Finite Group Databasebeta

← Group #13155411

Character table — Group #13155411

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222222222444444444444444444888888888888881212121212121212121212121212181818181818181824242424242424242424242424242424242424243636363636363636363636363636108108
order122233344666666666333666666666121212121212366612121212121212121212444444121212121212121222446666121212121212121212121212121212121212121288881212242424242424242444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ511111111111111111111111111111111111111111111111111-1-111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1111111
χ711111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
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
χ91-11-11111-1-1-1-1-1-1-1111111-1-1-1-1-11-111111-1-1-11-1-111-111-1-111-1-1i−i1-11-111-1-111-1-11-11-111-1-1ii−i−i1-11-1ii−i−i11-1-111-1-1i−ii−i1-1ii−i−iii−i−ii−i
χ101-11-11111-1-1-1-1-1-1-1111111-1-1-1-1-11-111111-1-1-11-1-111-111-1-111-1-1i−i1-1-1111-1-1-1-111-11-11-1-111ii−i−i1-1-11ii−i−i11-1-1-1-111i−i−ii-11ii−i−i−i−iii−ii
χ111-11-11111-1-1-1-1-1-1-1111111-1-1-1-1-11-111111-1-1-11-1-111-111-1-111-1-1i−i-111-1-1-11111-1-1-11-11-1-111ii−i−i-111-1ii−i−i-1-11111-1-1−iii−i-11−i−iiiii−i−i−ii
χ121-11-11111-1-1-1-1-1-1-1111111-1-1-1-1-11-111111-1-1-11-1-111-111-1-111-1-1i−i-11-11-1-111-1-1111-11-111-1-1ii−i−i-11-11ii−i−i-1-111-1-111−ii−ii1-1−i−iii−i−iiii−i
χ131-11-11111-1-1-1-1-1-1-1111111-1-1-1-1-11-111111-1-1-11-1-111-111-1-111-1-1−ii1-11-111-1-111-1-11-11-111-1-1−i−iii1-11-1−i−iii11-1-111-1-1−ii−ii1-1−i−iii−i−iii−ii
χ141-11-11111-1-1-1-1-1-1-1111111-1-1-1-1-11-111111-1-1-11-1-111-111-1-111-1-1−ii1-1-1111-1-1-1-111-11-11-1-111−i−iii1-1-11−i−iii11-1-1-1-111−iii−i-11−i−iiiii−i−ii−i
χ151-11-11111-1-1-1-1-1-1-1111111-1-1-1-1-11-111111-1-1-11-1-111-111-1-111-1-1−ii-111-1-1-11111-1-1-11-11-1-111−i−iii-111-1−i−iii-1-11111-1-1i−i−ii-11ii−i−i−i−iiii−i
χ161-11-11111-1-1-1-1-1-1-1111111-1-1-1-1-11-111111-1-1-11-1-111-111-1-111-1-1−ii-11-11-1-111-1-1111-11-111-1-1−i−iii-11-11−i−iii-1-111-1-111i−ii−i1-1ii−i−iii−i−i−ii
χ172222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-20000000000000022-2-22222000000000000000000000000-2-20000000000
χ182222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-200000000000000-2-222-2-2-2-2000000000000000000000000220000000000
χ19222222-12222-1-12222-12-1-12-1-1-1-122-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-1002222-1-1-1-1-1-1-1-12222-1-1-1-1000022220000-1-1-1-1-1-1-1-10000-1-10000000000
χ20222222-12222-1-12222-12-1-12-1-1-1-122-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-10022-2-2-1-1-1-11111-2-2-2-21111000022-2-20000-1-1-1-111110000110000000000
χ21222222-12222-1-12222-12-1-12-1-1-1-122-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-100-2-2221111-1-1-1-1-2-2-2-211110000-2-22200001111-1-1-1-10000110000000000
χ22222222-12222-1-12222-12-1-12-1-1-1-122-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-100-2-2-2-2111111112222-1-1-1-10000-2-2-2-20000111111110000-1-10000000000
χ23222222-1-2-222-1-12222-12-1-12-1-1-1-122-1-1-2-211-2-2-1-1-1-1-2-211111111000000−i3i3−i3i3−i3i3−i3i322-2-2-1-1-1-1000000000000−i3i3−i3i3−i3i3−i3i30000110000000000
χ24222222-1-2-222-1-12222-12-1-12-1-1-1-122-1-1-2-211-2-2-1-1-1-1-2-211111111000000−i3i3−i3i3i3−i3i3−i3-2-2221111000000000000−i3i3−i3i3i3−i3i3−i30000-1-10000000000
χ25222222-1-2-222-1-12222-12-1-12-1-1-1-122-1-1-2-211-2-2-1-1-1-1-2-211111111000000i3−i3i3−i3−i3i3−i3i3-2-2221111000000000000i3−i3i3−i3−i3i3−i3i30000-1-10000000000
χ26222222-1-2-222-1-12222-12-1-12-1-1-1-122-1-1-2-211-2-2-1-1-1-1-2-211111111000000i3−i3i3−i3i3−i3i3−i322-2-2-1-1-1-1000000000000i3−i3i3−i3i3−i3i3−i30000110000000000
χ2722222-12222-1222-12-12-12-1-122-1-1-1-12-12-1222-1-1-1-1-1-1-12-12-1-1-1-1-122002200002222000000002-12-100-1-1-1-1-1-10000-1-1-1-10022000000-1-1-1-100
χ2822222-12222-1222-12-12-12-1-122-1-1-1-12-12-1222-1-1-1-1-1-1-12-12-1-1-1-1-12200-2-20000-2-2-2-2000000002-12-10011-1-1-1-10000111100-2-2000000111100
χ2922222-12222-1222-12-12-12-1-122-1-1-1-12-12-1222-1-1-1-1-1-1-12-12-1-1-1-1-1-2-200220000222200000000-21-2100-1-111110000-1-1-1-100-2-2000000111100
χ3022222-12222-1222-12-12-12-1-122-1-1-1-12-12-1222-1-1-1-1-1-1-12-12-1-1-1-1-1-2-200-2-20000-2-2-2-200000000-21-2100111111000011110022000000-1-1-1-100
χ312222-12222-1222-12-122-1-12-1-1-122-1-1-12-1222-12-1-1-1-1-1-1-12-12-1-1-1-12222002222000000000000-12-12-1-100-1-1-1-1-1-1-1-10000220000-1-1-1-1000000
χ322222-12222-1222-12-122-1-12-1-1-122-1-1-12-1222-12-1-1-1-1-1-1-12-12-1-1-1-122-2-200-2-2-2-2000000000000-12-121100-1-1-1-111110000-2-200001111000000
χ332222-12222-1222-12-122-1-12-1-1-122-1-1-12-1222-12-1-1-1-1-1-1-12-12-1-1-1-1-2-2220022220000000000001-21-2-1-1001111-1-1-1-10000-2-200001111000000
χ342222-12222-1222-12-122-1-12-1-1-122-1-1-12-1222-12-1-1-1-1-1-1-12-12-1-1-1-1-2-2-2-200-2-2-2-20000000000001-21-21100111111110000220000-1-1-1-1000000
χ352-22-2222-22-2-2-2-2-2-2222222-2-2-2-2-22-222-2-2-22222-2-22-22-2-222-2-222000000000000002-2-2222-2-2000000000000000000000000-220000000000
χ362-22-2222-22-2-2-2-2-2-2222222-2-2-2-2-22-222-2-2-22222-2-22-22-2-222-2-22200000000000000-222-2-2-2220000000000000000000000002-20000000000
χ372-22-222-12-2-2-211-2-222-12-1-1-211112-2-1-122-11-2-2-111-12-2-1-111-1-111002-22-2-1-111-1-1112-22-2-1-11100002-22-20000-1-111-1-1110000-110000000000
χ382-22-222-12-2-2-211-2-222-12-1-1-211112-2-1-122-11-2-2-111-12-2-1-111-1-111002-2-22-1-11111-1-1-22-2211-1-100002-2-220000-1-11111-1-100001-10000000000
χ392-22-222-12-2-2-211-2-222-12-1-1-211112-2-1-122-11-2-2-111-12-2-1-111-1-11100-222-211-1-1-1-111-22-2211-1-10000-222-2000011-1-1-1-11100001-10000000000
χ402-22-222-12-2-2-211-2-222-12-1-1-211112-2-1-122-11-2-2-111-12-2-1-111-1-11100-22-2211-1-111-1-12-22-2-1-1110000-22-22000011-1-111-1-10000-110000000000
χ412-22-222-1-22-2-211-2-222-12-1-1-211112-2-1-1-2-21-122-111-1-2211-1-111-1-1000000−i3i3i3−i3−i3i3i3−i32-2-22-1-111000000000000−i3i3i3−i3−i3i3i3−i300001-10000000000
χ422-22-222-1-22-2-211-2-222-12-1-1-211112-2-1-1-2-21-122-111-1-2211-1-111-1-1000000−i3i3i3−i3i3−i3−i3i3-222-211-1-1000000000000−i3i3i3−i3i3−i3−i3i30000-110000000000
χ432-22-222-1-22-2-211-2-222-12-1-1-211112-2-1-1-2-21-122-111-1-2211-1-111-1-1000000i3−i3−i3i3−i3i3i3−i3-222-211-1-1000000000000i3−i3−i3i3−i3i3i3−i30000-110000000000
χ442-22-222-1-22-2-211-2-222-12-1-1-211112-2-1-1-2-21-122-111-1-2211-1-111-1-1000000i3−i3−i3i3i3−i3−i3i32-2-22-1-111000000000000i3−i3−i3i3i3−i3−i3i300001-10000000000
χ452-22-22-122-2-21-2-2-212-12-12-11-2-211-112-12-12-2-21-111-1-112-1-21-1-1112i−2i002-2000022-2-2000000002i−i−2ii00-11−i−iii0000-1-111002i−2i000000−i−iii00
χ462-22-22-122-2-21-2-2-212-12-12-11-2-211-112-12-12-2-21-111-1-112-1-21-1-1112i−2i00-220000-2-222000000002i−i−2ii001-1−i−iii000011-1-100−2i2i000000ii−i−i00
χ472-22-22-122-2-21-2-2-212-12-12-11-2-211-112-12-12-2-21-111-1-112-1-21-1-111−2i2i002-2000022-2-200000000−2ii2i−i00-11ii−i−i0000-1-11100−2i2i000000ii−i−i00
χ482-22-22-122-2-21-2-2-212-12-12-11-2-211-112-12-12-2-21-111-1-112-1-21-1-111−2i2i00-220000-2-22200000000−2ii2i−i001-1ii−i−i000011-1-1002i−2i000000−i−iii00
χ492-22-2-1222-21-2-2-21-2-122-1-12111-2-2-11-12-122-21-2-111-1-11-121-2-1-1112i−2i2-20022-2-2000000000000−i2ii−2i-1100−i−iii-1-11100002i−2i0000−i−iii000000
χ502-22-2-1222-21-2-2-21-2-122-1-12111-2-2-11-12-122-21-2-111-1-11-121-2-1-1112i−2i-2200-2-222000000000000−i2ii−2i1-100−i−iii11-1-10000−2i2i0000ii−i−i000000
χ512-22-2-1222-21-2-2-21-2-122-1-12111-2-2-11-12-122-21-2-111-1-11-121-2-1-111−2i2i2-20022-2-2000000000000i−2i−i2i-1100ii−i−i-1-1110000−2i2i0000ii−i−i000000
χ522-22-2-1222-21-2-2-21-2-122-1-12111-2-2-11-12-122-21-2-111-1-11-121-2-1-111−2i2i-2200-2-222000000000000i−2i−i2i1-100ii−i−i11-1-100002i−2i0000−i−iii000000
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χ834-44-4-24-2-442-4222-4-24-2-21-22-1-122-221-22-42-2-241-1-112-2-121-2-1-1110000002i3−2i3−2i32i3000000000000000000000000−i3i3i3−i300000000000000000000
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χ894-4-4444-200442-2-4-4-4-424-2-242-22-2-4-422000000-22-220000000000000000000000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ904-4-4444-200442-2-4-4-4-424-2-242-22-2-4-422000000-22-2200000000000000000000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ914-4-444-24004-2-44-42-42-4-24-2-2-442-222-42000000-22-2200000000000000000000000000000000000000000000000000000000000000i6−i6−i6i600
χ924-4-444-24004-2-44-42-42-4-24-2-2-442-222-42000000-22-2200000000000000000000000000000000000000000000000000000000000000−i6i6i6−i600
χ934-4-44-24400-24-442-42-4-4-2-24-22-2-44222-4000000-22-220000000000000000000000000000000000000000000000000000000000i6−i6−i6i6000000
χ944-4-44-24400-24-442-42-4-4-2-24-22-2-44222-4000000-22-220000000000000000000000000000000000000000000000000000000000−i6i6i6−i6000000
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
χ9788-8-88-4-400-84-448-4-844-4-424-442-24-44-200000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-48-4004-8-44-484-84-42-442-2-444-4-2400000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4800448-8-4-444-82-4-4-2-44-44-224400000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-40044-44-4-4444222-22-22-2-22-2-2000000-1-11100000033−3333−330000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-40044-44-4-4444222-22-22-2-22-2-2000000-1-111000000−3333−33330000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4-48-8444444-4-4-4222-2-2-2-2-22-222-4-4-4444-111-12-222-2-2-1-1110000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-4-88444444-4-4-4222-2-2-2-2-22-222444-4-4-4-111-1-22-2-22211-1-10000000000000000000000000000000000000000000000000000000000
χ1048-8-888-4-4008-44-4-84-844-4-42-44-4-22444-20000002-22-200000000000000000000000000000000000000000000000000000000000000000000
χ1058-8-88-48-400-484-44-84-84-42-4-4-224-444-240000002-22-200000000000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-4800-4-4-884444-82-4-424-44-4-2-2440000002-22-200000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-400-4-44-4444442222-22-22-2-2-2-2000000-11-1100000033−33−33330000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-400-4-44-4444442222-22-22-2-2-2-2000000-11-11000000−333333−330000000000000000000000000000000000000000000000000000000000

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