Finite Group Databasebeta

← Group #13173412

Character table — Group #13173412

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1122222224444444444444444444444444444444488888888888888888888888888888888888899181818181818183636363636363636108108108108108108108108
order1222236662333333466666666666666666666661212666666666666666666666666121212121212121212121212222226666246666121244444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ411111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ5111111111-1111111-111-1-1111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-1-1-111-1-111-1-1
χ6111111111-1111111-111-1-1111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-1-1-1-1-111-1-111
χ7111111111-1111111-111-1-1111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111ii−i−i−i−iii
χ8111111111-1111111-111-1-1111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−iiiii−i−i
χ9111-1-111111111111-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111111-1-1-111-1-1i−ii−ii−ii−i
χ10111-1-111111111111-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111111-1-1-111-1-1−ii−ii−ii−ii
χ11111-1-111111111111-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111-1-1111-11-1-11-11
χ12111-1-111111111111-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111-1-111-11-111-11-1
χ13111-1-11111-11111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-11111-11-1-1-1-111i−i−iii−i−ii
χ14111-1-11111-11111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-11111-11-1-1-1-111−iii−i−iii−i
χ15111-1-11111-11111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-111-1-1-1-11-11111-1-11-1-11-111-1
χ16111-1-11111-11111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-111-1-1-1-11-11111-1-1-111-11-1-11
χ1722222-1-1-1-1222-1-1-1-12-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222-1-1-1-122-1-1-1-1-1-100000000
χ1822222-1-1-1-1222-1-1-1-12-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-21111-2-211111100000000
χ1922222-1-1-1-1-222-1-1-1-1-2-1-1112222-1-1-1-1-1-1-1-122-1-1-1-1112222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-21111111122222-1-1-1-1-2-2-1-1111100000000
χ2022222-1-1-1-1-222-1-1-1-1-2-1-1112222-1-1-1-1-1-1-1-122-1-1-1-1112222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2-2-2-211112211-1-1-1-100000000
χ21222-2-2-1-1-1-1222-1-1-1-1-211-1-12222-1-1-1-1-1-1-1-122-1-1-1-111-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2-2-211111111222-2-2-1-1-1-12-211-1-11100000000
χ22222-2-2-1-1-1-1222-1-1-1-1-211-1-12222-1-1-1-1-1-1-1-122-1-1-1-111-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2221111-22-1-111-1-100000000
χ23222-2-2-1-1-1-1-222-1-1-1-1211112222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-211111111-2-2-2-2111111112222-1-1-1-1-1-1-1-1222-2-2-1-1-1-1-221111-1-100000000
χ24222-2-2-1-1-1-1-222-1-1-1-1211112222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-211111111-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2-22211112-2-1-1-1-11100000000
χ2522-22-22-2-22022222202-200-2-2-2-2-2-2-2-2-2-2-2-22222220022-2-22222-2-2-2-200000000000000000000000022-22-222-2-2002-2000000000000
χ2622-22-22-2-22022222202-200-2-2-2-2-2-2-2-2-2-2-2-22222220022-2-22222-2-2-2-2000000000000000000000000-2-22-22-2-22200-22000000000000
χ2722-22-2-111-1022-1-1-1-10-11−i3i3-2-2-2-21111111122-1-1-1-1−i3i322-2-2-1-1-1-111110000−i3−i3−i3−i3i3i3i3i30000−i3−i3−i3−i3i3i3i3i322-22-2-1-11100-11−i3i3−i3i300000000
χ2822-22-2-111-1022-1-1-1-10-11−i3i3-2-2-2-21111111122-1-1-1-1−i3i322-2-2-1-1-1-111110000−i3−i3−i3−i3i3i3i3i30000−i3−i3−i3−i3i3i3i3i3-2-22-2211-1-1001-1i3−i3i3−i300000000
χ2922-22-2-111-1022-1-1-1-10-11i3−i3-2-2-2-21111111122-1-1-1-1i3−i322-2-2-1-1-1-111110000i3i3i3i3−i3−i3−i3−i30000i3i3i3i3−i3−i3−i3−i322-22-2-1-11100-11i3−i3i3−i300000000
χ3022-22-2-111-1022-1-1-1-10-11i3−i3-2-2-2-21111111122-1-1-1-1i3−i322-2-2-1-1-1-111110000i3i3i3i3−i3−i3−i3−i30000i3i3i3i3−i3−i3−i3−i3-2-22-2211-1-1001-1−i3i3−i3i300000000
χ3122-2-222-2-2202222220-2200-2-2-2-2-2-2-2-2-2-2-2-222222200-2-222-2-2-2-2222200000000000000000000000022-2-2222-2-200-22000000000000
χ3222-2-222-2-2202222220-2200-2-2-2-2-2-2-2-2-2-2-2-222222200-2-222-2-2-2-22222000000000000000000000000-2-222-2-2-222002-2000000000000
χ3322-2-22-111-1022-1-1-1-101-1−i3i3-2-2-2-21111111122-1-1-1-1i3−i3-2-2221111-1-1-1-10000−i3−i3−i3−i3i3i3i3i30000i3i3i3i3−i3−i3−i3−i322-2-22-1-111001-1−i3i3i3−i300000000
χ3422-2-22-111-1022-1-1-1-101-1−i3i3-2-2-2-21111111122-1-1-1-1i3−i3-2-2221111-1-1-1-10000−i3−i3−i3−i3i3i3i3i30000i3i3i3i3−i3−i3−i3−i3-2-222-211-1-100-11i3−i3−i3i300000000
χ3522-2-22-111-1022-1-1-1-101-1i3−i3-2-2-2-21111111122-1-1-1-1−i3i3-2-2221111-1-1-1-10000i3i3i3i3−i3−i3−i3−i30000−i3−i3−i3−i3i3i3i3i322-2-22-1-111001-1i3−i3−i3i300000000
χ3622-2-22-111-1022-1-1-1-101-1i3−i3-2-2-2-21111111122-1-1-1-1−i3i3-2-2221111-1-1-1-10000i3i3i3i3−i3−i3−i3−i30000−i3−i3−i3−i3i3i3i3i3-2-222-211-1-100-11−i3i3i3−i300000000
χ3744444444441-211-2-24444411-2-21111-2-2-2-21-211-2-2441-21-211-2-211-2-211-2-211-2-211-2-211-2-211-2-211-2-20000000000000000000000000
χ384444444444-21-2-21144444-2-211-2-2-2-21111-21-2-21144-21-21-2-211-2-211-2-211-2-211-2-211-2-211-2-211-2-2110000000000000000000000000
χ39444444444-41-211-2-2-444-4-411-2-21111-2-2-2-21-211-2-2-4-41-21-211-2-211-2-2-1-122-1-122-1-122-1-122-1-122-1-1220000000000000000000000000
χ40444444444-4-21-2-211-444-4-4-2-211-2-2-2-21111-21-2-211-4-4-21-21-2-211-2-21122-1-122-1-122-1-122-1-122-1-122-1-10000000000000000000000000
χ4144444-2-2-2-241-2−1−3i32−1+3i32114-2-2-2-211-2-2−1−3i32−1−3i32−1+3i32−1+3i3211111-2−1−3i32−1+3i3211-2-21-21-2−1−3i32−1+3i3211−1−3i32−1+3i321111-2-2−1−3i32−1+3i3211−1−3i32−1+3i321111-2-2−1−3i32−1+3i3211−1−3i32−1+3i32110000000000000000000000000
χ4244444-2-2-2-241-2−1+3i32−1−3i32114-2-2-2-211-2-2−1+3i32−1+3i32−1−3i32−1−3i3211111-2−1+3i32−1−3i3211-2-21-21-2−1+3i32−1−3i3211−1+3i32−1−3i321111-2-2−1+3i32−1−3i3211−1+3i32−1−3i321111-2-2−1+3i32−1−3i3211−1+3i32−1−3i32110000000000000000000000000
χ4344444-2-2-2-24-2111−1−3i32−1+3i324-2-2-2-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2111−1−3i32−1+3i32-2-2-21-2111−1−3i32−1+3i3211−1−3i32−1+3i32-2-21111−1−3i32−1+3i3211−1−3i32−1+3i32-2-21111−1−3i32−1+3i3211−1−3i32−1+3i320000000000000000000000000
χ4444444-2-2-2-24-2111−1+3i32−1−3i324-2-2-2-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2111−1+3i32−1−3i32-2-2-21-2111−1+3i32−1−3i3211−1+3i32−1−3i32-2-21111−1+3i32−1−3i3211−1+3i32−1−3i32-2-21111−1+3i32−1−3i3211−1+3i32−1−3i320000000000000000000000000
χ4544444-2-2-2-2-41-2−1−3i32−1+3i3211-4-2-22211-2-2−1−3i32−1−3i32−1+3i32−1+3i3211111-2−1−3i32−1+3i3211221-21-2−1−3i32−1+3i3211−1−3i32−1+3i3211-1-1221+3i321−3i32-1-11+3i321−3i32-1-1-1-1221+3i321−3i32-1-11+3i321−3i32-1-10000000000000000000000000
χ4644444-2-2-2-2-41-2−1+3i32−1−3i3211-4-2-22211-2-2−1+3i32−1+3i32−1−3i32−1−3i3211111-2−1+3i32−1−3i3211221-21-2−1+3i32−1−3i3211−1+3i32−1−3i3211-1-1221−3i321+3i32-1-11−3i321+3i32-1-1-1-1221−3i321+3i32-1-11−3i321+3i32-1-10000000000000000000000000
χ4744444-2-2-2-2-4-2111−1−3i32−1+3i32-4-2-222-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2111−1−3i32−1+3i3222-21-2111−1−3i32−1+3i3211−1−3i32−1+3i3222-1-1-1-11+3i321−3i32-1-11+3i321−3i3222-1-1-1-11+3i321−3i32-1-11+3i321−3i320000000000000000000000000
χ4844444-2-2-2-2-4-2111−1+3i32−1−3i32-4-2-222-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2111−1+3i32−1−3i3222-21-2111−1+3i32−1−3i3211−1+3i32−1−3i3222-1-1-1-11−3i321+3i32-1-11−3i321+3i3222-1-1-1-11−3i321+3i32-1-11−3i321+3i320000000000000000000000000
χ49444-4-4444441-211-2-2-4-4-44411-2-21111-2-2-2-21-211-2-2-4-4-12-12-1-122-1-12211-2-211-2-211-2-2-1-122-1-122-1-1220000000000000000000000000
χ50444-4-444444-21-2-211-4-4-444-2-211-2-2-2-21111-21-2-211-4-42-12-122-1-122-1-1-2-211-2-211-2-21122-1-122-1-122-1-10000000000000000000000000
χ51444-4-44444-41-211-2-24-4-4-4-411-2-21111-2-2-2-21-211-2-244-12-12-1-122-1-122-1-122-1-122-1-12211-2-211-2-211-2-20000000000000000000000000
χ52444-4-44444-4-21-2-2114-4-4-4-4-2-211-2-2-2-21111-21-2-211442-12-122-1-122-1-122-1-122-1-122-1-1-2-211-2-211-2-2110000000000000000000000000
χ53444-4-4-2-2-2-241-2−1−3i32−1+3i3211-422-2-211-2-2−1−3i32−1−3i32−1+3i32−1+3i3211111-2−1−3i32−1+3i321122-12-121+3i321−3i32-1-11+3i321−3i32-1-111-2-2−1−3i32−1+3i3211−1−3i32−1+3i3211-1-1221+3i321−3i32-1-11+3i321−3i32-1-10000000000000000000000000
χ54444-4-4-2-2-2-241-2−1+3i32−1−3i3211-422-2-211-2-2−1+3i32−1+3i32−1−3i32−1−3i3211111-2−1+3i32−1−3i321122-12-121−3i321+3i32-1-11−3i321+3i32-1-111-2-2−1+3i32−1−3i3211−1+3i32−1−3i3211-1-1221−3i321+3i32-1-11−3i321+3i32-1-10000000000000000000000000
χ55444-4-4-2-2-2-24-2111−1−3i32−1+3i32-422-2-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2111−1−3i32−1+3i32222-12-1-1-11+3i321−3i32-1-11+3i321−3i32-2-21111−1−3i32−1+3i3211−1−3i32−1+3i3222-1-1-1-11+3i321−3i32-1-11+3i321−3i320000000000000000000000000
χ56444-4-4-2-2-2-24-2111−1+3i32−1−3i32-422-2-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2111−1+3i32−1−3i32222-12-1-1-11−3i321+3i32-1-11−3i321+3i32-2-21111−1+3i32−1−3i3211−1+3i32−1−3i3222-1-1-1-11−3i321+3i32-1-11−3i321+3i320000000000000000000000000
χ57444-4-4-2-2-2-2-41-2−1−3i32−1+3i32114222211-2-2−1−3i32−1−3i32−1+3i32−1+3i3211111-2−1−3i32−1+3i3211-2-2-12-121+3i321−3i32-1-11+3i321−3i32-1-1-1-1221+3i321−3i32-1-11+3i321−3i32-1-111-2-2−1−3i32−1+3i3211−1−3i32−1+3i32110000000000000000000000000
χ58444-4-4-2-2-2-2-41-2−1+3i32−1−3i32114222211-2-2−1+3i32−1+3i32−1−3i32−1−3i3211111-2−1+3i32−1−3i3211-2-2-12-121−3i321+3i32-1-11−3i321+3i32-1-1-1-1221−3i321+3i32-1-11−3i321+3i32-1-111-2-2−1+3i32−1−3i3211−1+3i32−1−3i32110000000000000000000000000
χ59444-4-4-2-2-2-2-4-2111−1−3i32−1+3i3242222-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2111−1−3i32−1+3i32-2-22-12-1-1-11+3i321−3i32-1-11+3i321−3i3222-1-1-1-11+3i321−3i32-1-11+3i321−3i32-2-21111−1−3i32−1+3i3211−1−3i32−1+3i320000000000000000000000000
χ60444-4-4-2-2-2-2-4-2111−1+3i32−1−3i3242222-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2111−1+3i32−1−3i32-2-22-12-1-1-11−3i321+3i32-1-11−3i321+3i3222-1-1-1-11−3i321+3i32-1-11−3i321+3i32-2-21111−1+3i32−1−3i3211−1+3i32−1−3i320000000000000000000000000
χ6144-44-44-4-4401-211-2-204-400-1-122-1-1-1-122221-211-2-2001-2-1211-2-2-1-1223-3003-300-33003-3003-300-33000000000000000000000000000
χ6244-44-44-4-4401-211-2-204-400-1-122-1-1-1-122221-211-2-2001-2-1211-2-2-1-122-3300-33003-300-3300-33003-3000000000000000000000000000
χ6344-44-44-4-440-21-2-21104-40022-1-12222-1-1-1-1-21-2-21100-212-1-2-21122-1-1003-3003-300-33003-3003-300-330000000000000000000000000
χ6444-44-44-4-440-21-2-21104-40022-1-12222-1-1-1-1-21-2-21100-212-1-2-21122-1-100-3300-33003-300-3300-33003-30000000000000000000000000
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Here i is the imaginary unit (i² = −1).