Finite Group Databasebeta

← Group #13155414

Character table — Group #13155414

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222222222444444444444444444888888888888881212121212121212121212121212181818181818181824242424242424242424242424242424242424243636363636363636363636363636108108
order12223334466666666633366666666612121212121236661212121212121212121244444412121212121212122244121212121212121212121212121212121212121212121212668888242424242424242444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ511111111111111111111111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1
χ611111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-111
χ711111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111
χ811111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91-1-111111-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-11-1-1111-1-11-111-1-1i−ii−i1-1ii−i−iii−i−i1-11-111-1-1i−ii−i11-1-1ii−i−iii−i−i11-1-11-1i−ii−iii−i−iii−i−i1-1
χ101-1-111111-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-11-1-1111-1-11-111-1-1i−ii−i-11ii−i−iii−i−i1-11-111-1-1i−ii−i-1-111ii−i−iii−i−i-1-1111-1−ii−ii−i−iii−i−iii-11
χ111-1-111111-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-11-1-1111-1-11-111-1-1i−i−ii1-1ii−i−i−i−iii-11-11-1-111i−i−ii11-1-1ii−i−i−i−iii11-1-1-11i−i−iiii−i−i−i−iii-11
χ121-1-111111-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-11-1-1111-1-11-111-1-1i−i−ii-11ii−i−i−i−iii-11-11-1-111i−i−ii-1-111ii−i−i−i−iii-1-111-11−iii−i−i−iiiii−i−i1-1
χ131-1-111111-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-11-1-1111-1-11-111-1-1−iii−i1-1−i−iiiii−i−i-11-11-1-111−iii−i11-1-1−i−iiiii−i−i11-1-1-11−iii−i−i−iiiii−i−i-11
χ141-1-111111-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-11-1-1111-1-11-111-1-1−iii−i-11−i−iiiii−i−i-11-11-1-111−iii−i-1-111−i−iiiii−i−i-1-111-11i−i−iiii−i−i−i−iii1-1
χ151-1-111111-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-11-1-1111-1-11-111-1-1−ii−ii1-1−i−iii−i−iii1-11-111-1-1−ii−ii11-1-1−i−iii−i−iii11-1-11-1−ii−ii−i−iii−i−iii1-1
χ161-1-111111-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-11-1-1111-1-11-111-1-1−ii−ii-11−i−iii−i−iii1-11-111-1-1−ii−ii-1-111−i−iii−i−iii-1-1111-1i−ii−iii−i−iii−i−i-11
χ172222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-20000000000000022-2-2-2-2-2-2000000000000000000002200000000000000
χ182222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-200000000000000-2-222222200000000000000000000-2-200000000000000
χ19222222-1222222-1-122-12-1-122-1-1-1-1-1-1222-1-122-1-1-1-1-1-1-1-122-1-1-1-1222200-1-1-1-1-1-1-1-12222-1-1-1-122220000-1-1-1-1-1-1-1-10000-1-100000000000000
χ20222222-1222222-1-122-12-1-122-1-1-1-1-1-1222-1-122-1-1-1-1-1-1-1-122-1-1-1-122-2-200-1-1-1-11111-2-2-2-2111122-2-20000-1-1-1-1111100001100000000000000
χ21222222-1222222-1-122-12-1-122-1-1-1-1-1-1222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-222001111-1-1-1-1-2-2-2-21111-2-22200001111-1-1-1-100001100000000000000
χ22222222-1222222-1-122-12-1-122-1-1-1-1-1-1222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-200111111112222-1-1-1-1-2-2-2-20000111111110000-1-100000000000000
χ23222222-1-2-22222-1-122-12-1-122-1-1-1-1-1-12-2-211-2-2-1-1-1-11111-2-21111000000−i3i3−i3i3−i3i3−i3i322-2-2111100000000−i3i3−i3i3−i3i3−i3i30000-1-100000000000000
χ24222222-1-2-22222-1-122-12-1-122-1-1-1-1-1-12-2-211-2-2-1-1-1-11111-2-21111000000−i3i3−i3i3i3−i3i3−i3-2-222-1-1-1-100000000−i3i3−i3i3i3−i3i3−i300001100000000000000
χ25222222-1-2-22222-1-122-12-1-122-1-1-1-1-1-12-2-211-2-2-1-1-1-11111-2-21111000000i3−i3i3−i3−i3i3−i3i3-2-222-1-1-1-100000000i3−i3i3−i3−i3i3−i3i300001100000000000000
χ26222222-1-2-22222-1-122-12-1-122-1-1-1-1-1-12-2-211-2-2-1-1-1-11111-2-21111000000i3−i3i3−i3i3−i3i3−i322-2-2111100000000i3−i3i3−i3i3−i3i3−i30000-1-100000000000000
χ2722222-12222-12-1222-12-12-1-1-12-12-12-1-12-1222-1-1-1-1-12-12-1-1-1-1-1-1-1002222000022220000000000-1-12-12-10000-1-1-1-1-1-1-1-10000220000-1-1-1-100
χ2822222-12222-12-1222-12-12-1-1-12-12-12-1-12-1222-1-1-1-1-12-12-1-1-1-1-1-1-10022-2-2000022220000000000-1-1-21-210000-1-1-1-111110000-2-20000111100
χ2922222-12222-12-1222-12-12-1-1-12-12-12-1-12-1222-1-1-1-1-12-12-1-1-1-1-1-1-100-2-2220000-2-2-2-20000000000112-12-100001111-1-1-1-10000-2-20000111100
χ3022222-12222-12-1222-12-12-1-1-12-12-12-1-12-1222-1-1-1-1-12-12-1-1-1-1-1-1-100-2-2-2-20000-2-2-2-2000000000011-21-210000111111110000220000-1-1-1-100
χ312222-12222-12-1222-122-1-12-1-1-12-12-12-1-1222-12-1-1-1-1-12-12-1-1-1-1-1-12200222222000000000000-1-100-12-12-1-1-1-10000-1-1-1-1002200-1-1-1-1000000
χ322222-12222-12-1222-122-1-12-1-1-12-12-12-1-1222-12-1-1-1-1-12-12-1-1-1-1-1-12200-2-22222000000000000-1-1001-21-2-1-1-1-10000111100-2-2001111000000
χ332222-12222-12-1222-122-1-12-1-1-12-12-12-1-1222-12-1-1-1-1-12-12-1-1-1-1-1-1-2-20022-2-2-2-20000000000001100-12-1211110000-1-1-1-100-2-2001111000000
χ342222-12222-12-1222-122-1-12-1-1-12-12-12-1-1222-12-1-1-1-1-12-12-1-1-1-1-1-1-2-200-2-2-2-2-2-200000000000011001-21-2111100001111002200-1-1-1-1000000
χ352-2-22222-22-2-2-2-2-2-2222222-2-2-2-222-2-22-2-2-22222-2-22-2-222-22-2-222000000000000002-2-22-2-222000000000000000000002-200000000000000
χ362-2-22222-22-2-2-2-2-2-2222222-2-2-2-222-2-22-2-2-22222-2-22-2-222-22-2-22200000000000000-222-222-2-200000000000000000000-2200000000000000
χ372-2-2222-12-2-2-2-2-21122-12-1-1-2-211-1-111222-11-2-2-111-1-1-1112-2-1-1112i−2i2i−2i00−i−iii−i−iii2-22-2-1-1112i−2i2i−2i0000−i−iii−i−iii0000-1100000000000000
χ382-2-2222-12-2-2-2-2-21122-12-1-1-2-211-1-111222-11-2-2-111-1-1-1112-2-1-1112i−2i−2i2i00−i−iiiii−i−i-22-2211-1-12i−2i−2i2i0000−i−iiiii−i−i00001-100000000000000
χ392-2-2222-12-2-2-2-2-21122-12-1-1-2-211-1-111222-11-2-2-111-1-1-1112-2-1-111−2i2i2i−2i00ii−i−i−i−iii-22-2211-1-1−2i2i2i−2i0000ii−i−i−i−iii00001-100000000000000
χ402-2-2222-12-2-2-2-2-21122-12-1-1-2-211-1-111222-11-2-2-111-1-1-1112-2-1-111−2i2i−2i2i00ii−i−iii−i−i2-22-2-1-111−2i2i−2i2i0000ii−i−iii−i−i0000-1100000000000000
χ412-2-2222-1-22-2-2-2-21122-12-1-1-2-211-1-1112-2-21-122-111-111-1-1-2211-1-10000003−3−333−3−332-2-2211-1-1000000003−3−333−3−330000-1100000000000000
χ422-2-2222-1-22-2-2-2-21122-12-1-1-2-211-1-1112-2-21-122-111-111-1-1-2211-1-10000003−3−33−333−3-222-2-1-111000000003−3−33−333−300001-100000000000000
χ432-2-2222-1-22-2-2-2-21122-12-1-1-2-211-1-1112-2-21-122-111-111-1-1-2211-1-1000000−333−33−3−33-222-2-1-11100000000−333−33−3−3300001-100000000000000
χ442-2-2222-1-22-2-2-2-21122-12-1-1-2-211-1-1112-2-21-122-111-111-1-1-2211-1-1000000−333−3−333−32-2-2211-1-100000000−333−3−333−30000-1100000000000000
χ452-2-222-122-2-21-21-2-22-12-12-111-212-1-21-12-12-2-21-111-12-1-21-11-1-111002i−2i2-200002i2i−2i−2i0000000000−ii2-1-210000−i−iii-1-11100002i−2i0000−i−iii00
χ462-2-222-122-2-21-21-2-22-12-12-111-212-1-21-12-12-2-21-111-12-1-21-11-1-111002i−2i-2200002i2i−2i−2i0000000000−ii-212-10000−i−iii11-1-10000−2i2i0000ii−i−i00
χ472-2-222-122-2-21-21-2-22-12-12-111-212-1-21-12-12-2-21-111-12-1-21-11-1-11100−2i2i2-20000−2i−2i2i2i0000000000i−i2-1-210000ii−i−i-1-1110000−2i2i0000ii−i−i00
χ482-2-222-122-2-21-21-2-22-12-12-111-212-1-21-12-12-2-21-111-12-1-21-11-1-11100−2i2i-220000−2i−2i2i2i0000000000i−i-212-10000ii−i−i11-1-100002i−2i0000−i−iii00
χ492-2-22-1222-21-21-2-2-2-122-1-12111-2-121-2-1-122-21-2-111-1-121-2-11-1-1112i−2i002-22i2i−2i−2i000000000000−ii00-121-2−i−iii0000-1-111002i−2i00−i−iii000000
χ502-2-22-1222-21-21-2-2-2-122-1-12111-2-121-2-1-122-21-2-111-1-121-2-11-1-1112i−2i00-222i2i−2i−2i000000000000−ii001-2-12−i−iii000011-1-100−2i2i00ii−i−i000000
χ512-2-22-1222-21-21-2-2-2-122-1-12111-2-121-2-1-122-21-2-111-1-121-2-11-1-111−2i2i002-2−2i−2i2i2i000000000000i−i00-121-2ii−i−i0000-1-11100−2i2i00ii−i−i000000
χ522-2-22-1222-21-21-2-2-2-122-1-12111-2-121-2-1-122-21-2-111-1-121-2-11-1-111−2i2i00-22−2i−2i2i2i000000000000i−i001-2-12ii−i−i000011-1-1002i−2i00−i−iii000000
χ5344444-24-4-44-24-2444-24-24-2-2-24-24-24-2-2-42-4-4-42-2-2-2-2-42-422222220000000000000000000000000000000000000000000000000000000000
χ5444444-2-2444-24-2-2-24-2-2-2-21-2-2-21-21-21-24-2-2-24-21111-21-21-2-211110044000000-2-2-2-20000000000-2-200000000111100000000000000000000
χ5544444-2-2444-24-2-2-24-2-2-2-21-2-2-21-21-21-24-2-2-24-21111-21-21-2-2111100-4-4000000222200000000002200000000-1-1-1-100000000000000000000
χ5644444-2-2-4-44-24-2-2-24-2-2-2-21-2-2-21-21-21-2-4222-4211112-12-122-1-1-1-10000000000−2i32i3−2i32i300000000000000000000i3−i3i3−i300000000000000000000
χ5744444-2-2-4-44-24-2-2-24-2-2-2-21-2-2-21-21-21-2-4222-4211112-12-122-1-1-1-100000000002i3−2i32i3−2i300000000000000000000−i3i3−i3i300000000000000000000
χ584444-244-4-4-24-2444-244-2-24-2-2-24-24-24-22-4-4-42-4-2-2-2-22-42-42222220000000000000000000000000000000000000000000000000000000000
χ594444-24-244-24-24-2-2-24-2-21-2-2-21-21-21-2-2-24-2-2-2411111-21-2-2-21111440000-2-2-2-2000000000000-2-20000001111000000000000000000000000
χ604444-24-244-24-24-2-2-24-2-21-2-2-21-21-21-2-2-24-2-2-2411111-21-2-2-21111-4-40000222200000000000022000000-1-1-1-1000000000000000000000000
χ614444-24-2-4-4-24-24-2-2-24-2-21-2-2-21-21-21-2-22-4222-41111-12-1222-1-1-1-1000000−2i32i3−2i32i300000000000000000000i3−i3i3−i3000000000000000000000000
χ624444-24-2-4-4-24-24-2-2-24-2-21-2-2-21-21-21-2-22-4222-41111-12-1222-1-1-1-10000002i3−2i32i3−2i300000000000000000000−i3i3−i3i3000000000000000000000000
χ634444-2-2444-2-2-2-244-2-241-2-211-2-2-2-2-2-21-2-244-2-21111-2-2-2-211111100004400000000000000000000-2-2-2-20000000011110000000000000000
χ644444-2-2444-2-2-2-244-2-241-2-211-2-2-2-2-2-21-2-244-2-21111-2-2-2-21111110000-4-400000000000000000000222200000000-1-1-1-10000000000000000
χ654444-2-24-4-4-2-2-2-244-2-241-2-211-2-2-2-2-2-2122-4-42211112222-1-1-1-1-1-1000000000000000000000000000000000000003-33-30000000000000000
χ664444-2-24-4-4-2-2-2-244-2-241-2-211-2-2-2-2-2-2122-4-42211112222-1-1-1-1-1-100000000000000000000000000000000000000-33-330000000000000000
χ6744-4-4444004-4-444-4-4-4-44444-44-4-4-4-44-400000044-4-400000000000000000000000000000000000000000000000000000000000000000000
χ6844-4-444-2004-4-44-22-4-424-2-24-4-22222-2-4000000-2-222000000000000000000000000000023−2323−23000000000000000000000000000000000000
χ6944-4-444-2004-4-44-22-4-424-2-24-4-22222-2-4000000-2-2220000000000000000000000000000−2323−2323000000000000000000000000000000000000
χ7044-4-44-240042-4-24-4-42-4-24-2-2242-42-4-22000000-2-222000000000000000000000000000000000000000000000000000000000000006−66−600
χ7144-4-44-240042-4-24-4-42-4-24-2-2242-42-4-22000000-2-22200000000000000000000000000000000000000000000000000000000000000−66−6600
χ7244-4-4-24400-2-4244-42-4-4-2-24-22-2-42-4242000000-2-2220000000000000000000000000000000000000000000000000000000000i6−i6i6−i6000000
χ7344-4-4-24400-2-4244-42-4-4-2-24-22-2-42-4242000000-2-2220000000000000000000000000000000000000000000000000000000000−i6i6−i6i6000000
χ744-44-444400-444-4-44-4-4-4444-44-44-4-44-4-40000004-44-400000000000000000000000000000000000000000000000000000000000000000000
χ754-44-444-200-444-42-2-4-424-2-2-442-222-22-4000000-22-22000000000000000000000000000023−23−2323000000000000000000000000000000000000
χ764-44-444-200-444-42-2-4-424-2-2-442-222-22-4000000-22-220000000000000000000000000000−232323−23000000000000000000000000000000000000
χ774-44-44-2400-4-242-44-42-4-24-22-2-4-2-42422000000-22-2200000000000000000000000000000000000000000000000000000000000000i6−i6−i6i600
χ784-44-44-2400-4-242-44-42-4-24-22-2-4-2-42422000000-22-2200000000000000000000000000000000000000000000000000000000000000−i6i6i6−i600
χ794-44-4-2440024-2-4-442-4-4-2-242-2242-4-2-42000000-22-2200000000000000000000000000000000000000000000000000000000006−6−66000000
χ804-44-4-2440024-2-4-442-4-4-2-242-2242-4-2-42000000-22-220000000000000000000000000000000000000000000000000000000000−666−6000000
χ814-4-444-24-44-42-42-4-44-24-24-222-424-2-42-2-42-444-2-222-2-424-22-222-2-20000000000000000000000000000000000000000000000000000000000
χ824-4-444-2-24-4-42-42224-2-2-2-21222-1-212-1-24-2-22-421-1-11-212-1-2211-1-1004i−4i000000−2i−2i2i2i0000000000−2i2i00000000ii−i−i00000000000000000000
χ834-4-444-2-24-4-42-42224-2-2-2-21222-1-212-1-24-2-22-421-1-11-212-1-2211-1-100−4i4i0000002i2i−2i−2i00000000002i−2i00000000−i−iii00000000000000000000
χ844-4-444-2-2-44-42-42224-2-2-2-21222-1-212-1-2-422-24-21-1-112-1-212-2-1-111000000000023−23−232300000000000000000000−333−300000000000000000000
χ854-4-444-2-2-44-42-42224-2-2-2-21222-1-212-1-2-422-24-21-1-112-1-212-2-1-1110000000000−232323−23000000000000000000003−3−3300000000000000000000
χ864-4-44-244-442-42-4-4-4-244-2-24222-4-242-4-22-4-44-24-222-22-4-242-222-2-20000000000000000000000000000000000000000000000000000000000
χ874-4-44-24-24-42-42-422-24-2-21-222-121-2-12-2-24-222-41-1-111-2-12-2211-1-14i−4i0000−2i−2i2i2i000000000000−2i2i000000ii−i−i000000000000000000000000
χ884-4-44-24-24-42-42-422-24-2-21-222-121-2-12-2-24-222-41-1-111-2-12-2211-1-1−4i4i00002i2i−2i−2i0000000000002i−2i000000−i−iii000000000000000000000000
χ894-4-44-24-2-442-42-422-24-2-21-222-121-2-12-22-42-2-241-1-11-121-22-2-1-11100000023−23−232300000000000000000000−333−3000000000000000000000000
χ904-4-44-24-2-442-42-422-24-2-21-222-121-2-12-22-42-2-241-1-11-121-22-2-1-111000000−232323−23000000000000000000003−3−33000000000000000000000000
χ914-4-44-2-244-42222-4-4-2-241-2-2-1-122-2-2221-2-24-4221-1-11-2-2221-111-1-100004-400000000000000000000-2-2220000000011-1-10000000000000000
χ924-4-44-2-244-42222-4-4-2-241-2-2-1-122-2-2221-2-24-4221-1-11-2-2221-111-1-10000-440000000000000000000022-2-200000000-1-1110000000000000000
χ934-4-44-2-24-442222-4-4-2-241-2-2-1-122-2-222122-44-2-21-1-1122-2-2-11-1-111000000000000000000000000000000000000003-3-330000000000000000
χ944-4-44-2-24-442222-4-4-2-241-2-2-1-122-2-222122-44-2-21-1-1122-2-2-11-1-11100000000000000000000000000000000000000-333-30000000000000000
χ958888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-4-4-4-1-1-1-1222222-1-1-1-10000000000000000000000000000000000000000000000000000000000
χ968888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444444-1-1-1-1-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000000000
χ9788-8-88-4-40084-8-4-44-844-4-42-44-4-24-242400000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-48-400-4-848-444-84-42-4-4424-24-2-4400000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4800-444-48-844-82-4-42-2-44444-4-200000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-400-444-4-444442222-22-2-2-2-22-2000000-1-11100000033−3333−330000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-400-444-4-444442222-22-2-2-2-22-2000000-1-111000000−3333−33330000000000000000000000000000000000000000000000000000000000
χ1028-88-88-4-400-8-4844-4-844-4-424-4424-2-4-240000002-22-200000000000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-48-40048-4-84-44-84-42-44-4-2-4-242440000002-22-200000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-48004-4-44-8844-82-4-4-224-444-44-20000002-22-200000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-4004-4-444-4444222-22-22-2-22-2-2000000-11-1100000033−33−33330000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-4004-4-444-4444222-22-22-2-22-2-2000000-11-11000000−333333−330000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-48-8444444-4-4-4222-2-2-2-222-2-22-4-4-4444-111-122-2-22-2-1-1110000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4-88444444-4-4-4222-2-2-2-222-2-22444-4-4-4-111-1-2-222-2211-1-10000000000000000000000000000000000000000000000000000000000

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