Finite Group Databasebeta

← Group #13173437

Character table — Group #13173437

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1122222224444444444444444444444444444444488888888888888888888888888888888888899181818181818183636363636363636108108108108108108108108
order1223446121223333334666666666121212121212121212121212121212666666666666666666121212121212121212121212121212121212442246612122466612121244448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ411111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii
χ5111111111-1111111-11-1-11111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-11-1-11111-1-1-1-1
χ6111111111-1111111-11-1-11111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-11-1-1-1-1-1-11111
χ7111111111-1111111-11-1-11111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-111ii−i−i−i−iii
χ8111111111-1111111-11-1-11111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-111−i−iiiii−i−i
χ911-111-11-1-11111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-111-111-1-1-1111-11-11-11-1
χ1011-111-11-1-11111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-111-111-1-1-111-11-11-11-11
χ1111-111-11-1-11111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-11-1-1111-1-1i−i−iii−i−ii
χ1211-111-11-1-11111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-11-1-1111-1-1−iii−i−iii−i
χ1311-111-11-1-1-11111111-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-11-1-1-1111-1111-1-1-11-11-1-11-11
χ1411-111-11-1-1-11111111-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-11-1-1-1111-1111-1-1-1-11-111-11-1
χ1511-111-11-1-1-11111111-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-11-1111-1-1-11-1-1-1111i−i−ii−iii−i
χ1611-111-11-1-1-11111111-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-11-1111-1-1-11-1-1-1111−iii−ii−i−ii
χ172222-2-22-2-202222220200222222-200-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000-2-2-2-2-2-200000000000022-2-22-2-22200-20020000000000
χ182222-2-22-2-202222220200222222-200-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000-2-2-2-2-2-2000000000000-2-222-222-2-200200-20000000000
χ19222-122-1-1-1222-1-1-1-12-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-122222-1-1-1-122-1-1-1-1-1-100000000
χ20222-122-1-1-1222-1-1-1-12-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-21111-2-211111100000000
χ21222-122-1-1-1-222-1-1-1-1-2-11122-1-1-1-1-1112222-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-21111111122-1-1-1-1-2-2-2-21111111122222-1-1-1-1-2-2-111-11100000000
χ22222-122-1-1-1-222-1-1-1-1-2-11122-1-1-1-1-1112222-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-21111111122-1-1-1-1-2-2-2-211111111-2-2-2-2-21111221-1-11-1-100000000
χ23222-1-2-2-111022-1-1-1-10-1−i3i322-1-1-1-11−i3i3-2-2-2-21111111122-1-1-1-10000−i3−i3−i3−i3i3i3i3i3-2-211110000−i3−i3−i3−i3i3i3i3i322-2-2211-1-1001−i3i3-1−i3i300000000
χ24222-1-2-2-111022-1-1-1-10-1−i3i322-1-1-1-11−i3i3-2-2-2-21111111122-1-1-1-10000−i3−i3−i3−i3i3i3i3i3-2-211110000−i3−i3−i3−i3i3i3i3i3-2-222-2-1-11100-1i3−i31i3−i300000000
χ25222-1-2-2-111022-1-1-1-10-1i3−i322-1-1-1-11i3−i3-2-2-2-21111111122-1-1-1-10000i3i3i3i3−i3−i3−i3−i3-2-211110000i3i3i3i3−i3−i3−i3−i322-2-2211-1-1001i3−i3-1i3−i300000000
χ26222-1-2-2-111022-1-1-1-10-1i3−i322-1-1-1-11i3−i3-2-2-2-21111111122-1-1-1-10000i3i3i3i3−i3−i3−i3−i3-2-211110000i3i3i3i3−i3−i3−i3−i3-2-222-2-1-11100-1−i3i31−i3i300000000
χ2722-22-2222202222220-200222222-200222222222222-2-2-2-2-2-2000000000000-2-2-2-2-2-2000000000000222-2-2222200-200-20000000000
χ2822-22-2222202222220-200222222-200222222222222-2-2-2-2-2-2000000000000-2-2-2-2-2-2000000000000-2-2-222-2-2-2-20020020000000000
χ2922-2-12-2-111222-1-1-1-1-21-1-122-1-1-1-1-111-2-2-2-211111111-2-211112222-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-21111111122-22-211-1-1-22-1111-1-100000000
χ3022-2-12-2-111222-1-1-1-1-21-1-122-1-1-1-1-111-2-2-2-211111111-2-211112222-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-211111111-2-22-22-1-1112-21-1-1-11100000000
χ3122-2-12-2-111-222-1-1-1-1211122-1-1-1-1-1-1-1-2-2-2-211111111-2-21111-2-2-2-21111111122-1-1-1-12222-1-1-1-1-1-1-1-122-22-211-1-12-2-1-1-111100000000
χ3222-2-12-2-111-222-1-1-1-1211122-1-1-1-1-1-1-1-2-2-2-211111111-2-21111-2-2-2-21111111122-1-1-1-12222-1-1-1-1-1-1-1-1-2-22-22-1-111-22111-1-1-100000000
χ3322-2-1-22-1-1-1022-1-1-1-101−i3i322-1-1-1-11i3−i32222-1-1-1-1-1-1-1-1-2-211110000−i3−i3−i3−i3i3i3i3i3-2-211110000i3i3i3i3−i3−i3−i3−i3222-2-2-1-1-1-1001i3−i31−i3i300000000
χ3422-2-1-22-1-1-1022-1-1-1-101−i3i322-1-1-1-11i3−i32222-1-1-1-1-1-1-1-1-2-211110000−i3−i3−i3−i3i3i3i3i3-2-211110000i3i3i3i3−i3−i3−i3−i3-2-2-222111100-1−i3i3-1i3−i300000000
χ3522-2-1-22-1-1-1022-1-1-1-101i3−i322-1-1-1-11−i3i32222-1-1-1-1-1-1-1-1-2-211110000i3i3i3i3−i3−i3−i3−i3-2-211110000−i3−i3−i3−i3i3i3i3i3222-2-2-1-1-1-1001−i3i31i3−i300000000
χ3622-2-1-22-1-1-1022-1-1-1-101i3−i322-1-1-1-11−i3i32222-1-1-1-1-1-1-1-1-2-211110000i3i3i3i3−i3−i3−i3−i3-2-211110000−i3−i3−i3−i3i3i3i3i3-2-2-222111100-1i3−i3-1−i3i300000000
χ3744444444441-211-2-244441-211-2-244411-2-21111-2-2-2-21-211-2-211-2-211-2-211-2-21-211-2-211-2-211-2-211-2-20000000000000000000000000
χ384444444444-21-2-2114444-21-2-211444-2-211-2-2-2-21111-21-2-211-2-211-2-211-2-211-21-2-211-2-211-2-211-2-2110000000000000000000000000
χ39444444444-41-211-2-2-44-4-41-211-2-24-4-411-2-21111-2-2-2-21-211-2-2-1-122-1-122-1-1221-211-2-2-1-122-1-122-1-1220000000000000000000000000
χ40444444444-4-21-2-211-44-4-4-21-2-2114-4-4-2-211-2-2-2-21111-21-2-21122-1-122-1-122-1-1-21-2-21122-1-122-1-122-1-10000000000000000000000000
χ414444-4-44-4-401-211-2-204001-211-2-2-400-1-122-1-1-1-122221-211-2-23-3003-3003-300-12-1-1223-3003-3003-3000000000000000000000000000
χ424444-4-44-4-401-211-2-204001-211-2-2-400-1-122-1-1-1-122221-211-2-2-3300-3300-3300-12-1-122-3300-3300-33000000000000000000000000000
χ434444-4-44-4-40-21-2-2110400-21-2-211-40022-1-12222-1-1-1-1-21-2-211003-3003-3003-32-122-1-1003-3003-3003-30000000000000000000000000
χ444444-4-44-4-40-21-2-2110400-21-2-211-40022-1-12222-1-1-1-1-21-2-21100-3300-3300-332-122-1-100-3300-3300-330000000000000000000000000
χ45444-244-2-2-241-2−1−3i32−1+3i32114-2-2-21-2−1−3i32−1+3i3211-2-2-211-2-2−1−3i32−1−3i32−1+3i32−1+3i3211111-2−1−3i32−1+3i321111-2-2−1−3i32−1+3i3211−1+3i32−1−3i32111-2−1−3i32−1+3i321111-2-2−1−3i32−1+3i3211−1+3i32−1−3i32110000000000000000000000000
χ46444-244-2-2-241-2−1+3i32−1−3i32114-2-2-21-2−1+3i32−1−3i3211-2-2-211-2-2−1+3i32−1+3i32−1−3i32−1−3i3211111-2−1+3i32−1−3i321111-2-2−1+3i32−1−3i3211−1−3i32−1+3i32111-2−1+3i32−1−3i321111-2-2−1+3i32−1−3i3211−1−3i32−1+3i32110000000000000000000000000
χ47444-244-2-2-24-2111−1−3i32−1+3i324-2-2-2-2111−1−3i32−1+3i32-2-2-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2111−1−3i32−1+3i32-2-21111−1−3i32−1+3i3211−1+3i32−1−3i32-2111−1−3i32−1+3i32-2-21111−1−3i32−1+3i3211−1+3i32−1−3i320000000000000000000000000
χ48444-244-2-2-24-2111−1+3i32−1−3i324-2-2-2-2111−1+3i32−1−3i32-2-2-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2111−1+3i32−1−3i32-2-21111−1+3i32−1−3i3211−1−3i32−1+3i32-2111−1+3i32−1−3i32-2-21111−1+3i32−1−3i3211−1−3i32−1+3i320000000000000000000000000
χ49444-244-2-2-2-41-2−1−3i32−1+3i3211-4-2221-2−1−3i32−1+3i3211-22211-2-2−1−3i32−1−3i32−1+3i32−1+3i3211111-2−1−3i32−1+3i3211-1-1221+3i321−3i32-1-11−3i321+3i32-1-11-2−1−3i32−1+3i3211-1-1221+3i321−3i32-1-11−3i321+3i32-1-10000000000000000000000000
χ50444-244-2-2-2-41-2−1+3i32−1−3i3211-4-2221-2−1+3i32−1−3i3211-22211-2-2−1+3i32−1+3i32−1−3i32−1−3i3211111-2−1+3i32−1−3i3211-1-1221−3i321+3i32-1-11+3i321−3i32-1-11-2−1+3i32−1−3i3211-1-1221−3i321+3i32-1-11+3i321−3i32-1-10000000000000000000000000
χ51444-244-2-2-2-4-2111−1−3i32−1+3i32-4-222-2111−1−3i32−1+3i32-222-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2111−1−3i32−1+3i3222-1-1-1-11+3i321−3i32-1-11−3i321+3i32-2111−1−3i32−1+3i3222-1-1-1-11+3i321−3i32-1-11−3i321+3i320000000000000000000000000
χ52444-244-2-2-2-4-2111−1+3i32−1−3i32-4-222-2111−1+3i32−1−3i32-222-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2111−1+3i32−1−3i3222-1-1-1-11−3i321+3i32-1-11+3i321−3i32-2111−1+3i32−1−3i3222-1-1-1-11−3i321+3i32-1-11+3i321−3i320000000000000000000000000
χ53444-2-4-4-22201-2−1−3i32−1+3i32110-2−2i32i31-2−1−3i32−1+3i32112−2i32i3-1-1221+3i321+3i321−3i321−3i32-1-1-1-11-2−1−3i32−1+3i32113-300−3−i323−i32i3i3−3+i323+i32−i3−i3-121+3i321−3i32-1-13-300−3−i323−i32i3i3−3+i323+i32−i3−i30000000000000000000000000
χ54444-2-4-4-22201-2−1−3i32−1+3i32110-22i3−2i31-2−1−3i32−1+3i321122i3−2i3-1-1221+3i321+3i321−3i321−3i32-1-1-1-11-2−1−3i32−1+3i3211-33003+i32−3+i32−i3−i33−i32−3−i32i3i3-121+3i321−3i32-1-1-33003+i32−3+i32−i3−i33−i32−3−i32i3i30000000000000000000000000
χ55444-2-4-4-22201-2−1+3i32−1−3i32110-2−2i32i31-2−1+3i32−1−3i32112−2i32i3-1-1221−3i321−3i321+3i321+3i32-1-1-1-11-2−1+3i32−1−3i3211-33003−i32−3−i32i3i33+i32−3+i32−i3−i3-121−3i321+3i32-1-1-33003−i32−3−i32i3i33+i32−3+i32−i3−i30000000000000000000000000
χ56444-2-4-4-22201-2−1+3i32−1−3i32110-22i3−2i31-2−1+3i32−1−3i321122i3−2i3-1-1221−3i321−3i321+3i321+3i32-1-1-1-11-2−1+3i32−1−3i32113-300−3+i323+i32−i3−i3−3−i323−i32i3i3-121−3i321+3i32-1-13-300−3+i323+i32−i3−i3−3−i323−i32i3i30000000000000000000000000
χ57444-2-4-4-2220-2111−1−3i32−1+3i320-2−2i32i3-2111−1−3i32−1+3i322−2i32i322-1-1-1-1-1-11+3i321+3i321−3i321−3i32-2111−1−3i32−1+3i32003-3i3i3−3−i323−i32−i3−i3−3+i323+i322-1-1-11+3i321−3i32003-3i3i3−3−i323−i32−i3−i3−3+i323+i320000000000000000000000000
χ58444-2-4-4-2220-2111−1−3i32−1+3i320-22i3−2i3-2111−1−3i32−1+3i3222i3−2i322-1-1-1-1-1-11+3i321+3i321−3i321−3i32-2111−1−3i32−1+3i3200-33−i3−i33+i32−3+i32i3i33−i32−3−i322-1-1-11+3i321−3i3200-33−i3−i33+i32−3+i32i3i33−i32−3−i320000000000000000000000000
χ59444-2-4-4-2220-2111−1+3i32−1−3i320-2−2i32i3-2111−1+3i32−1−3i322−2i32i322-1-1-1-1-1-11−3i321−3i321+3i321+3i32-2111−1+3i32−1−3i3200-33i3i33−i32−3−i32−i3−i33+i32−3+i322-1-1-11−3i321+3i3200-33i3i33−i32−3−i32−i3−i33+i32−3+i320000000000000000000000000
χ60444-2-4-4-2220-2111−1+3i32−1−3i320-22i3−2i3-2111−1+3i32−1−3i3222i3−2i322-1-1-1-1-1-11−3i321−3i321+3i321+3i32-2111−1+3i32−1−3i32003-3−i3−i3−3+i323+i32i3i3−3−i323−i322-1-1-11−3i321+3i32003-3−i3−i3−3+i323+i32i3i3−3−i323−i320000000000000000000000000
χ6144-444-44-4-441-211-2-2-4-4441-211-2-24-4-4-1-122-1-1-1-12222-12-1-12211-2-211-2-211-2-21-211-2-2-1-122-1-122-1-1220000000000000000000000000
χ6244-444-44-4-44-21-2-211-4-444-21-2-2114-4-422-1-12222-1-1-1-12-122-1-1-2-211-2-211-2-211-21-2-21122-1-122-1-122-1-10000000000000000000000000
χ6344-444-44-4-4-41-211-2-24-4-4-41-211-2-2444-1-122-1-1-1-12222-12-1-122-1-122-1-122-1-1221-211-2-211-2-211-2-211-2-20000000000000000000000000
χ6444-444-44-4-4-4-21-2-2114-4-4-4-21-2-21144422-1-12222-1-1-1-12-122-1-122-1-122-1-122-1-1-21-2-211-2-211-2-211-2-2110000000000000000000000000
χ6544-44-4444401-211-2-20-4001-211-2-2-40011-2-21111-2-2-2-2-12-1-1223-3003-3003-300-12-1-122-3300-3300-33000000000000000000000000000
χ6644-44-4444401-211-2-20-4001-211-2-2-40011-2-21111-2-2-2-2-12-1-122-3300-3300-3300-12-1-1223-3003-3003-3000000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.