Finite Group Databasebeta

← Group #13180650

Character table — Group #13180650

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size134489121216161616275454545472134489121216161616275454545472134489121216161616275454545472134489121216161616275454545472
order12333266333324444644121212412121212121244444122266626666662444464412121241212121212124444412
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111-1-1-1-111111111111111-1-1-1-111111111111111-1-1-1-111111111111111-1-1-1-11
χ311111-1111111-1i−ii−i-111111-1111111-1i−ii−i-111111-1111111-1i−ii−i-111111-1111111-1i−ii−i-1
χ411111-1111111-1−ii−ii-111111-1111111-1−ii−ii-111111-1111111-1−ii−ii-111111-1111111-1−ii−ii-1
χ52222-1222-1-1-1-120000-12222-1222-1-1-1-120000-12222-1222-1-1-1-120000-12222-1222-1-1-1-120000-1
χ62222-1-222-1-1-1-1-2000012222-1-222-1-1-1-1-2000012222-1-222-1-1-1-1-2000012222-1-222-1-1-1-1-200001
χ73-13303-1-10000-111-1-103-13303-1-10000-111-1-103-13303-1-10000-111-1-103-13303-1-10000-111-1-10
χ83-13303-1-10000-1-1-11103-13303-1-10000-1-1-11103-13303-1-10000-1-1-11103-13303-1-10000-1-1-1110
χ93-1330-3-1-100001i−i−ii03-1330-3-1-100001i−i−ii03-1330-3-1-100001i−i−ii03-1330-3-1-100001i−i−ii0
χ103-1330-3-1-100001−iii−i03-1330-3-1-100001−iii−i03-1330-3-1-100001−iii−i03-1330-3-1-100001−iii−i0
χ11441-2401-211-2-2000000441-2401-211-2-2000000441-2401-211-2-2000000441-2401-211-2-2000000
χ12441-2-201-2−1−3i32−1+3i3211000000441-2-201-2−1−3i32−1+3i3211000000441-2-201-2−1−3i32−1+3i3211000000441-2-201-2−1−3i32−1+3i3211000000
χ13441-2-201-2−1+3i32−1−3i3211000000441-2-201-2−1+3i32−1−3i3211000000441-2-201-2−1+3i32−1−3i3211000000441-2-201-2−1+3i32−1−3i3211000000
χ1444-2140-21-2-21100000044-2140-21-2-21100000044-2140-21-2-21100000044-2140-21-2-211000000
χ1544-21-20-2111−1−3i32−1+3i3200000044-21-20-2111−1−3i32−1+3i3200000044-21-20-2111−1−3i32−1+3i3200000044-21-20-2111−1−3i32−1+3i32000000
χ1644-21-20-2111−1+3i32−1−3i3200000044-21-20-2111−1+3i32−1−3i3200000044-21-20-2111−1+3i32−1−3i3200000044-21-20-2111−1+3i32−1−3i32000000
χ1712-43-600-12000000000012-43-600-12000000000012-43-600-12000000000012-43-600-120000000000
χ1812-4-63002-1000000000012-4-63002-1000000000012-4-63002-1000000000012-4-63002-10000000000
χ19111111111111111111iiiiiiiiiiiiiiiiii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i
χ201111111111111-1-1-1-11iiiiiiiiiiiii−i−i−i−ii-1-1-1-1-1-1-1-1-1-1-1-1-11111-1−i−i−i−i−i−i−i−i−i−i−i−i−iiiii−i
χ2111111-1111111-1i−ii−i-1iiiii−iiiiiii−i-11-11−i-1-1-1-1-11-1-1-1-1-1-11−ii−ii1−i−i−i−i−ii−i−i−i−i−i−ii1-11-1i
χ2211111-1111111-1−ii−ii-1iiiii−iiiiiii−i1-11-1−i-1-1-1-1-11-1-1-1-1-1-11i−ii−i1−i−i−i−i−ii−i−i−i−i−i−ii-11-11i
χ232222-1222-1-1-1-120000-12i2i2i2i−i2i2i2i−i−i−i−i2i0000−i-2-2-2-21-2-2-21111-200001−2i−2i−2i−2ii−2i−2i−2iiiii−2i0000i
χ242222-1-222-1-1-1-1-2000012i2i2i2i−i−2i2i2i−i−i−i−i−2i0000i-2-2-2-212-2-2111120000-1−2i−2i−2i−2ii2i−2i−2iiiii2i0000−i
χ253-13303-1-10000-111-1-103i−i3i3i03i−i−i0000−iii−i−i0-31-3-30-31100001-1-1110−3ii−3i−3i0−3iii0000i−i−iii0
χ263-13303-1-10000-1-1-11103i−i3i3i03i−i−i0000−i−i−iii0-31-3-30-3110000111-1-10−3ii−3i−3i0−3iii0000iii−i−i0
χ273-1330-3-1-100001i−i−ii03i−i3i3i0−3i−i−i0000i-111-10-31-3-303110000-1−iii−i0−3ii−3i−3i03iii0000−i1-1-110
χ283-1330-3-1-100001−iii−i03i−i3i3i0−3i−i−i0000i1-1-110-31-3-303110000-1i−i−ii0−3ii−3i−3i03iii0000−i-111-10
χ29441-2401-211-2-20000004i4ii−2i4i0i−2iii−2i−2i000000-4-4-12-40-12-1-122000000−4i−4i−i2i−4i0−i2i−i−i2i2i000000
χ30441-2-201-2−1−3i32−1+3i32110000004i4ii−2i−2i0i−2i−ζ7+2ζ112ζ7−ζ11ii000000-4-4-1220-121+3i321−3i32-1-1000000−4i−4i−i2i2i0−i2iζ7−2ζ11−2ζ7+ζ11−i−i000000
χ31441-2-201-2−1+3i32−1−3i32110000004i4ii−2i−2i0i−2i2ζ7−ζ11−ζ7+2ζ11ii000000-4-4-1220-121−3i321+3i32-1-1000000−4i−4i−i2i2i0−i2i−2ζ7+ζ11ζ7−2ζ11−i−i000000
χ3244-2140-21-2-2110000004i4i−2ii4i0−2ii−2i−2iii000000-4-42-1-402-122-1-1000000−4i−4i2i−i−4i02i−i2i2i−i−i000000
χ3344-21-20-2111−1−3i32−1+3i320000004i4i−2ii−2i0−2iiii−ζ7+2ζ112ζ7−ζ11000000-4-42-1202-1-1-11+3i321−3i32000000−4i−4i2i−i2i02i−i−i−iζ7−2ζ11−2ζ7+ζ11000000
χ3444-21-20-2111−1+3i32−1−3i320000004i4i−2ii−2i0−2iiii2ζ7−ζ11−ζ7+2ζ11000000-4-42-1202-1-1-11−3i321+3i32000000−4i−4i2i−i2i02i−i−i−i−2ζ7+ζ11ζ7−2ζ11000000
χ3512-43-600-12000000000012i−4i3i−6i00−i2i0000000000-124-36001-20000000000−12i4i−3i6i00i−2i0000000000
χ3612-4-63002-1000000000012i−4i−6i3i002i−i0000000000-1246-300-210000000000−12i4i6i−3i00−2ii0000000000
χ37111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ381111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-11111-1
χ3911111-1111111-1i−ii−i-1-1-1-1-1-11-1-1-1-1-1-11−ii−ii111111-1111111-1i−ii−i-1-1-1-1-1-11-1-1-1-1-1-11−ii−ii1
χ4011111-1111111-1−ii−ii-1-1-1-1-1-11-1-1-1-1-1-11i−ii−i111111-1111111-1−ii−ii-1-1-1-1-1-11-1-1-1-1-1-11i−ii−i1
χ412222-1222-1-1-1-120000-1-2-2-2-21-2-2-21111-2000012222-1222-1-1-1-120000-1-2-2-2-21-2-2-21111-200001
χ422222-1-222-1-1-1-1-200001-2-2-2-212-2-2111120000-12222-1-222-1-1-1-1-200001-2-2-2-212-2-2111120000-1
χ433-13303-1-10000-111-1-10-31-3-30-31100001-1-11103-13303-1-10000-111-1-10-31-3-30-31100001-1-1110
χ443-13303-1-10000-1-1-1110-31-3-30-3110000111-1-103-13303-1-10000-1-1-1110-31-3-30-3110000111-1-10
χ453-1330-3-1-100001i−i−ii0-31-3-303110000-1−iii−i03-1330-3-1-100001i−i−ii0-31-3-303110000-1−iii−i0
χ463-1330-3-1-100001−iii−i0-31-3-303110000-1i−i−ii03-1330-3-1-100001−iii−i0-31-3-303110000-1i−i−ii0
χ47441-2401-211-2-2000000-4-4-12-40-12-1-122000000441-2401-211-2-2000000-4-4-12-40-12-1-122000000
χ48441-2-201-2−1−3i32−1+3i3211000000-4-4-1220-121+3i321−3i32-1-1000000441-2-201-2−1−3i32−1+3i3211000000-4-4-1220-121+3i321−3i32-1-1000000
χ49441-2-201-2−1+3i32−1−3i3211000000-4-4-1220-121−3i321+3i32-1-1000000441-2-201-2−1+3i32−1−3i3211000000-4-4-1220-121−3i321+3i32-1-1000000
χ5044-2140-21-2-211000000-4-42-1-402-122-1-100000044-2140-21-2-211000000-4-42-1-402-122-1-1000000
χ5144-21-20-2111−1−3i32−1+3i32000000-4-42-1202-1-1-11+3i321−3i3200000044-21-20-2111−1−3i32−1+3i32000000-4-42-1202-1-1-11+3i321−3i32000000
χ5244-21-20-2111−1+3i32−1−3i32000000-4-42-1202-1-1-11−3i321+3i3200000044-21-20-2111−1+3i32−1−3i32000000-4-42-1202-1-1-11−3i321+3i32000000
χ5312-43-600-120000000000-124-36001-2000000000012-43-600-120000000000-124-36001-20000000000
χ5412-4-63002-10000000000-1246-300-21000000000012-4-63002-10000000000-1246-300-210000000000
χ55111111111111111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiiiii
χ561111111111111-1-1-1-11−i−i−i−i−i−i−i−i−i−i−i−i−iiiii−i-1-1-1-1-1-1-1-1-1-1-1-1-11111-1iiiiiiiiiiiii−i−i−i−ii
χ5711111-1111111-1i−ii−i-1−i−i−i−i−ii−i−i−i−i−i−ii1-11-1i-1-1-1-1-11-1-1-1-1-1-11−ii−ii1iiiii−iiiiiii−i-11-11−i
χ5811111-1111111-1−ii−ii-1−i−i−i−i−ii−i−i−i−i−i−ii-11-11i-1-1-1-1-11-1-1-1-1-1-11i−ii−i1iiiii−iiiiiii−i1-11-1−i
χ592222-1222-1-1-1-120000-1−2i−2i−2i−2ii−2i−2i−2iiiii−2i0000i-2-2-2-21-2-2-21111-2000012i2i2i2i−i2i2i2i−i−i−i−i2i0000−i
χ602222-1-222-1-1-1-1-200001−2i−2i−2i−2ii2i−2i−2iiiii2i0000−i-2-2-2-212-2-2111120000-12i2i2i2i−i−2i2i2i−i−i−i−i−2i0000i
χ613-13303-1-10000-111-1-10−3ii−3i−3i0−3iii0000i−i−iii0-31-3-30-31100001-1-11103i−i3i3i03i−i−i0000−iii−i−i0
χ623-13303-1-10000-1-1-1110−3ii−3i−3i0−3iii0000iii−i−i0-31-3-30-3110000111-1-103i−i3i3i03i−i−i0000−i−i−iii0
χ633-1330-3-1-100001i−i−ii0−3ii−3i−3i03iii0000−i1-1-110-31-3-303110000-1−iii−i03i−i3i3i0−3i−i−i0000i-111-10
χ643-1330-3-1-100001−iii−i0−3ii−3i−3i03iii0000−i-111-10-31-3-303110000-1i−i−ii03i−i3i3i0−3i−i−i0000i1-1-110
χ65441-2401-211-2-2000000−4i−4i−i2i−4i0−i2i−i−i2i2i000000-4-4-12-40-12-1-1220000004i4ii−2i4i0i−2iii−2i−2i000000
χ66441-2-201-2−1−3i32−1+3i3211000000−4i−4i−i2i2i0−i2iζ7−2ζ11−2ζ7+ζ11−i−i000000-4-4-1220-121+3i321−3i32-1-10000004i4ii−2i−2i0i−2i−ζ7+2ζ112ζ7−ζ11ii000000
χ67441-2-201-2−1+3i32−1−3i3211000000−4i−4i−i2i2i0−i2i−2ζ7+ζ11ζ7−2ζ11−i−i000000-4-4-1220-121−3i321+3i32-1-10000004i4ii−2i−2i0i−2i2ζ7−ζ11−ζ7+2ζ11ii000000
χ6844-2140-21-2-211000000−4i−4i2i−i−4i02i−i2i2i−i−i000000-4-42-1-402-122-1-10000004i4i−2ii4i0−2ii−2i−2iii000000
χ6944-21-20-2111−1−3i32−1+3i32000000−4i−4i2i−i2i02i−i−i−iζ7−2ζ11−2ζ7+ζ11000000-4-42-1202-1-1-11+3i321−3i320000004i4i−2ii−2i0−2iiii−ζ7+2ζ112ζ7−ζ11000000
χ7044-21-20-2111−1+3i32−1−3i32000000−4i−4i2i−i2i02i−i−i−i−2ζ7+ζ11ζ7−2ζ11000000-4-42-1202-1-1-11−3i321+3i320000004i4i−2ii−2i0−2iiii2ζ7−ζ11−ζ7+2ζ11000000
χ7112-43-600-120000000000−12i4i−3i6i00i−2i0000000000-124-36001-2000000000012i−4i3i−6i00−i2i0000000000
χ7212-4-63002-10000000000−12i4i6i−3i00−2ii0000000000-1246-300-21000000000012i−4i−6i3i002i−i0000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.