Finite Group Databasebeta

← Group #88813

Character table — Group #88813

Order 432.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111122222222222244444444444444444444999999999999181818181818181818181818
order122233366666666633333666666666666666444444444444121212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ511-1-111111-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i
χ611-1-111111-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1−i−iii−i−iii11-1-1−i−iii−i−iii
χ711-1-111111-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii-1-111ii−i−i−i−iii
χ811-1-111111-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i-1-111−i−iiiii−i−i
χ91-11-1111-1-111-1-1-11-111111-1-1-1-1-111111-1-1-1-1-1i−ii−i1-11-1i−ii−ii−ii−i1-11-1i−ii−i
χ101-11-1111-1-111-1-1-11-111111-1-1-1-1-111111-1-1-1-1-1i−ii−i-11-11−ii−iii−ii−i-11-11−ii−ii
χ111-11-1111-1-111-1-1-11-111111-1-1-1-1-111111-1-1-1-1-1−ii−ii1-11-1−ii−ii−ii−ii1-11-1−ii−ii
χ121-11-1111-1-111-1-1-11-111111-1-1-1-1-111111-1-1-1-1-1−ii−ii-11-11i−ii−i−ii−ii-11-11i−ii−i
χ131-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-111111i−i−iii−i−ii-111-1i−i−iii−i−ii-111-1
χ141-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-111111i−i−ii−iii−i1-1-11i−i−ii−iii−i1-1-11
χ151-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-111111−iii−ii−i−ii1-1-11−iii−ii−i−ii1-1-11
χ161-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-111111−iii−i−iii−i-111-1−iii−i−iii−i-111-1
χ17222222-1222-12-1-1222-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1-1222200000000-1-1-1-100000000
χ18222222-1222-12-1-1222-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1-1-2-2-2-200000000111100000000
χ1922222-122-122-122-12-12-1-1-1-12-1-1-1-12-1-1-1-12-1-1-10000222200000000-1-1-1-10000
χ2022222-122-122-122-12-12-1-1-1-12-1-1-1-12-1-1-1-12-1-1-10000-2-2-2-20000000011110000
χ212222-122-12-122222-1-1-12-1-1-1-12-1-1-1-12-1-1-1-12-1-100000000222200000000-1-1-1-1
χ222222-122-12-122222-1-1-12-1-1-1-12-1-1-1-12-1-1-1-12-1-100000000-2-2-2-2000000001111
χ2322-2-222-122-21-21-1-2-22-1-1-1-12-1-1-1-1-21111-2111122-2-200000000-1-11100000000
χ2422-2-222-122-21-21-1-2-22-1-1-1-12-1-1-1-1-21111-21111-2-2220000000011-1-100000000
χ2522-2-22-122-1-2-21-221-2-12-1-1-1-12-1-1-11-21111-211100002i2i−2i−2i00000000−i−iii0000
χ2622-2-22-122-1-2-21-221-2-12-1-1-1-12-1-1-11-21111-21110000−2i−2i2i2i00000000ii−i−i0000
χ2722-2-2-122-121-2-2-22-21-1-12-1-1-1-12-1-111-21111-211000000002i2i−2i−2i00000000−i−iii
χ2822-2-2-122-121-2-2-22-21-1-12-1-1-1-12-1-111-21111-21100000000−2i−2i2i2i00000000ii−i−i
χ292-22-222-1-2-22-1-2112-22-1-1-1-1-211112-1-1-1-1-211112i−2i2i−2i00000000−ii−ii00000000
χ302-22-222-1-2-22-1-2112-22-1-1-1-1-211112-1-1-1-1-21111−2i2i−2i2i00000000i−ii−i00000000
χ312-22-22-12-21221-2-2-1-2-12-1-1-11-2111-12-1-1-11-211100002-22-200000000-11-110000
χ322-22-22-12-21221-2-2-1-2-12-1-1-11-2111-12-1-1-11-21110000-22-22000000001-11-10000
χ332-22-2-1221-2-12-2-2-221-1-12-1-111-211-1-12-1-111-211000000002i−2i2i−2i00000000−ii−ii
χ342-22-2-1221-2-12-2-2-221-1-12-1-111-211-1-12-1-111-21100000000−2i2i−2i2i00000000i−ii−i
χ352-2-2222-1-2-2-212-11-222-1-1-1-1-21111-211112-1-1-1-12i−2i−2i2i00000000−iii−i00000000
χ362-2-2222-1-2-2-212-11-222-1-1-1-1-21111-211112-1-1-1-1−2i2i2i−2i00000000i−i−ii00000000
χ372-2-222-12-21-2-2-12-212-12-1-1-11-21111-2111-12-1-1-100002i−2i−2i2i00000000−iii−i0000
χ382-2-222-12-21-2-2-12-212-12-1-1-11-21111-2111-12-1-1-10000−2i2i2i−2i00000000i−i−ii0000
χ392-2-22-1221-21-222-2-2-1-1-12-1-111-21111-211-1-12-1-1000000002-2-2200000000-111-1
χ402-2-22-1221-21-222-2-2-1-1-12-1-111-21111-211-1-12-1-100000000-222-2000000001-1-11
χ4144444-2-24-24-2-2-2-2-24-2-2111-2-2111-2-2111-2-2111000000000000000000000000
χ424444-24-2-24-2-24-2-24-2-21-211-21-211-21-211-21-211000000000000000000000000
χ434444-2-24-2-2-24-244-2-21-2-2111-2-2111-2-2111-2-211000000000000000000000000
χ444444-2-2-2-2-2-2-2-2-2-2-2-2111−1−3i32−1+3i32111−1−3i32−1+3i32111−1−3i32−1+3i32111−1−3i32−1+3i32000000000000000000000000
χ454444-2-2-2-2-2-2-2-2-2-2-2-2111−1+3i32−1−3i32111−1+3i32−1−3i32111−1+3i32−1−3i32111−1+3i32−1−3i32000000000000000000000000
χ4644-4-44-2-24-2-4222-22-4-2-2111-2-211122-1-1-122-1-1-1000000000000000000000000
χ4744-4-4-24-2-2422-42-2-42-21-211-21-2112-12-1-12-12-1-1000000000000000000000000
χ4844-4-4-2-24-2-22-42-44221-2-2111-2-211-122-1-1-122-1-1000000000000000000000000
χ4944-4-4-2-2-2-2-22222-222111−1−3i32−1+3i32111−1−3i32−1+3i32-1-1-11+3i321−3i32-1-1-11+3i321−3i32000000000000000000000000
χ5044-4-4-2-2-2-2-22222-222111−1+3i32−1−3i32111−1+3i32−1−3i32-1-1-11−3i321+3i32-1-1-11−3i321+3i32000000000000000000000000
χ514-44-44-2-2-424-2222-2-4-2-211122-1-1-1-2-211122-1-1-1000000000000000000000000
χ524-44-4-24-22-4-2-2-42242-21-2112-12-1-1-21-2112-12-1-1000000000000000000000000
χ534-44-4-2-2422-242-4-4-221-2-211-122-1-11-2-211-122-1-1000000000000000000000000
χ544-44-4-2-2-222-2-2222-22111−1−3i32−1+3i32-1-1-11+3i321−3i32111−1−3i32−1+3i32-1-1-11+3i321−3i32000000000000000000000000
χ554-44-4-2-2-222-2-2222-22111−1+3i32−1−3i32-1-1-11−3i321+3i32111−1+3i32−1−3i32-1-1-11−3i321+3i32000000000000000000000000
χ564-4-444-2-2-42-42-2-2224-2-211122-1-1-122-1-1-1-2-2111000000000000000000000000
χ574-4-44-24-22-4224-22-4-2-21-2112-12-1-12-12-1-1-21-211000000000000000000000000
χ584-4-44-2-24222-4-24-42-21-2-211-122-1-1-122-1-11-2-211000000000000000000000000
χ594-4-44-2-2-22222-2-222-2111−1−3i32−1+3i32-1-1-11+3i321−3i32-1-1-11+3i321−3i32111−1−3i32−1+3i32000000000000000000000000
χ604-4-44-2-2-22222-2-222-2111−1+3i32−1−3i32-1-1-11−3i321+3i32-1-1-11−3i321+3i32111−1+3i32−1−3i32000000000000000000000000

Here i is the imaginary unit (i² = −1).