-4-2-4-2-2-21-2−1−3i32−1+3i321121-2−1−3i32−1+3i32110021-21-2−1−3i32−1+3i3211−1−3i32−1+3i3211−2i32i3−2i32i3-121+3i321−3i32-1-1-121+3i321−3i32-1-13-300−3−i323−i32i3i33+i32−3+i32−i3−i33-300−3−i323−i32i3i33+i32−3+i32−i3−i3000000000000000000000000000000
χ624444-4-2-4-2-2-21-2−1−3i32−1+3i321121-2−1−3i32−1+3i32110021-21-2−1−3i32−1+3i3211−1−3i32−1+3i32112i3−2i32i3−2i3-121+3i321−3i32-1-1-121+3i321−3i32-1-1-33003+i32−3+i32−i3−i3−3−i323−i32i3i3-33003+i32−3+i32−i3−i3−3−i323−i32i3i3000000000000000000000000000000
χ634444-4-2-4-2-2-21-2−1+3i32−1−3i321121-2−1+3i32−1−3i32110021-21-2−1+3i32−1−3i3211−1+3i32−1−3i3211−2i32i3−2i32i3-121−3i321+3i32-1-1-121−3i321+3i32-1-1-33003−i32−3−i32i3i3−3+i323+i32−i3−i3-33003−i32−3−i32i3i3−3+i323+i32−i3−i3000000000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.