Finite Group Databasebeta

← Group #13173372

Character table — Group #13173372

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1122222224444444444444444444444444444444488888888888888888888888888888888888899181818181818183636363636363636108108108108108108108108
order12234461212333333666666688121212121212121212121212122424242466666612121212121224242424242424242424242424242424242424242424242422244661212688122424242444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1i−iiii−i−i−i
χ411111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−ii−i−i−iiii
χ51111111111111111111111-1-11111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11-1-1-1-1111-1-11-1-1
χ61111111111111111111111-1-11111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11-1-1-1-1-1-1-111-111
χ71111111111111111111111-1-11111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111i−ii−i−i−iii
χ81111111111111111111111-1-11111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111−ii−iiii−i−i
χ911-11-11111111111-11111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-11-11111-11-1-111-1-111-11-1-11-1
χ1011-11-11111111111-11111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-11-11111-11-1-111-1-1-1-11-111-11
χ1111-11-11111111111-11111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-11-111-1-111i−i−ii−ii−ii
χ1211-11-11111111111-11111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-11-111-1-111−iii−ii−ii−i
χ1311-11-11111111111-1111111-11-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-11-11111-1-11-1-1-11111-1-11-1-11
χ1411-11-11111111111-1111111-11-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-11-11111-1-11-1-1-111-1-111-111-1
χ1511-11-11111111111-1111111-11-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11-11-1-1-1-111-1111-1-1i−i−i−iiii−i
χ1611-11-11111111111-1111111-11-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11-11-1-1-1-111-1111-1-1−iiii−i−i−ii
χ172222-2-22-2-2222222222222200-2-2-2-2-2-2-2-2-2-2-2-2-20000222222-2-2-2-2-2-2000000000000000000000000222-2-222-2-2200-2000000000000
χ182222-2-22-2-2222222222222200-2-2-2-2-2-2-2-2-2-2-2-2-20000222222-2-2-2-2-2-2000000000000000000000000-2-2-222-2-222-2002000000000000
χ19222-122-1-1-122-1-1-1-1-122-1-1-1-122-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222-1-1-1-1-122-1-1-1-1-100000000
χ20222-122-1-1-122-1-1-1-1-122-1-1-1-122-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-211111-2-21111100000000
χ21222-122-1-1-122-1-1-1-1-122-1-1-1-1-2-2-12222-1-1-1-1-1-1-1-1111122-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-21111111122222-1-1-1-1-1-2-2-1111100000000
χ22222-122-1-1-122-1-1-1-1-122-1-1-1-1-2-2-12222-1-1-1-1-1-1-1-1111122-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2-2-2-211111221-1-1-1-100000000
χ23222-1-2-2-11122-1-1-1-1-122-1-1-1-1001-2-2-2-2111111113−33−322-1-1-1-1-2-2111100003333−3−3−3−300003333−3−3−3−3222-2-2-1-111-10013−33−300000000
χ24222-1-2-2-11122-1-1-1-1-122-1-1-1-1001-2-2-2-2111111113−33−322-1-1-1-1-2-2111100003333−3−3−3−300003333−3−3−3−3-2-2-22211-1-1100-1−33−3300000000
χ25222-1-2-2-11122-1-1-1-1-122-1-1-1-1001-2-2-2-211111111−33−3322-1-1-1-1-2-211110000−3−3−3−333330000−3−3−3−33333222-2-2-1-111-1001−33−3300000000
χ26222-1-2-2-11122-1-1-1-1-122-1-1-1-1001-2-2-2-211111111−33−3322-1-1-1-1-2-211110000−3−3−3−333330000−3−3−3−33333-2-2-22211-1-1100-13−33−300000000
χ2722-222-22-2-2222222-2222222002-2-2-2-2-2-2-2-2-2-2-2-20000-2-2-2-2-2-222222200000000000000000000000022-2-2222-2-2-2002000000000000
χ2822-222-22-2-2222222-2222222002-2-2-2-2-2-2-2-2-2-2-2-20000-2-2-2-2-2-2222222000000000000000000000000-2-222-2-2-222200-2000000000000
χ2922-2-12-2-11122-1-1-1-1122-1-1-1-100-1-2-2-2-2111111113−3−33-2-2111122-1-1-1-100003333−3−3−3−30000−3−3−3−3333322-2-22-1-111100-13−3−3300000000
χ3022-2-12-2-11122-1-1-1-1122-1-1-1-100-1-2-2-2-2111111113−3−33-2-2111122-1-1-1-100003333−3−3−3−30000−3−3−3−33333-2-222-211-1-1-1001−333−300000000
χ3122-2-12-2-11122-1-1-1-1122-1-1-1-100-1-2-2-2-211111111−333−3-2-2111122-1-1-1-10000−3−3−3−3333300003333−3−3−3−322-2-22-1-111100-1−333−300000000
χ3222-2-12-2-11122-1-1-1-1122-1-1-1-100-1-2-2-2-211111111−333−3-2-2111122-1-1-1-10000−3−3−3−3333300003333−3−3−3−3-2-222-211-1-1-10013−3−3300000000
χ3322-2-1-22-1-1-122-1-1-1-1122-1-1-1-12-212222-1-1-1-1-1-1-1-1-1-111-2-21111-2-211112222-1-1-1-1-1-1-1-1-2-2-2-21111111122-22-2-1-1-1-112-21-1-11100000000
χ3422-2-1-22-1-1-122-1-1-1-1122-1-1-1-12-212222-1-1-1-1-1-1-1-1-1-111-2-21111-2-211112222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-22-221111-1-22-111-1-100000000
χ3522-2-1-22-1-1-122-1-1-1-1122-1-1-1-1-2212222-1-1-1-1-1-1-1-111-1-1-2-21111-2-21111-2-2-2-2111111112222-1-1-1-1-1-1-1-122-22-2-1-1-1-11-22111-1-100000000
χ3622-2-1-22-1-1-122-1-1-1-1122-1-1-1-1-2212222-1-1-1-1-1-1-1-111-1-1-2-21111-2-21111-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-22-221111-12-2-1-1-11100000000
χ374444444441-211-2-241-211-2-244411-2-21111-2-2-2-244441-211-2-21-211-2-211-2-211-2-211-2-211-2-211-2-211-2-20000000000000000000000000
χ384444444441-211-2-241-211-2-2-4-4411-2-21111-2-2-2-2-4-4-4-41-211-2-21-211-2-2-1-122-1-122-1-122-1-122-1-122-1-1220000000000000000000000000
χ39444444444-21-2-2114-21-2-211444-2-211-2-2-2-211114444-21-2-211-21-2-211-2-211-2-211-2-211-2-211-2-211-2-2110000000000000000000000000
χ40444444444-21-2-2114-21-2-211-4-44-2-211-2-2-2-21111-4-4-4-4-21-2-211-21-2-21122-1-122-1-122-1-122-1-122-1-122-1-10000000000000000000000000
χ414444-4-44-4-41-211-2-241-211-2-200-4-1-122-1-1-1-1222200001-211-2-2-12-1-1223i−3i003i−3i003i−3i003i−3i003i−3i003i−3i000000000000000000000000000
χ424444-4-44-4-41-211-2-241-211-2-200-4-1-122-1-1-1-1222200001-211-2-2-12-1-122−3i3i00−3i3i00−3i3i00−3i3i00−3i3i00−3i3i000000000000000000000000000
χ434444-4-44-4-4-21-2-2114-21-2-21100-422-1-12222-1-1-1-10000-21-2-2112-122-1-1003i−3i003i−3i003i−3i003i−3i003i−3i003i−3i0000000000000000000000000
χ444444-4-44-4-4-21-2-2114-21-2-21100-422-1-12222-1-1-1-10000-21-2-2112-122-1-100−3i3i00−3i3i00−3i3i00−3i3i00−3i3i00−3i3i0000000000000000000000000
χ45444-244-2-2-21-2−1−3i32−1+3i3211-21-2−1−3i32−1+3i321144-211-2-2−1−3i32−1−3i32−1+3i32−1+3i321111-2-2-2-21-2−1−3i32−1+3i32111-2−1−3i32−1+3i321111-2-2−1−3i32−1+3i3211−1+3i32−1−3i321111-2-2−1−3i32−1+3i3211−1+3i32−1−3i32110000000000000000000000000
χ46444-244-2-2-21-2−1−3i32−1+3i3211-21-2−1−3i32−1+3i3211-4-4-211-2-2−1−3i32−1−3i32−1+3i32−1+3i32111122221-2−1−3i32−1+3i32111-2−1−3i32−1+3i3211-1-1221+3i321−3i32-1-11−3i321+3i32-1-1-1-1221+3i321−3i32-1-11−3i321+3i32-1-10000000000000000000000000
χ47444-244-2-2-21-2−1+3i32−1−3i3211-21-2−1+3i32−1−3i321144-211-2-2−1+3i32−1+3i32−1−3i32−1−3i321111-2-2-2-21-2−1+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+3i32110000000000000000000000000
χ48444-244-2-2-21-2−1+3i32−1−3i3211-21-2−1+3i32−1−3i3211-4-4-211-2-2−1+3i32−1+3i32−1−3i32−1−3i32111122221-2−1+3i32−1−3i32111-2−1+3i32−1−3i3211-1-1221−3i321+3i32-1-11+3i321−3i32-1-1-1-1221−3i321+3i32-1-11+3i321−3i32-1-10000000000000000000000000
χ49444-244-2-2-2-2111−1−3i32−1+3i32-2-2111−1−3i32−1+3i3244-2-2-2111111−1−3i32−1−3i32−1+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+3i32−1−3i320000000000000000000000000
χ50444-244-2-2-2-2111−1−3i32−1+3i32-2-2111−1−3i32−1+3i32-4-4-2-2-2111111−1−3i32−1−3i32−1+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+3i320000000000000000000000000
χ51444-244-2-2-2-2111−1+3i32−1−3i32-2-2111−1+3i32−1−3i3244-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2-2-2-2-2111−1+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+3i320000000000000000000000000
χ52444-244-2-2-2-2111−1+3i32−1−3i32-2-2111−1+3i32−1−3i32-4-4-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i322222-2111−1+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+3i321−3i320000000000000000000000000
χ53444-2-4-4-2221-2−1−3i32−1+3i3211-21-2−1−3i32−1+3i3211002-1-1221+3i321+3i321−3i321−3i32-1-1-1-123−2323−231-2−1−3i32−1+3i3211-121+3i321−3i32-1-13i−3i00ζ7+2ζ11−2ζ7−ζ11−3−32ζ7+ζ11−ζ7−2ζ11333i−3i00ζ7+2ζ11−2ζ7−ζ11−3−32ζ7+ζ11−ζ7−2ζ11330000000000000000000000000
χ54444-2-4-4-2221-2−1−3i32−1+3i3211-21-2−1−3i32−1+3i3211002-1-1221+3i321+3i321−3i321−3i32-1-1-1-1−2323−23231-2−1−3i32−1+3i3211-121+3i321−3i32-1-1−3i3i00−ζ7−2ζ112ζ7+ζ1133−2ζ7−ζ11ζ7+2ζ11−3−3−3i3i00−ζ7−2ζ112ζ7+ζ1133−2ζ7−ζ11ζ7+2ζ11−3−30000000000000000000000000
χ55444-2-4-4-2221-2−1+3i32−1−3i3211-21-2−1+3i32−1−3i3211002-1-1221−3i321−3i321+3i321+3i32-1-1-1-123−2323−231-2−1+3i32−1−3i3211-121−3i321+3i32-1-1−3i3i00−2ζ7−ζ11ζ7+2ζ11−3−3−ζ7−2ζ112ζ7+ζ1133−3i3i00−2ζ7−ζ11ζ7+2ζ11−3−3−ζ7−2ζ112ζ7+ζ11330000000000000000000000000
χ56444-2-4-4-2221-2−1+3i32−1−3i3211-21-2−1+3i32−1−3i3211002-1-1221−3i321−3i321+3i321+3i32-1-1-1-1−2323−23231-2−1+3i32−1−3i3211-121−3i321+3i32-1-13i−3i002ζ7+ζ11−ζ7−2ζ1133ζ7+2ζ11−2ζ7−ζ11−3−33i−3i002ζ7+ζ11−ζ7−2ζ1133ζ7+2ζ11−2ζ7−ζ11−3−30000000000000000000000000
χ57444-2-4-4-222-2111−1−3i32−1+3i32-2-2111−1−3i32−1+3i3200222-1-1-1-1-1-11+3i321+3i321−3i321−3i3223−2323−23-2111−1−3i32−1+3i322-1-1-11+3i321−3i32003i−3i−3−3ζ7+2ζ11−2ζ7−ζ11332ζ7+ζ11−ζ7−2ζ11003i−3i−3−3ζ7+2ζ11−2ζ7−ζ11332ζ7+ζ11−ζ7−2ζ110000000000000000000000000
χ58444-2-4-4-222-2111−1−3i32−1+3i32-2-2111−1−3i32−1+3i3200222-1-1-1-1-1-11+3i321+3i321−3i321−3i32−2323−2323-2111−1−3i32−1+3i322-1-1-11+3i321−3i3200−3i3i33−ζ7−2ζ112ζ7+ζ11−3−3−2ζ7−ζ11ζ7+2ζ1100−3i3i33−ζ7−2ζ112ζ7+ζ11−3−3−2ζ7−ζ11ζ7+2ζ110000000000000000000000000
χ59444-2-4-4-222-2111−1+3i32−1−3i32-2-2111−1+3i32−1−3i3200222-1-1-1-1-1-11−3i321−3i321+3i321+3i3223−2323−23-2111−1+3i32−1−3i322-1-1-11−3i321+3i3200−3i3i−3−3−2ζ7−ζ11ζ7+2ζ1133−ζ7−2ζ112ζ7+ζ1100−3i3i−3−3−2ζ7−ζ11ζ7+2ζ1133−ζ7−2ζ112ζ7+ζ110000000000000000000000000
χ60444-2-4-4-222-2111−1+3i32−1−3i32-2-2111−1+3i32−1−3i3200222-1-1-1-1-1-11−3i321−3i321+3i321+3i32−2323−2323-2111−1+3i32−1−3i322-1-1-11−3i321+3i32003i−3i332ζ7+ζ11−ζ7−2ζ11−3−3ζ7+2ζ11−2ζ7−ζ11003i−3i332ζ7+ζ11−ζ7−2ζ11−3−3ζ7+2ζ11−2ζ7−ζ110000000000000000000000000
χ6144-444-44-4-41-211-2-2-41-211-2-2004-1-122-1-1-1-122220000-12-1-1221-211-2-23i−3i003i−3i003i−3i00−3i3i00−3i3i00−3i3i000000000000000000000000000
χ6244-444-44-4-41-211-2-2-41-211-2-2004-1-122-1-1-1-122220000-12-1-1221-211-2-2−3i3i00−3i3i00−3i3i003i−3i003i−3i003i−3i000000000000000000000000000
χ6344-444-44-4-4-21-2-211-4-21-2-21100422-1-12222-1-1-1-100002-122-1-1-21-2-211003i−3i003i−3i003i−3i00−3i3i00−3i3i00−3i3i0000000000000000000000000
χ6444-444-44-4-4-21-2-211-4-21-2-21100422-1-12222-1-1-1-100002-122-1-1-21-2-21100−3i3i00−3i3i00−3i3i003i−3i003i−3i003i−3i0000000000000000000000000
χ6544-44-444441-211-2-2-41-211-2-24-4-411-2-21111-2-2-2-244-4-4-12-1-122-12-1-12211-2-211-2-211-2-2-1-122-1-122-1-1220000000000000000000000000
χ6644-44-444441-211-2-2-41-211-2-2-44-411-2-21111-2-2-2-2-4-444-12-1-122-12-1-122-1-122-1-122-1-12211-2-211-2-211-2-20000000000000000000000000
χ6744-44-44444-21-2-211-4-21-2-2114-4-4-2-211-2-2-2-2111144-4-42-122-1-12-122-1-1-2-211-2-211-2-21122-1-122-1-122-1-10000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.