Finite Group Databasebeta

← Group #89043

Character table — Group #89043

Order 432.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size122244444999181818122244444999181818122244444999181818122244444999181818
order1333333332226664121212121212121244412121226666666622266641212121212121212444121212
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111-1-11-1-11111111111-1-11-1-11111111111-1-11-1-11111111111-1-11-1-1
χ3111111111-11-1-11-1111111111-11-1-11-1111111111-11-1-11-1111111111-11-1-11-1
χ4111111111-1-11-1-11111111111-1-11-1-11111111111-1-11-1-11111111111-1-11-1-11
χ5222-12-1-1-1-100200-1222-12-1-1-1-100200-1222-12-1-1-1-100200-1222-12-1-1-1-100200-1
χ6222-12-1-1-1-100-2001222-12-1-1-1-100-2001222-12-1-1-1-100-2001222-12-1-1-1-100-2001
χ722-12-12-1-1-10200-1022-12-12-1-1-10200-1022-12-12-1-1-10200-1022-12-12-1-1-10200-10
χ822-12-12-1-1-10-2001022-12-12-1-1-10-2001022-12-12-1-1-10-2001022-12-12-1-1-10-20010
χ92-122-1-12-1-1200-1002-122-1-12-1-1200-1002-122-1-12-1-1200-1002-122-1-12-1-1200-100
χ102-122-1-12-1-1-2001002-122-1-12-1-1-2001002-122-1-12-1-1-2001002-122-1-12-1-1-200100
χ1144-2-2-2-211100000044-2-2-2-211100000044-2-2-2-211100000044-2-2-2-2111000000
χ124-24-2-21-2110000004-24-2-21-2110000004-24-2-21-2110000004-24-2-21-211000000
χ134-2-241-2-2110000004-2-241-2-2110000004-2-241-2-2110000004-2-241-2-211000000
χ144-2-2-2111−1+3i32−1−3i320000004-2-2-2111−1+3i32−1−3i320000004-2-2-2111−1+3i32−1−3i320000004-2-2-2111−1+3i32−1−3i32000000
χ154-2-2-2111−1−3i32−1+3i320000004-2-2-2111−1−3i32−1+3i320000004-2-2-2111−1−3i32−1+3i320000004-2-2-2111−1−3i32−1+3i32000000
χ16111111111111111iiiiiiiiiiiiiii-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
χ171111111111-1-11-1-1iiiiiiiiii−i−ii−i−i-1-1-1-1-1-1-1-1-1-111-111−i−i−i−i−i−i−i−i−i−iii−iii
χ18111111111-11-1-11-1iiiiiiiii−ii−i−ii−i-1-1-1-1-1-1-1-1-11-111-11−i−i−i−i−i−i−i−i−ii−iii−ii
χ19111111111-1-11-1-11iiiiiiiii−i−ii−i−ii-1-1-1-1-1-1-1-1-111-111-1−i−i−i−i−i−i−i−i−iii−iii−i
χ20222-12-1-1-1-100200-12i2i2i−i2i−i−i−i−i002i00−i-2-2-21-2111100-2001−2i−2i−2ii−2iiiii00−2i00i
χ21222-12-1-1-1-100-20012i2i2i−i2i−i−i−i−i00−2i00i-2-2-21-2111100200-1−2i−2i−2ii−2iiiii002i00−i
χ2222-12-12-1-1-10200-102i2i−i2i−i2i−i−i−i02i00−i0-2-21-21-21110-20010−2i−2ii−2ii−2iiii0−2i00i0
χ2322-12-12-1-1-10-200102i2i−i2i−i2i−i−i−i0−2i00i0-2-21-21-21110200-10−2i−2ii−2ii−2iiii02i00−i0
χ242-122-1-12-1-1200-1002i−i2i2i−i−i2i−i−i2i00−i00-21-2-211-211-200100−2ii−2i−2iii−2iii−2i00i00
χ252-122-1-12-1-1-2001002i−i2i2i−i−i2i−i−i−2i00i00-21-2-211-211200-100−2ii−2i−2iii−2iii2i00−i00
χ2644-2-2-2-21110000004i4i−2i−2i−2i−2iiii000000-4-42222-1-1-1000000−4i−4i2i2i2i2i−i−i−i000000
χ274-24-2-21-2110000004i−2i4i−2i−2ii−2iii000000-42-422-12-1-1000000−4i2i−4i2i2i−i2i−i−i000000
χ284-2-241-2-2110000004i−2i−2i4ii−2i−2iii000000-422-4-122-1-1000000−4i2i2i−4i−i2i2i−i−i000000
χ294-2-2-2111−1+3i32−1−3i320000004i−2i−2i−2iiii2ζ7−ζ11−ζ7+2ζ11000000-4222-1-1-11−3i321+3i32000000−4i2i2i2i−i−i−i−2ζ7+ζ11ζ7−2ζ11000000
χ304-2-2-2111−1−3i32−1+3i320000004i−2i−2i−2iiii−ζ7+2ζ112ζ7−ζ11000000-4222-1-1-11+3i321−3i32000000−4i2i2i2i−i−i−iζ7−2ζ11−2ζ7+ζ11000000
χ31111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ321111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-111-111
χ33111111111-11-1-11-1-1-1-1-1-1-1-1-1-11-111-11111111111-11-1-11-1-1-1-1-1-1-1-1-1-11-111-11
χ34111111111-1-11-1-11-1-1-1-1-1-1-1-1-111-111-1111111111-1-11-1-11-1-1-1-1-1-1-1-1-111-111-1
χ35222-12-1-1-1-100200-1-2-2-21-2111100-2001222-12-1-1-1-100200-1-2-2-21-2111100-2001
χ36222-12-1-1-1-100-2001-2-2-21-2111100200-1222-12-1-1-1-100-2001-2-2-21-2111100200-1
χ3722-12-12-1-1-10200-10-2-21-21-21110-2001022-12-12-1-1-10200-10-2-21-21-21110-20010
χ3822-12-12-1-1-10-20010-2-21-21-21110200-1022-12-12-1-1-10-20010-2-21-21-21110200-10
χ392-122-1-12-1-1200-100-21-2-211-211-2001002-122-1-12-1-1200-100-21-2-211-211-200100
χ402-122-1-12-1-1-200100-21-2-211-211200-1002-122-1-12-1-1-200100-21-2-211-211200-100
χ4144-2-2-2-2111000000-4-42222-1-1-100000044-2-2-2-2111000000-4-42222-1-1-1000000
χ424-24-2-21-211000000-42-422-12-1-10000004-24-2-21-211000000-42-422-12-1-1000000
χ434-2-241-2-211000000-422-4-122-1-10000004-2-241-2-211000000-422-4-122-1-1000000
χ444-2-2-2111−1+3i32−1−3i32000000-4222-1-1-11−3i321+3i320000004-2-2-2111−1+3i32−1−3i32000000-4222-1-1-11−3i321+3i32000000
χ454-2-2-2111−1−3i32−1+3i32000000-4222-1-1-11+3i321−3i320000004-2-2-2111−1−3i32−1+3i32000000-4222-1-1-11+3i321−3i32000000
χ46111111111111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiii
χ471111111111-1-11-1-1−i−i−i−i−i−i−i−i−i−iii−iii-1-1-1-1-1-1-1-1-1-111-111iiiiiiiiii−i−ii−i−i
χ48111111111-11-1-11-1−i−i−i−i−i−i−i−i−ii−iii−ii-1-1-1-1-1-1-1-1-11-111-11iiiiiiiii−ii−i−ii−i
χ49111111111-1-11-1-11−i−i−i−i−i−i−i−i−iii−iii−i-1-1-1-1-1-1-1-1-111-111-1iiiiiiiii−i−ii−i−ii
χ50222-12-1-1-1-100200-1−2i−2i−2ii−2iiiii00−2i00i-2-2-21-2111100-20012i2i2i−i2i−i−i−i−i002i00−i
χ51222-12-1-1-1-100-2001−2i−2i−2ii−2iiiii002i00−i-2-2-21-2111100200-12i2i2i−i2i−i−i−i−i00−2i00i
χ5222-12-12-1-1-10200-10−2i−2ii−2ii−2iiii0−2i00i0-2-21-21-21110-200102i2i−i2i−i2i−i−i−i02i00−i0
χ5322-12-12-1-1-10-20010−2i−2ii−2ii−2iiii02i00−i0-2-21-21-21110200-102i2i−i2i−i2i−i−i−i0−2i00i0
χ542-122-1-12-1-1200-100−2ii−2i−2iii−2iii−2i00i00-21-2-211-211-2001002i−i2i2i−i−i2i−i−i2i00−i00
χ552-122-1-12-1-1-200100−2ii−2i−2iii−2iii2i00−i00-21-2-211-211200-1002i−i2i2i−i−i2i−i−i−2i00i00
χ5644-2-2-2-2111000000−4i−4i2i2i2i2i−i−i−i000000-4-42222-1-1-10000004i4i−2i−2i−2i−2iiii000000
χ574-24-2-21-211000000−4i2i−4i2i2i−i2i−i−i000000-42-422-12-1-10000004i−2i4i−2i−2ii−2iii000000
χ584-2-241-2-211000000−4i2i2i−4i−i2i2i−i−i000000-422-4-122-1-10000004i−2i−2i4ii−2i−2iii000000
χ594-2-2-2111−1+3i32−1−3i32000000−4i2i2i2i−i−i−i−2ζ7+ζ11ζ7−2ζ11000000-4222-1-1-11−3i321+3i320000004i−2i−2i−2iiii2ζ7−ζ11−ζ7+2ζ11000000
χ604-2-2-2111−1−3i32−1+3i32000000−4i2i2i2i−i−i−iζ7−2ζ11−2ζ7+ζ11000000-4222-1-1-11+3i321−3i320000004i−2i−2i−2iiii−ζ7+2ζ112ζ7−ζ11000000

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