Finite Group Databasebeta

← Group #13180849

Character table — Group #13180849

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size122346689121616161618181818273636363672122346689121616161618181818273636363672122346689121616161618181818273636363672122346689121616161618181818273636363672
order133236632633332244266121264121241212121241212121212444441212121212266266662666662244266121264121241212121241212121212444441212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111-1-1-1-11-1-1-1-1111111111111111-1-1-1-11-1-1-1-1111111111111111-1-1-1-11-1-1-1-1111111111111111-1-1-1-11-1-1-1-11
χ311111111-1111111-11-1-11-11-1-111111111-1111111-11-1-11-11-1-111111111-1111111-11-1-11-11-1-111111111-1111111-11-1-11-11-1-1
χ411111111-111111-11-11-1-11-11-111111111-111111-11-11-1-11-11-111111111-111111-11-11-1-11-11-111111111-111111-11-11-1-11-11-1
χ52222222-122-1-1-1-1000020000-12222222-122-1-1-1-1000020000-12222222-122-1-1-1-1000020000-12222222-122-1-1-1-1000020000-1
χ62222222-1-22-1-1-1-10000-2000012222222-1-22-1-1-1-10000-2000012222222-1-22-1-1-1-10000-2000012222222-1-22-1-1-1-10000-200001
χ722-12-12-120-12-1-1-1020200-10-1022-12-12-120-12-1-1-1020200-10-1022-12-12-120-12-1-1-1020200-10-1022-12-12-120-12-1-1-1020200-10-10
χ822-12-12-120-12-1-1-10-20-200101022-12-12-120-12-1-1-10-20-200101022-12-12-120-12-1-1-10-20-200101022-12-12-120-12-1-1-10-20-2001010
χ92-122-1-1220-1-12-1-120200-10-1002-122-1-1220-1-12-1-120200-10-1002-122-1-1220-1-12-1-120200-10-1002-122-1-1220-1-12-1-120200-10-100
χ102-122-1-1220-1-12-1-1-20-200101002-122-1-1220-1-12-1-1-20-200101002-122-1-1220-1-12-1-1-20-200101002-122-1-1220-1-12-1-1-20-20010100
χ11333-13-1-103-1000011-1-1-111-1-10333-13-1-103-1000011-1-1-111-1-10333-13-1-103-1000011-1-1-111-1-10333-13-1-103-1000011-1-1-111-1-10
χ12333-13-1-103-10000-1-111-1-1-1110333-13-1-103-10000-1-111-1-1-1110333-13-1-103-10000-1-111-1-1-1110333-13-1-103-10000-1-111-1-1-1110
χ13333-13-1-10-3-100001-1-1111-1-110333-13-1-10-3-100001-1-1111-1-110333-13-1-10-3-100001-1-1111-1-110333-13-1-10-3-100001-1-1111-1-110
χ14333-13-1-10-3-10000-111-11-111-10333-13-1-10-3-10000-111-11-111-10333-13-1-10-3-10000-111-11-111-10333-13-1-10-3-10000-111-11-111-10
χ1544-24-24-2-20-2-2111000000000044-24-24-2-20-2-2111000000000044-24-24-2-20-2-2111000000000044-24-24-2-20-2-21110000000000
χ164-244-2-24-20-21-21100000000004-244-2-24-20-21-21100000000004-244-2-24-20-21-21100000000004-244-2-24-20-21-2110000000000
χ174-2-241-2-2401-2-21100000000004-2-241-2-2401-2-21100000000004-2-241-2-2401-2-21100000000004-2-241-2-2401-2-2110000000000
χ184-2-241-2-2-20111−1+3i32−1−3i3200000000004-2-241-2-2-20111−1+3i32−1−3i3200000000004-2-241-2-2-20111−1+3i32−1−3i3200000000004-2-241-2-2-20111−1+3i32−1−3i320000000000
χ194-2-241-2-2-20111−1−3i32−1+3i3200000000004-2-241-2-2-20111−1−3i32−1+3i3200000000004-2-241-2-2-20111−1−3i32−1+3i3200000000004-2-241-2-2-20111−1−3i32−1+3i320000000000
χ2066-3-2-3-210010000020-200-101066-3-2-3-210010000020-200-101066-3-2-3-210010000020-200-101066-3-2-3-210010000020-200-1010
χ2166-3-2-3-2100100000-2020010-1066-3-2-3-2100100000-2020010-1066-3-2-3-2100100000-2020010-1066-3-2-3-2100100000-2020010-10
χ226-36-2-31-2001000020-200-101006-36-2-31-2001000020-200-101006-36-2-31-2001000020-200-101006-36-2-31-2001000020-200-10100
χ236-36-2-31-20010000-2020010-1006-36-2-31-20010000-2020010-1006-36-2-31-20010000-2020010-1006-36-2-31-20010000-2020010-100
χ2412-6-6-432200-10000000000000012-6-6-432200-10000000000000012-6-6-432200-10000000000000012-6-6-432200-100000000000000
χ25111111111111111111111111iiiiiiiiiiiiiiiiiiiiiiii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i
χ2611111111111111-1-1-1-11-1-1-1-11iiiiiiiiiiiiii−i−i−i−ii−i−i−i−ii-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiii−iiiii−i
χ2711111111-1111111-11-1-11-11-1-1iiiiiiii−iiiiiii−ii−i−ii−ii−i−i-1-1-1-1-1-1-1-11-1-1-1-1-1-11-111-11-111−i−i−i−i−i−i−i−ii−i−i−i−i−i−ii−iii−ii−iii
χ2811111111-111111-11-11-1-11-11-1iiiiiiii−iiiiii−ii−ii−i−ii−ii−i-1-1-1-1-1-1-1-11-1-1-1-1-11-11-111-11-11−i−i−i−i−i−i−i−ii−i−i−i−i−ii−ii−iii−ii−ii
χ292222222-122-1-1-1-1000020000-12i2i2i2i2i2i2i−i2i2i−i−i−i−i00002i0000−i-2-2-2-2-2-2-21-2-211110000-200001−2i−2i−2i−2i−2i−2i−2ii−2i−2iiiii0000−2i0000i
χ302222222-1-22-1-1-1-10000-2000012i2i2i2i2i2i2i−i−2i2i−i−i−i−i0000−2i0000i-2-2-2-2-2-2-212-21111000020000-1−2i−2i−2i−2i−2i−2i−2ii2i−2iiiii00002i0000−i
χ3122-12-12-120-12-1-1-1020200-10-102i2i−i2i−i2i−i2i0−i2i−i−i−i02i02i00−i0−i0-2-21-21-21-201-21110-20-2001010−2i−2ii−2ii−2ii−2i0i−2iiii0−2i0−2i00i0i0
χ3222-12-12-120-12-1-1-10-20-20010102i2i−i2i−i2i−i2i0−i2i−i−i−i0−2i0−2i00i0i0-2-21-21-21-201-2111020200-10-10−2i−2ii−2ii−2ii−2i0i−2iiii02i02i00−i0−i0
χ332-122-1-1220-1-12-1-120200-10-1002i−i2i2i−i−i2i2i0−i−i2i−i−i2i02i00−i0−i00-21-2-211-2-2011-211-20-20010100−2ii−2i−2iii−2i−2i0ii−2iii−2i0−2i00i0i00
χ342-122-1-1220-1-12-1-1-20-200101002i−i2i2i−i−i2i2i0−i−i2i−i−i−2i0−2i00i0i00-21-2-211-2-2011-21120200-10-100−2ii−2i−2iii−2i−2i0ii−2iii2i02i00−i0−i00
χ35333-13-1-103-1000011-1-1-111-1-103i3i3i−i3i−i−i03i−i0000ii−i−i−iii−i−i0-3-3-31-3110-310000-1-1111-1-1110−3i−3i−3ii−3iii0−3ii0000−i−iiii−i−iii0
χ36333-13-1-103-10000-1-111-1-1-11103i3i3i−i3i−i−i03i−i0000−i−iii−i−i−iii0-3-3-31-3110-31000011-1-1111-1-10−3i−3i−3ii−3iii0−3ii0000ii−i−iiii−i−i0
χ37333-13-1-10-3-100001-1-1111-1-1103i3i3i−i3i−i−i0−3i−i0000i−i−iiii−i−ii0-3-3-31-3110310000-111-1-1-111-10−3i−3i−3ii−3iii03ii0000−iii−i−i−iii−i0
χ38333-13-1-10-3-10000-111-11-111-103i3i3i−i3i−i−i0−3i−i0000−iii−ii−iii−i0-3-3-31-31103100001-1-11-11-1-110−3i−3i−3ii−3iii03ii0000i−i−ii−ii−i−ii0
χ3944-24-24-2-20-2-211100000000004i4i−2i4i−2i4i−2i−2i0−2i−2iiii0000000000-4-42-42-422022-1-1-10000000000−4i−4i2i−4i2i−4i2i2i02i2i−i−i−i0000000000
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χ414-2-241-2-2401-2-21100000000004i−2i−2i4ii−2i−2i4i0i−2i−2iii0000000000-422-4-122-40-122-1-10000000000−4i2i2i−4i−i2i2i−4i0−i2i2i−i−i0000000000
χ424-2-241-2-2-20111−1+3i32−1−3i3200000000004i−2i−2i4ii−2i−2i−2i0iii2ζ7−ζ11−ζ7+2ζ110000000000-422-4-12220-1-1-11−3i321+3i320000000000−4i2i2i−4i−i2i2i2i0−i−i−i−2ζ7+ζ11ζ7−2ζ110000000000
χ434-2-241-2-2-20111−1−3i32−1+3i3200000000004i−2i−2i4ii−2i−2i−2i0iii−ζ7+2ζ112ζ7−ζ110000000000-422-4-12220-1-1-11+3i321−3i320000000000−4i2i2i−4i−i2i2i2i0−i−i−iζ7−2ζ11−2ζ7+ζ110000000000
χ4466-3-2-3-210010000020-200-10106i6i−3i−2i−3i−2ii00i000002i0−2i00−i0i0-6-63232-100-100000-2020010-10−6i−6i3i2i3i2i−i00−i00000−2i02i00i0−i0
χ4566-3-2-3-2100100000-2020010-106i6i−3i−2i−3i−2ii00i00000−2i02i00i0−i0-6-63232-100-10000020-200-1010−6i−6i3i2i3i2i−i00−i000002i0−2i00−i0i0
χ466-36-2-31-2001000020-200-101006i−3i6i−2i−3ii−2i00i00002i0−2i00−i0i00-63-623-1200-10000-2020010-100−6i3i−6i2i3i−i2i00−i0000−2i02i00i0−i00
χ476-36-2-31-20010000-2020010-1006i−3i6i−2i−3ii−2i00i0000−2i02i00i0−i00-63-623-1200-1000020-200-10100−6i3i−6i2i3i−i2i00−i00002i0−2i00−i0i00
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χ49111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ5011111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1
χ5111111111-1111111-11-1-11-11-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11-111-11-11111111111-1111111-11-1-11-11-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11-111-11-111
χ5211111111-111111-11-11-1-11-11-1-1-1-1-1-1-1-1-11-1-1-1-1-11-11-111-11-1111111111-111111-11-11-1-11-11-1-1-1-1-1-1-1-1-11-1-1-1-1-11-11-111-11-11
χ532222222-122-1-1-1-1000020000-1-2-2-2-2-2-2-21-2-211110000-2000012222222-122-1-1-1-1000020000-1-2-2-2-2-2-2-21-2-211110000-200001
χ542222222-1-22-1-1-1-10000-200001-2-2-2-2-2-2-212-21111000020000-12222222-1-22-1-1-1-10000-200001-2-2-2-2-2-2-212-21111000020000-1
χ5522-12-12-120-12-1-1-1020200-10-10-2-21-21-21-201-21110-20-200101022-12-12-120-12-1-1-1020200-10-10-2-21-21-21-201-21110-20-2001010
χ5622-12-12-120-12-1-1-10-20-2001010-2-21-21-21-201-2111020200-10-1022-12-12-120-12-1-1-10-20-2001010-2-21-21-21-201-2111020200-10-10
χ572-122-1-1220-1-12-1-120200-10-100-21-2-211-2-2011-211-20-200101002-122-1-1220-1-12-1-120200-10-100-21-2-211-2-2011-211-20-20010100
χ582-122-1-1220-1-12-1-1-20-20010100-21-2-211-2-2011-21120200-10-1002-122-1-1220-1-12-1-1-20-20010100-21-2-211-2-2011-21120200-10-100
χ59333-13-1-103-1000011-1-1-111-1-10-3-3-31-3110-310000-1-1111-1-1110333-13-1-103-1000011-1-1-111-1-10-3-3-31-3110-310000-1-1111-1-1110
χ60333-13-1-103-10000-1-111-1-1-1110-3-3-31-3110-31000011-1-1111-1-10333-13-1-103-10000-1-111-1-1-1110-3-3-31-3110-31000011-1-1111-1-10
χ61333-13-1-10-3-100001-1-1111-1-110-3-3-31-3110310000-111-1-1-111-10333-13-1-10-3-100001-1-1111-1-110-3-3-31-3110310000-111-1-1-111-10
χ62333-13-1-10-3-10000-111-11-111-10-3-3-31-31103100001-1-11-11-1-110333-13-1-10-3-10000-111-11-111-10-3-3-31-31103100001-1-11-11-1-110
χ6344-24-24-2-20-2-21110000000000-4-42-42-422022-1-1-1000000000044-24-24-2-20-2-21110000000000-4-42-42-422022-1-1-10000000000
χ644-244-2-24-20-21-2110000000000-42-4-422-4202-12-1-100000000004-244-2-24-20-21-2110000000000-42-4-422-4202-12-1-10000000000
χ654-2-241-2-2401-2-2110000000000-422-4-122-40-122-1-100000000004-2-241-2-2401-2-2110000000000-422-4-122-40-122-1-10000000000
χ664-2-241-2-2-20111−1+3i32−1−3i320000000000-422-4-12220-1-1-11−3i321+3i3200000000004-2-241-2-2-20111−1+3i32−1−3i320000000000-422-4-12220-1-1-11−3i321+3i320000000000
χ674-2-241-2-2-20111−1−3i32−1+3i320000000000-422-4-12220-1-1-11+3i321−3i3200000000004-2-241-2-2-20111−1−3i32−1+3i320000000000-422-4-12220-1-1-11+3i321−3i320000000000
χ6866-3-2-3-210010000020-200-1010-6-63232-100-100000-2020010-1066-3-2-3-210010000020-200-1010-6-63232-100-100000-2020010-10
χ6966-3-2-3-2100100000-2020010-10-6-63232-100-10000020-200-101066-3-2-3-2100100000-2020010-10-6-63232-100-10000020-200-1010
χ706-36-2-31-2001000020-200-10100-63-623-1200-10000-2020010-1006-36-2-31-2001000020-200-10100-63-623-1200-10000-2020010-100
χ716-36-2-31-20010000-2020010-100-63-623-1200-1000020-200-101006-36-2-31-20010000-2020010-100-63-623-1200-1000020-200-10100
χ7212-6-6-432200-100000000000000-12664-3-2-20010000000000000012-6-6-432200-100000000000000-12664-3-2-200100000000000000
χ73111111111111111111111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiiiiiiiiiii
χ7411111111111111-1-1-1-11-1-1-1-11−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiii−iiiii−i-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1iiiiiiiiiiiiii−i−i−i−ii−i−i−i−ii
χ7511111111-1111111-11-1-11-11-1-1−i−i−i−i−i−i−i−ii−i−i−i−i−i−ii−iii−ii−iii-1-1-1-1-1-1-1-11-1-1-1-1-1-11-111-11-111iiiiiiii−iiiiiii−ii−i−ii−ii−i−i
χ7611111111-111111-11-11-1-11-11-1−i−i−i−i−i−i−i−ii−i−i−i−i−ii−ii−iii−ii−ii-1-1-1-1-1-1-1-11-1-1-1-1-11-11-111-11-11iiiiiiii−iiiiii−ii−ii−i−ii−ii−i
χ772222222-122-1-1-1-1000020000-1−2i−2i−2i−2i−2i−2i−2ii−2i−2iiiii0000−2i0000i-2-2-2-2-2-2-21-2-211110000-2000012i2i2i2i2i2i2i−i2i2i−i−i−i−i00002i0000−i
χ782222222-1-22-1-1-1-10000-200001−2i−2i−2i−2i−2i−2i−2ii2i−2iiiii00002i0000−i-2-2-2-2-2-2-212-21111000020000-12i2i2i2i2i2i2i−i−2i2i−i−i−i−i0000−2i0000i
χ7922-12-12-120-12-1-1-1020200-10-10−2i−2ii−2ii−2ii−2i0i−2iiii0−2i0−2i00i0i0-2-21-21-21-201-21110-20-20010102i2i−i2i−i2i−i2i0−i2i−i−i−i02i02i00−i0−i0
χ8022-12-12-120-12-1-1-10-20-2001010−2i−2ii−2ii−2ii−2i0i−2iiii02i02i00−i0−i0-2-21-21-21-201-2111020200-10-102i2i−i2i−i2i−i2i0−i2i−i−i−i0−2i0−2i00i0i0
χ812-122-1-1220-1-12-1-120200-10-100−2ii−2i−2iii−2i−2i0ii−2iii−2i0−2i00i0i00-21-2-211-2-2011-211-20-200101002i−i2i2i−i−i2i2i0−i−i2i−i−i2i02i00−i0−i00
χ822-122-1-1220-1-12-1-1-20-20010100−2ii−2i−2iii−2i−2i0ii−2iii2i02i00−i0−i00-21-2-211-2-2011-21120200-10-1002i−i2i2i−i−i2i2i0−i−i2i−i−i−2i0−2i00i0i00
χ83333-13-1-103-1000011-1-1-111-1-10−3i−3i−3ii−3iii0−3ii0000−i−iiii−i−iii0-3-3-31-3110-310000-1-1111-1-11103i3i3i−i3i−i−i03i−i0000ii−i−i−iii−i−i0
χ84333-13-1-103-10000-1-111-1-1-1110−3i−3i−3ii−3iii0−3ii0000ii−i−iiii−i−i0-3-3-31-3110-31000011-1-1111-1-103i3i3i−i3i−i−i03i−i0000−i−iii−i−i−iii0
χ85333-13-1-10-3-100001-1-1111-1-110−3i−3i−3ii−3iii03ii0000−iii−i−i−iii−i0-3-3-31-3110310000-111-1-1-111-103i3i3i−i3i−i−i0−3i−i0000i−i−iiii−i−ii0
χ86333-13-1-10-3-10000-111-11-111-10−3i−3i−3ii−3iii03ii0000i−i−ii−ii−i−ii0-3-3-31-31103100001-1-11-11-1-1103i3i3i−i3i−i−i0−3i−i0000−iii−ii−iii−i0
χ8744-24-24-2-20-2-21110000000000−4i−4i2i−4i2i−4i2i2i02i2i−i−i−i0000000000-4-42-42-422022-1-1-100000000004i4i−2i4i−2i4i−2i−2i0−2i−2iiii0000000000
χ884-244-2-24-20-21-2110000000000−4i2i−4i−4i2i2i−4i2i02i−i2i−i−i0000000000-42-4-422-4202-12-1-100000000004i−2i4i4i−2i−2i4i−2i0−2ii−2iii0000000000
χ894-2-241-2-2401-2-2110000000000−4i2i2i−4i−i2i2i−4i0−i2i2i−i−i0000000000-422-4-122-40-122-1-100000000004i−2i−2i4ii−2i−2i4i0i−2i−2iii0000000000
χ904-2-241-2-2-20111−1+3i32−1−3i320000000000−4i2i2i−4i−i2i2i2i0−i−i−i−2ζ7+ζ11ζ7−2ζ110000000000-422-4-12220-1-1-11−3i321+3i3200000000004i−2i−2i4ii−2i−2i−2i0iii2ζ7−ζ11−ζ7+2ζ110000000000
χ914-2-241-2-2-20111−1−3i32−1+3i320000000000−4i2i2i−4i−i2i2i2i0−i−i−iζ7−2ζ11−2ζ7+ζ110000000000-422-4-12220-1-1-11+3i321−3i3200000000004i−2i−2i4ii−2i−2i−2i0iii−ζ7+2ζ112ζ7−ζ110000000000
χ9266-3-2-3-210010000020-200-1010−6i−6i3i2i3i2i−i00−i00000−2i02i00i0−i0-6-63232-100-100000-2020010-106i6i−3i−2i−3i−2ii00i000002i0−2i00−i0i0
χ9366-3-2-3-2100100000-2020010-10−6i−6i3i2i3i2i−i00−i000002i0−2i00−i0i0-6-63232-100-10000020-200-10106i6i−3i−2i−3i−2ii00i00000−2i02i00i0−i0
χ946-36-2-31-2001000020-200-10100−6i3i−6i2i3i−i2i00−i0000−2i02i00i0−i00-63-623-1200-10000-2020010-1006i−3i6i−2i−3ii−2i00i00002i0−2i00−i0i00
χ956-36-2-31-20010000-2020010-100−6i3i−6i2i3i−i2i00−i00002i0−2i00−i0i00-63-623-1200-1000020-200-101006i−3i6i−2i−3ii−2i00i0000−2i02i00i0−i00
χ9612-6-6-432200-100000000000000−12i6i6i4i−3i−2i−2i00i00000000000000-12664-3-2-20010000000000000012i−6i−6i−4i3i2i2i00−i00000000000000

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