Finite Group Databasebeta

← Group #13155707

Character table — Group #13155707

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222222222444444444444444444888888888888881212121212121212121212121212181818181818181824242424242424242424242424242424242424243636363636363636363636363636108108
order1222333446666666663336666666661212121212123666121212121212121212124444441212121212121212444412121212121212121212121212121212121212121212121288881212242424242424242444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ511111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1
χ611111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ711111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
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
χ91-1-111111-1-11-1-1-111-1-1111-1-1-1-111-1-11-111-11-11-1-1111-1-11-111-1-1i−ii−i1-111-1-1ii−i−iii−i−iii−i−ii−iii−i−i1-1ii−i−iii−i−i11-1-11-1i−ii−i11-1-1ii−i−i1-1
χ101-1-111111-1-11-1-1-111-1-1111-1-1-1-111-1-11-111-11-11-1-1111-1-11-111-1-1i−ii−i-11-1-111ii−i−i−i−iii−i−iiii−iii−i−i-11ii−i−iii−i−i-1-1111-1−ii−ii11-1-1−i−iii-11
χ111-1-111111-1-11-1-1-111-1-1111-1-1-1-111-1-11-111-11-11-1-1111-1-11-111-1-1i−i−ii1-111-1-1ii−i−iii−i−iii−i−ii−i−i−iii1-1ii−i−i−i−iii11-1-1-11−iii−i-1-111−i−iii-11
χ121-1-111111-1-11-1-1-111-1-1111-1-1-1-111-1-11-111-11-11-1-1111-1-11-111-1-1i−i−ii-11-1-111ii−i−i−i−iii−i−iiii−i−i−iii-11ii−i−i−i−iii-1-111-11i−i−ii-1-111ii−i−i1-1
χ131-1-111111-1-11-1-1-111-1-1111-1-1-1-111-1-11-111-11-11-1-1111-1-11-111-1-1−iii−i1-111-1-1−i−iii−i−iii−i−iii−iiii−i−i1-1−i−iiiii−i−i11-1-1-11i−i−ii-1-111ii−i−i-11
χ141-1-111111-1-11-1-1-111-1-1111-1-1-1-111-1-11-111-11-11-1-1111-1-11-111-1-1−iii−i-11-1-111−i−iiiii−i−iii−i−i−iiii−i−i-11−i−iiiii−i−i-1-111-11−iii−i-1-111−i−iii1-1
χ151-1-111111-1-11-1-1-111-1-1111-1-1-1-111-1-11-111-11-11-1-1111-1-11-111-1-1−ii−ii1-111-1-1−i−iii−i−iii−i−iii−ii−i−iii1-1−i−iii−i−iii11-1-11-1−ii−ii11-1-1−i−iii1-1
χ161-1-111111-1-11-1-1-111-1-1111-1-1-1-111-1-11-111-11-11-1-1111-1-11-111-1-1−ii−ii-11-1-111−i−iiiii−i−iii−i−i−ii−i−iii-11−i−iii−i−iii-1-1111-1i−ii−i11-1-1ii−i−i-11
χ172222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2000000000000002-22-22222000000000000000000000000-2-20000000000
χ182222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-200000000000000-22-22-2-2-2-2000000000000000000000000220000000000
χ19222222-122222222-1-1-12-1-12-1-1-12-12-1-122-1-122-1-1-1-12-12-1-1-1-1-1-1-1220022-1-1-1-1-1-1-1-12222-1-1-1-122000022-1-1-1-10000-1-1-1-10000-1-10000000000
χ20222222-122222222-1-1-12-1-12-1-1-12-12-1-122-1-122-1-1-1-12-12-1-1-1-1-1-1-12200-2-21111-1-1-1-1-2-2-2-21111220000-2-2-1-1-1-1000011110000110000000000
χ21222222-122222222-1-1-12-1-12-1-1-12-12-1-122-1-122-1-1-1-12-12-1-1-1-1-1-1-1-2-20022-1-1-1-11111-2-2-2-21111-2-200002211110000-1-1-1-10000110000000000
χ22222222-122222222-1-1-12-1-12-1-1-12-12-1-122-1-122-1-1-1-12-12-1-1-1-1-1-1-1-2-200-2-2111111112222-1-1-1-1-2-20000-2-21111000011110000-1-10000000000
χ23222222-1-2-2222222-1-1-12-1-12-1-1-12-12-1-1-2-211-2-2-1-1-1-1-21-21111111000000−i3i3−i3i3−i3i3−i3i32-22-2-1-1-1-100000000−i3i3−i3i30000−i3i3−i3i30000110000000000
χ24222222-1-2-2222222-1-1-12-1-12-1-1-12-12-1-1-2-211-2-2-1-1-1-1-21-21111111000000−i3i3−i3i3i3−i3i3−i3-22-22111100000000i3−i3i3−i30000−i3i3−i3i30000-1-10000000000
χ25222222-1-2-2222222-1-1-12-1-12-1-1-12-12-1-1-2-211-2-2-1-1-1-1-21-21111111000000i3−i3i3−i3−i3i3−i3i3-22-22111100000000−i3i3−i3i30000i3−i3i3−i30000-1-10000000000
χ26222222-1-2-2222222-1-1-12-1-12-1-1-12-12-1-1-2-211-2-2-1-1-1-1-21-21111111000000i3−i3i3−i3i3−i3i3−i32-22-2-1-1-1-100000000i3−i3i3−i30000i3−i3i3−i30000110000000000
χ2722222-12222-12-1-12222-12-1-122-1-1-1-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-12222000000222200000000-1-12-12-100-1-1-1-1-1-1-1-10000220000-1-1-1-1000000
χ2822222-12222-12-1-12222-12-1-122-1-1-1-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-122-2-2000000222200000000-1-1-21-2100-1-1-1-111110000-2-200001111000000
χ2922222-12222-12-1-12222-12-1-122-1-1-1-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-1-2-222000000-2-2-2-200000000112-12-1001111-1-1-1-10000-2-200001111000000
χ3022222-12222-12-1-12222-12-1-122-1-1-1-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2000000-2-2-2-20000000011-21-2100111111110000220000-1-1-1-1000000
χ312222-12222-12-122-1222-1-12-1-1-12-12-12-12-1222-1-1-1-1-1-12-12-1-1-1-1-1-1002222222200000000000000-12-12-1-10000-1-1-1-1-1-1-1-10022000000-1-1-1-100
χ322222-12222-12-122-1222-1-12-1-1-12-12-12-12-1222-1-1-1-1-1-12-12-1-1-1-1-1-10022-2-2-2-2-2-200000000000000-12-12110000-1-1-1-1111100-2-2000000111100
χ332222-12222-12-122-1222-1-12-1-1-12-12-12-12-1222-1-1-1-1-1-12-12-1-1-1-1-1-100-2-2222222000000000000001-21-2-1-100001111-1-1-1-100-2-2000000111100
χ342222-12222-12-122-1222-1-12-1-1-12-12-12-12-1222-1-1-1-1-1-12-12-1-1-1-1-1-100-2-2-2-2-2-2-2-2000000000000001-21-2110000111111110022000000-1-1-1-100
χ352-2-22222-22-22-2-2-222-2-2222-2-2-2-222-2-222-2-22-222-2-22-2-222-22-2-222000000000000002i−2i−2i2i2i2i−2i−2i000000000000000000000000−2i2i0000000000
χ362-2-22222-22-22-2-2-222-2-2222-2-2-2-222-2-222-2-22-222-2-22-2-222-22-2-22200000000000000−2i2i2i−2i−2i−2i2i2i0000000000000000000000002i−2i0000000000
χ372-2-2222-12-2-22-2-2-22-1112-1-1-21112-1-21-1-22-112-2-111-12-1-21-11-1-1112i−2i002-2-1-111−i−iii2i2i−2i−2i−i−iii2i−2i00002-2−i−iii0000-1-1110000−ii0000000000
χ382-2-2222-12-2-22-2-2-22-1112-1-1-21112-1-21-1-22-112-2-111-12-1-21-11-1-1112i−2i00-2211-1-1−i−iii−2i−2i2i2iii−i−i2i−2i0000-22−i−iii000011-1-10000i−i0000000000
χ392-2-2222-12-2-22-2-2-22-1112-1-1-21112-1-21-1-22-112-2-111-12-1-21-11-1-111−2i2i002-2-1-111ii−i−i−2i−2i2i2iii−i−i−2i2i00002-2ii−i−i0000-1-1110000i−i0000000000
χ402-2-2222-12-2-22-2-2-22-1112-1-1-21112-1-21-1-22-112-2-111-12-1-21-11-1-111−2i2i00-2211-1-1ii−i−i2i2i−2i−2i−i−iii−2i2i0000-22ii−i−i000011-1-10000−ii0000000000
χ412-2-2222-1-22-22-2-2-22-1112-1-1-21112-1-21-12-21-1-22-111-1-212-11-111-1-1000000−i3i3i3−i33−3−332i−2i−2i2i−i−iii000000003−3−330000−i3i3i3−i30000i−i0000000000
χ422-2-2222-1-22-22-2-2-22-1112-1-1-21112-1-21-12-21-1-22-111-1-212-11-111-1-1000000−i3i3i3−i3−333−3−2i2i2i−2iii−i−i00000000−333−30000−i3i3i3−i30000−ii0000000000
χ432-2-2222-1-22-22-2-2-22-1112-1-1-21112-1-21-12-21-1-22-111-1-212-11-111-1-1000000i3−i3−i3i33−3−33−2i2i2i−2iii−i−i000000003−3−330000i3−i3−i3i30000−ii0000000000
χ442-2-2222-1-22-22-2-2-22-1112-1-1-21112-1-21-12-21-1-22-111-1-212-11-111-1-1000000i3−i3−i3i3−333−32i−2i−2i2i−i−iii00000000−333−30000i3−i3−i3i30000i−i0000000000
χ452-2-222-122-2-2-1-21122-2-2-12-11-2-21-1-1112122-2-1-2-111-1-1-1112-2-1-1112i−2i2i−2i0000002i2i−2i−2i00000000−ii2i−i−2ii00−i−iii−i−iii00002-20000-1-111000000
χ462-2-222-122-2-2-1-21122-2-2-12-11-2-21-1-1112122-2-1-2-111-1-1-1112-2-1-1112i−2i−2i2i0000002i2i−2i−2i00000000−ii−2ii2i−i00−i−iiiii−i−i0000-22000011-1-1000000
χ472-2-222-122-2-2-1-21122-2-2-12-11-2-21-1-1112122-2-1-2-111-1-1-1112-2-1-111−2i2i2i−2i000000−2i−2i2i2i00000000i−i2i−i−2ii00ii−i−i−i−iii0000-22000011-1-1000000
χ482-2-222-122-2-2-1-21122-2-2-12-11-2-21-1-1112122-2-1-2-111-1-1-1112-2-1-111−2i2i−2i2i000000−2i−2i2i2i00000000i−i−2ii2i−i00ii−i−iii−i−i00002-20000-1-111000000
χ492-2-22-1222-2121-2-2-12-2-2-1-12111-2-121-2-1-2-12-221-111-1-121-2-11-1-111002i−2i2-222-2-200000000000000−i2ii−2i-110000−i−iii-1-111002i−2i000000−i−iii00
χ502-2-22-1222-2121-2-2-12-2-2-1-12111-2-121-2-1-2-12-221-111-1-121-2-11-1-111002i−2i-22-2-22200000000000000−i2ii−2i1-10000−i−iii11-1-100−2i2i000000ii−i−i00
χ512-2-22-1222-2121-2-2-12-2-2-1-12111-2-121-2-1-2-12-221-111-1-121-2-11-1-11100−2i2i2-222-2-200000000000000i−2i−i2i-110000ii−i−i-1-11100−2i2i000000ii−i−i00
χ522-2-22-1222-2121-2-2-12-2-2-1-12111-2-121-2-1-2-12-221-111-1-121-2-11-1-11100−2i2i-22-2-22200000000000000i−2i−i2i1-10000ii−i−i11-1-1002i−2i000000−i−iii00
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χ5544444-2-2444-24-2-24-2-2-2-2-21-2-2-21-21-21-2-24-2-2-241111-21-21-2-21111-4-40000000022220000000022000000-1-1-1-1000000000000000000000000
χ5644444-2-2-4-44-24-2-24-2-2-2-2-21-2-2-21-21-21-22-4222-411112-12-122-1-1-1-10000000000−2i32i3−2i32i30000000000000000i3−i3i3−i3000000000000000000000000
χ5744444-2-2-4-44-24-2-24-2-2-2-2-21-2-2-21-21-21-22-4222-411112-12-122-1-1-1-100000000002i3−2i32i3−2i30000000000000000−i3i3−i3i3000000000000000000000000
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χ614444-24-2-4-4-24-244-2-2-2-2-21-2-211-2-2-2-2-21-4222-4211112222-1-1-1-1-1-1000000−2i32i3−2i32i30000000000000000000000000000i3−i3i3−i30000000000000000
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χ834-4-444-2-24-4-4-2-4224-222-2-21222-1-212-1-224-22-2-41-1-11-212-1-2211-1-1−4i4i000000002i2i−2i−2i000000002i−2i000000−i−iii000000000000000000000000
χ844-4-444-2-2-44-4-2-4224-222-2-21222-1-212-1-2-2-42-2241-1-112-1-212-2-1-111000000000023−23−23230000000000000000−333−3000000000000000000000000
χ854-4-444-2-2-44-4-2-4224-222-2-21222-1-212-1-2-2-42-2241-1-112-1-212-2-1-1110000000000−232323−2300000000000000003−3−33000000000000000000000000
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χ874-4-44-24-24-4242-4-4-2-222-21-22-1-12-2-2221-4-2-22421-1-11-2-2221-111-1-100004-4-2-222000000000000000000-220000000011-1-10000000000000000
χ884-4-44-24-24-4242-4-4-2-222-21-22-1-12-2-2221-4-2-22421-1-11-2-2221-111-1-10000-4422-2-20000000000000000002-200000000-1-1110000000000000000
χ894-4-44-24-2-44242-4-4-2-222-21-22-1-12-2-2221422-2-4-21-1-1122-2-2-11-1-111000000−2i32i32i3−2i30000000000000000000000000000i3−i3−i3i30000000000000000
χ904-4-44-24-2-44242-4-4-2-222-21-22-1-12-2-2221422-2-4-21-1-1122-2-2-11-1-1110000002i3−2i3−2i32i30000000000000000000000000000−i3i3i3−i30000000000000000
χ914-4-44-2-244-42-2222-24-4-41-2-2-12221-2-12-22-24-4-221-1-111-2-12-2211-1-1004i−4i00000000000000000000−2i−2i2i2i000000ii−i−i00000000000000000000
χ924-4-44-2-244-42-2222-24-4-41-2-2-12221-2-12-22-24-4-221-1-111-2-12-2211-1-100−4i4i000000000000000000002i2i−2i−2i000000−i−iii00000000000000000000
χ934-4-44-2-24-442-2222-24-4-41-2-2-12221-2-12-2-22-442-21-1-11-121-22-2-1-11100000000000000000000000000000000003i−3i−3i3i00000000000000000000
χ944-4-44-2-24-442-2222-24-4-41-2-2-12221-2-12-2-22-442-21-1-11-121-22-2-1-1110000000000000000000000000000000000−3i3i3i−3i00000000000000000000
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
χ9788-8-88-4-40084-8-44-844-4-4-42-4-44-24-242400000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-48-400-4-848-8444-4-42-4-42-24444-4-200000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4800-444-444-8-882-4-42-444-24-2-4400000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-400-444-44444-422222-2-2-2-2-22-2000000-1-11100000033−3333−330000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-400-444-44444-422222-2-2-2-2-22-2000000-1-111000000−3333−33330000000000000000000000000000000000000000000000000000000000
χ1028-88-88-4-400-8484-4-84-44-4-4244-424-2-4-240000002-22-200000000000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-48-4004-8-4-8844-44-42-44-22-444-44-20000002-22-200000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-480044-44-44-88-82-4-4-24-4-4-242440000002-22-200000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-40044-44-444-44222-2-222-2-22-2-2000000-11-1100000033−33−33330000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-40044-44-444-44222-2-222-2-22-2-2000000-11-11000000−333333−330000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-48-84-4444-4-444222-2-2-2-222-2-224-4-44-44-111-122-2-22-2-1-1110000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4-884-4444-4-444222-2-2-2-222-2-22-444-44-4-111-1-2-222-2211-1-10000000000000000000000000000000000000000000000000000000000

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