Finite Group Databasebeta

← Group #13166111

Character table — Group #13166111

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222222333344446666666688889999121212121616161616161616161616161616161618181818181818181818181818181818272727273636363636363636363636363636363672727272
order12223366666622223666666666663666444466663333666666666666444444444444444444441212121212121212121212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ511-1-1111-1-1-11-11-11-111-1-1111-1-1-11-111-1-1ii−i−i11-1-111111111-1-1-1-1-1-1-1-111-1-1ii−i−i11-1-1ii−i−iii−i−i11-1-1ii−i−i11-1-1ii−i−iii−i−i
χ611-1-1111-1-1-11-11-11-111-1-1111-1-1-11-111-1-1ii−i−i11-1-111111111-1-1-1-1-1-1-1-1-1-111−i−iii-1-111−i−iiiii−i−i-1-111−i−iii-1-111−i−iiiii−i−i
χ711-1-1111-1-1-11-11-11-111-1-1111-1-1-11-111-1-1−i−iii11-1-111111111-1-1-1-1-1-1-1-111-1-1−i−iii11-1-1−i−iii−i−iii11-1-1−i−iii11-1-1−i−iii−i−iii
χ811-1-1111-1-1-11-11-11-111-1-1111-1-1-11-111-1-1−i−iii11-1-111111111-1-1-1-1-1-1-1-1-1-111ii−i−i-1-111ii−i−i−i−iii-1-111ii−i−i-1-111ii−i−i−i−iii
χ91-11-111-11-1-1-111-1-111-11-111-11-1-1-111-11-1i−ii−i1-11-11111-1-1-1-11111-1-1-1-1i−ii−i1-11-1i−ii−i1-11-1i−ii−ii−ii−i1-11-1i−ii−i1-11-1i−ii−i
χ101-11-111-11-1-1-111-1-111-11-111-11-1-1-111-11-1i−ii−i1-11-11111-1-1-1-11111-1-1-1-1−ii−ii-11-11−ii−ii-11-11i−ii−i−ii−ii-11-11−ii−ii-11-11i−ii−i
χ111-11-111-11-1-1-111-1-111-11-111-11-1-1-111-11-1−ii−ii1-11-11111-1-1-1-11111-1-1-1-1i−ii−i-11-11i−ii−i-11-11−ii−iii−ii−i-11-11i−ii−i-11-11−ii−ii
χ121-11-111-11-1-1-111-1-111-11-111-11-1-1-111-11-1−ii−ii1-11-11111-1-1-1-11111-1-1-1-1−ii−ii1-11-1−ii−ii1-11-1−ii−ii−ii−ii1-11-1−ii−ii1-11-1−ii−ii
χ131-1-1111-1-111-1-111-1-11-1-1111-1-111-1-11-1-111-1-111-1-111111-1-1-1-1-1-1-1-11111i−i−ii−iii−ii−i−ii−iii−i1-1-11i−i−ii−iii−ii−i−ii−iii−i1-1-11
χ141-1-1111-1-111-1-111-1-11-1-1111-1-111-1-11-1-111-1-111-1-111111-1-1-1-1-1-1-1-11111−iii−ii−i−ii−iii−ii−i−ii1-1-11−iii−ii−i−ii−iii−ii−i−ii1-1-11
χ151-1-1111-1-111-1-111-1-11-1-1111-1-111-1-11-1-11-111-11-1-111111-1-1-1-1-1-1-1-11111i−i−iii−i−iii−i−iii−i−ii-111-1i−i−iii−i−iii−i−iii−i−ii-111-1
χ161-1-1111-1-111-1-111-1-11-1-1111-1-111-1-11-1-11-111-11-1-111111-1-1-1-1-1-1-1-11111−iii−i−iii−i−iii−i−iii−i-111-1−iii−i−iii−i−iii−i−iii−i-111-1
χ172222222222222222222222222222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022220000000000000000-1-1-1-1
χ182222222222222222222222222222-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-200000000000000001111
χ1922222-12-12-1-122222-1-1-1-12-12-12-1-1222220000-1-1-1-12-1-1-12-1-1-12-1-1-12-1-1-122220000222200000000-1-1-1-10000-1-1-1-100000000
χ2022222-12-12-1-122222-1-1-1-12-12-12-1-1222220000-1-1-1-12-1-1-12-1-1-12-1-1-12-1-1-1-2-2-2-20000-2-2-2-20000000011110000111100000000
χ212222-12-12-122-12222-1-1-1-1-12-12-122-122220000-1-1-1-1-12-1-1-12-1-1-12-1-1-12-1-1000022220000222200000000-1-1-1-10000-1-1-1-10000
χ222222-12-12-122-12222-1-1-1-1-12-12-122-122220000-1-1-1-1-12-1-1-12-1-1-12-1-1-12-1-10000-2-2-2-20000-2-2-2-2000000001111000011110000
χ2322-2-2222-2-2-22-22-22-222-2-2222-2-2-22-2-1-1112i2i−2i−2i22-2-2-1-1-1-1-1-1-1-11111111100000000000000002i2i−2i−2i0000000000000000−i−iii
χ2422-2-2222-2-2-22-22-22-222-2-2222-2-2-22-2-1-111−2i−2i2i2i22-2-2-1-1-1-1-1-1-1-1111111110000000000000000−2i−2i2i2i0000000000000000ii−i−i
χ2522-2-22-121-21-1-22-22-2-1-1112-121-21-1-222-2-20000-1-1112-1-1-12-1-1-1-2111-211122-2-2000022-2-200000000-1-1110000-1-11100000000
χ2622-2-22-121-21-1-22-22-2-1-1112-121-21-1-222-2-20000-1-1112-1-1-12-1-1-1-2111-2111-2-2220000-2-2220000000011-1-1000011-1-100000000
χ2722-2-2-12-1-21-2212-22-2-1-111-12-1-21-22122-2-20000-1-111-12-1-1-12-1-11-2111-21100002i2i−2i−2i00002i2i−2i−2i00000000−i−iii0000−i−iii0000
χ2822-2-2-12-1-21-2212-22-2-1-111-12-1-21-22122-2-20000-1-111-12-1-1-12-1-11-2111-2110000−2i−2i2i2i0000−2i−2i2i2i00000000ii−i−i0000ii−i−i0000
χ292-22-222-22-2-2-222-2-222-22-222-22-2-2-22-11-112i−2i2i−2i2-22-2-1-1-1-11111-1-1-1-1111100000000000000002i−2i2i−2i0000000000000000−ii−ii
χ302-22-222-22-2-2-222-2-222-22-222-22-2-2-22-11-11−2i2i−2i2i2-22-2-1-1-1-11111-1-1-1-111110000000000000000−2i2i−2i2i0000000000000000i−ii−i
χ312-22-22-1-2-1-21122-2-22-11-112-1-2-1-21122-22-20000-11-112-1-1-1-21112-1-1-1-21112i−2i2i−2i00002i−2i2i−2i00000000−ii−ii0000−ii−ii00000000
χ322-22-22-1-2-1-21122-2-22-11-112-1-2-1-21122-22-20000-11-112-1-1-1-21112-1-1-1-2111−2i2i−2i2i0000−2i2i−2i2i00000000i−ii−i0000i−ii−i00000000
χ332-22-2-12121-2-2-12-2-22-11-11-12121-2-2-12-22-20000-11-11-12-1-11-211-12-1-11-21100002-22-200002-22-200000000-11-110000-11-110000
χ342-22-2-12121-2-2-12-2-22-11-11-12121-2-2-12-22-20000-11-11-12-1-11-211-12-1-11-2110000-22-220000-22-22000000001-11-100001-11-10000
χ352-2-2222-2-222-2-222-2-22-2-2222-2-222-2-2-111-12-2-222-2-22-1-1-1-111111111-1-1-1-100000000000000002-2-220000000000000000-111-1
χ362-2-2222-2-222-2-222-2-22-2-2222-2-222-2-2-111-1-222-22-2-22-1-1-1-111111111-1-1-1-10000000000000000-222-200000000000000001-1-11
χ372-2-222-1-212-11-222-2-2-111-12-1-212-11-22-2-220000-111-12-1-1-1-2111-21112-1-1-12i−2i−2i2i00002i−2i−2i2i00000000−iii−i0000−iii−i00000000
χ382-2-222-1-212-11-222-2-2-111-12-1-212-11-22-2-220000-111-12-1-1-1-2111-21112-1-1-1−2i2i2i−2i0000−2i2i2i−2i00000000i−i−ii0000i−i−ii00000000
χ392-2-22-121-2-12-2122-2-2-111-1-121-2-12-212-2-220000-111-1-12-1-11-2111-211-12-1-100002i−2i−2i2i00002i−2i−2i2i00000000−iii−i0000−iii−i0000
χ402-2-22-121-2-12-2122-2-2-111-1-121-2-12-212-2-220000-111-1-12-1-11-2111-211-12-1-10000−2i2i2i−2i0000−2i2i2i−2i00000000i−i−ii0000i−i−ii0000
χ41333333333333-1-1-1-13333-1-1-1-1-1-1-1-100003333-1-1-1-1000000000000000011111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-10000
χ42333333333333-1-1-1-13333-1-1-1-1-1-1-1-100003333-1-1-1-10000000000000000-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111110000
χ43333333333333-1-1-1-13333-1-1-1-1-1-1-1-10000-3-3-3-3-1-1-1-100000000000000001111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111110000
χ44333333333333-1-1-1-13333-1-1-1-1-1-1-1-10000-3-3-3-3-1-1-1-10000000000000000-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-10000
χ4533-3-3333-3-3-33-3-11-1133-3-3-1-1-1111-1100003i3i−3i−3i-1-111000000000000000011-1-1ii−i−i-1-111−i−iii−i−iii11-1-1ii−i−i-1-111−i−iii0000
χ4633-3-3333-3-3-33-3-11-1133-3-3-1-1-1111-1100003i3i−3i−3i-1-1110000000000000000-1-111−i−iii11-1-1ii−i−i−i−iii-1-111−i−iii11-1-1ii−i−i0000
χ4733-3-3333-3-3-33-3-11-1133-3-3-1-1-1111-110000−3i−3i3i3i-1-111000000000000000011-1-1−i−iii-1-111ii−i−iii−i−i11-1-1−i−iii-1-111ii−i−i0000
χ4833-3-3333-3-3-33-3-11-1133-3-3-1-1-1111-110000−3i−3i3i3i-1-1110000000000000000-1-111ii−i−i11-1-1−i−iiiii−i−i-1-111ii−i−i11-1-1−i−iii0000
χ493-33-333-33-3-3-33-111-13-33-3-1-11-1111-100003i−3i3i−3i-11-110000000000000000i−ii−i1-11-1−ii−ii-11-11−ii−iii−ii−i1-11-1−ii−ii-11-110000
χ503-33-333-33-3-3-33-111-13-33-3-1-11-1111-100003i−3i3i−3i-11-110000000000000000−ii−ii-11-11i−ii−i1-11-1−ii−ii−ii−ii-11-11i−ii−i1-11-10000
χ513-33-333-33-3-3-33-111-13-33-3-1-11-1111-10000−3i3i−3i3i-11-110000000000000000i−ii−i-11-11−ii−ii1-11-1i−ii−ii−ii−i-11-11−ii−ii1-11-10000
χ523-33-333-33-3-3-33-111-13-33-3-1-11-1111-10000−3i3i−3i3i-11-110000000000000000−ii−ii1-11-1i−ii−i-11-11i−ii−i−ii−ii1-11-1i−ii−i-11-110000
χ533-3-3333-3-333-3-3-1-1113-3-33-1-111-1-11100003-3-33-111-10000000000000000i−i−ii−iii−i−iii−ii−i−ii-111-1i−i−ii−iii−i−iii−ii−i−ii0000
χ543-3-3333-3-333-3-3-1-1113-3-33-1-111-1-11100003-3-33-111-10000000000000000−iii−ii−i−iii−i−ii−iii−i-111-1−iii−ii−i−iii−i−ii−iii−i0000
χ553-3-3333-3-333-3-3-1-1113-3-33-1-111-1-1110000-333-3-111-10000000000000000i−i−iii−i−ii−iii−i−iii−i1-1-11i−i−iii−i−ii−iii−i−iii−i0000
χ563-3-3333-3-333-3-3-1-1113-3-33-1-111-1-1110000-333-3-111-10000000000000000−iii−i−iii−ii−i−iii−i−ii1-1-11−iii−i−iii−ii−i−iii−i−ii0000
χ5744444-24-24-2-244444-2-2-2-24-24-24-2-24-2-2-2-20000-2-2-2-2-2111-2111-2111-21110000000000000000000000000000000000000000
χ584444-24-24-244-24444-2-2-2-2-24-24-244-2-2-2-2-20000-2-2-2-21-2111-2111-2111-2110000000000000000000000000000000000000000
χ594444-2-2-2-2-2-2-2-244441111-2-2-2-2-2-2-2-2444400001111-2-211-2-211-2-211-2-2110000000000000000000000000000000000000000
χ604444-2-2-2-2-2-2-2-244441111-2-2-2-2-2-2-2-2-2-2-2-20000111111−1−3i32−1+3i3211−1−3i32−1+3i3211−1−3i32−1+3i3211−1−3i32−1+3i320000000000000000000000000000000000000000
χ614444-2-2-2-2-2-2-2-244441111-2-2-2-2-2-2-2-2-2-2-2-20000111111−1+3i32−1−3i3211−1+3i32−1−3i3211−1+3i32−1−3i3211−1+3i32−1−3i320000000000000000000000000000000000000000
χ6244-4-44-242-42-2-44-44-4-2-2224-242-42-2-4-2-2220000-2-222-2111-21112-1-1-12-1-1-10000000000000000000000000000000000000000
χ6344-4-4-24-2-42-4424-44-4-2-222-24-2-42-442-2-2220000-2-2221-2111-211-12-1-1-12-1-10000000000000000000000000000000000000000
χ6444-4-4-2-2-2222-224-44-411-1-1-2-2-2222-2244-4-4000011-1-1-2-211-2-21122-1-122-1-10000000000000000000000000000000000000000
χ6544-4-4-2-2-2222-224-44-411-1-1-2-2-2222-22-2-222000011-1-111−1−3i32−1+3i3211−1−3i32−1+3i32-1-11+3i321−3i32-1-11+3i321−3i320000000000000000000000000000000000000000
χ6644-4-4-2-2-2222-224-44-411-1-1-2-2-2222-22-2-222000011-1-111−1+3i32−1−3i3211−1+3i32−1−3i32-1-11−3i321+3i32-1-11−3i321+3i320000000000000000000000000000000000000000
χ674-44-44-2-4-2-42244-4-44-22-224-2-4-2-4224-22-220000-22-22-21112-1-1-1-21112-1-1-10000000000000000000000000000000000000000
χ684-44-4-24242-4-4-24-4-44-22-22-24242-4-4-2-22-220000-22-221-211-12-1-11-211-12-1-10000000000000000000000000000000000000000
χ694-44-4-2-22-2222-24-4-441-11-1-2-22-2222-24-44-400001-11-1-2-21122-1-1-2-21122-1-10000000000000000000000000000000000000000
χ704-44-4-2-22-2222-24-4-441-11-1-2-22-2222-2-22-2200001-11-111−1−3i32−1+3i32-1-11+3i321−3i3211−1−3i32−1+3i32-1-11+3i321−3i320000000000000000000000000000000000000000
χ714-44-4-2-22-2222-24-4-441-11-1-2-22-2222-2-22-2200001-11-111−1+3i32−1−3i32-1-11−3i321+3i3211−1+3i32−1−3i32-1-11−3i321+3i320000000000000000000000000000000000000000
χ724-4-444-2-424-22-444-4-4-222-24-2-424-22-4-222-20000-222-2-21112-1-1-12-1-1-1-21110000000000000000000000000000000000000000
χ734-4-44-242-4-24-4244-4-4-222-2-242-4-24-42-222-20000-222-21-211-12-1-1-12-1-11-2110000000000000000000000000000000000000000
χ744-4-44-2-222-2-22244-4-41-1-11-2-222-2-2224-4-4400001-1-11-2-21122-1-122-1-1-2-2110000000000000000000000000000000000000000
χ754-4-44-2-222-2-22244-4-41-1-11-2-222-2-222-222-200001-1-1111−1−3i32−1+3i32-1-11+3i321−3i32-1-11+3i321−3i3211−1−3i32−1+3i320000000000000000000000000000000000000000
χ764-4-44-2-222-2-22244-4-41-1-11-2-222-2-222-222-200001-1-1111−1+3i32−1−3i32-1-11−3i321+3i32-1-11−3i321+3i3211−1+3i32−1−3i320000000000000000000000000000000000000000
χ7766666-36-36-3-36-2-2-2-2-3-3-3-3-21-21-211-2000000001111000000000000000022220000-2-2-2-200000000-1-1-1-10000111100000000
χ7866666-36-36-3-36-2-2-2-2-3-3-3-3-21-21-211-20000000011110000000000000000-2-2-2-2000022220000000011110000-1-1-1-100000000
χ796666-36-36-366-3-2-2-2-2-3-3-3-31-21-21-2-210000000011110000000000000000000022220000-2-2-2-200000000-1-1-1-1000011110000
χ806666-36-36-366-3-2-2-2-2-3-3-3-31-21-21-2-2100000000111100000000000000000000-2-2-2-2000022220000000011110000-1-1-1-10000
χ8166-6-66-363-63-3-6-22-22-3-333-21-2-12-1120000000011-1-1000000000000000022-2-20000-2-22200000000-1-111000011-1-100000000
χ8266-6-66-363-63-3-6-22-22-3-333-21-2-12-1120000000011-1-10000000000000000-2-222000022-2-20000000011-1-10000-1-11100000000
χ8366-6-6-36-3-63-663-22-22-3-3331-212-12-2-10000000011-1-1000000000000000000002i2i−2i−2i0000−2i−2i2i2i00000000−i−iii0000ii−i−i0000
χ8466-6-6-36-3-63-663-22-22-3-3331-212-12-2-10000000011-1-100000000000000000000−2i−2i2i2i00002i2i−2i−2i00000000ii−i−i0000−i−iii0000
χ856-66-66-3-6-3-6336-222-2-33-33-21212-1-1-2000000001-11-100000000000000002i−2i2i−2i0000−2i2i−2i2i00000000−ii−ii0000i−ii−i00000000
χ866-66-66-3-6-3-6336-222-2-33-33-21212-1-1-2000000001-11-10000000000000000−2i2i−2i2i00002i−2i2i−2i00000000i−ii−i0000−ii−ii00000000
χ876-66-6-36363-6-6-3-222-2-33-331-2-1-2-1221000000001-11-1000000000000000000002-22-20000-22-2200000000-11-1100001-11-10000
χ886-66-6-36363-6-6-3-222-2-33-331-2-1-2-1221000000001-11-100000000000000000000-22-2200002-22-2000000001-11-10000-11-110000
χ896-6-666-3-636-33-6-2-222-333-3-212-1-21-12000000001-1-1100000000000000002i−2i−2i2i0000−2i2i2i−2i00000000−iii−i0000i−i−ii00000000
χ906-6-666-3-636-33-6-2-222-333-3-212-1-21-12000000001-1-110000000000000000−2i2i2i−2i00002i−2i−2i2i00000000i−i−ii0000−iii−i00000000
χ916-6-66-363-6-36-63-2-222-333-31-2-121-22-1000000001-1-11000000000000000000002i−2i−2i2i0000−2i2i2i−2i00000000−iii−i0000i−i−ii0000
χ926-6-66-363-6-36-63-2-222-333-31-2-121-22-1000000001-1-1100000000000000000000−2i2i2i−2i00002i−2i−2i2i00000000i−i−ii0000−iii−i0000
χ9312121212-6-6-6-6-6-6-6-6-4-4-4-433332222222200000000-1-1-1-100000000000000000000000000000000000000000000000000000000
χ941212-12-12-6-6-6666-66-44-4433-3-3222-2-2-22-200000000-1-11100000000000000000000000000000000000000000000000000000000
χ9512-1212-12-6-66-6666-6-444-43-33-322-22-2-2-2200000000-11-1100000000000000000000000000000000000000000000000000000000
χ9612-12-1212-6-666-6-666-4-4443-3-3322-2-222-2-200000000-111-100000000000000000000000000000000000000000000000000000000

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