Finite Group Databasebeta

← Group #13155688

Character table — Group #13155688

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222222222444444444444444444888888888888881212121212121212121212121212181818181818181824242424242424242424242424242424242424243636363636363636363636363636108108
order122233344666666666333666666666121212121212366612121212121212121212224444666612121212444412121212666666121212121212121212121212121288881212242424242424242444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-11111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ511111111111111111111111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-11111-1-1
χ611111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111
χ711111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111
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
χ91-1-111111-1-1-1111-1-1-1-1111-1-1-1-1111-1-111-1-11-11-1-11111-1-1-111-1-11-1i−ii−i11-1-1ii−i−ii−ii−iii−i−i1-111-1-1i−ii−ii−iii−i−iii−i−ii−i1-1i−iii−i−i11-1-11-1
χ101-1-111111-1-1-1111-1-1-1-1111-1-1-1-1111-1-111-1-11-11-1-11111-1-1-111-1-11-1i−i−ii11-1-1ii−i−ii−ii−iii−i−i1-111-1-1−iii−i−iiii−i−i−i−iii−ii-11i−i−i−iii-1-111-11
χ111-1-111111-1-1-1111-1-1-1-1111-1-1-1-1111-1-111-1-11-11-1-11111-1-1-111-1-11-1−iii−i11-1-1−i−iii−ii−ii−i−iii1-111-1-1i−i−iii−i−i−iiiii−i−ii−i-11−iiii−i−i-1-111-11
χ121-1-111111-1-1-1111-1-1-1-1111-1-1-1-1111-1-111-1-11-11-1-11111-1-1-111-1-11-1−ii−ii11-1-1−i−iii−ii−ii−i−iii1-111-1-1−ii−ii−ii−i−iii−i−iii−ii1-1−ii−i−iii11-1-11-1
χ131-1-111111-1-1-1111-1-1-1-1111-1-1-1-1111-1-111-1-11-11-1-11111-1-1-111-1-1-11i−ii−i-1-111ii−i−i−ii−ii−i−iii-11-1-111i−ii−ii−iii−i−iii−i−i−ii1-1−ii−i−iii11-1-1-11
χ141-1-111111-1-1-1111-1-1-1-1111-1-1-1-1111-1-111-1-11-11-1-11111-1-1-111-1-1-11i−i−ii-1-111ii−i−i−ii−ii−i−iii-11-1-111−iii−i−iiii−i−i−i−iiii−i-11−iiii−i−i-1-1111-1
χ151-1-111111-1-1-1111-1-1-1-1111-1-1-1-1111-1-111-1-11-11-1-11111-1-1-111-1-1-11−iii−i-1-111−i−iiii−ii−iii−i−i-11-1-111i−i−iii−i−i−iiiii−i−i−ii-11i−i−i−iii-1-1111-1
χ161-1-111111-1-1-1111-1-1-1-1111-1-1-1-1111-1-111-1-11-11-1-11111-1-1-111-1-1-11−ii−ii-1-111−i−iiii−ii−iii−i−i-11-1-111−ii−ii−ii−i−iii−i−iiii−i1-1i−iii−i−i11-1-1-11
χ172222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-20000000000000022-2-2-2-2-2-2000000000000000000000000220000000000
χ182222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-200000000000000-2-2222222000000000000000000000000-2-20000000000
χ19222222-1222222-12-12-12-1-12-1-1-12-1-12-12-12-122-1-1-1-12-1-12-1-1-1-1-1-1222200-1-1-1-1-1-1-1-12222-1-1-1-122-1-1-1-1002200-1-1-1-100000000-1-10000000000
χ20222222-1222222-12-12-12-1-12-1-1-12-1-12-12-12-122-1-1-1-12-1-12-1-1-1-1-1-122-2-200-1-1-1-11111-2-2-2-2111122-1-1-1-100-2-200111100000000110000000000
χ21222222-1222222-12-12-12-1-12-1-1-12-1-12-12-12-122-1-1-1-12-1-12-1-1-1-1-1-1-2-222001111-1-1-1-1-2-2-2-21111-2-21111002200-1-1-1-100000000110000000000
χ22222222-1222222-12-12-12-1-12-1-1-12-1-12-12-12-122-1-1-1-12-1-12-1-1-1-1-1-1-2-2-2-200111111112222-1-1-1-1-2-2111100-2-200111100000000-1-10000000000
χ23222222-1-2-22222-12-12-12-1-12-1-1-12-1-12-1-21-21-2-2-1-1-1-1-211-2111111000000−i3i3−i3i3−i3i3−i3i322-2-2111100−i3i3−i3i3000000−i3i3−i3i300000000-1-10000000000
χ24222222-1-2-22222-12-12-12-1-12-1-1-12-1-12-1-21-21-2-2-1-1-1-1-211-2111111000000−i3i3−i3i3i3−i3i3−i3-2-222-1-1-1-100−i3i3−i3i3000000i3−i3i3−i300000000110000000000
χ25222222-1-2-22222-12-12-12-1-12-1-1-12-1-12-1-21-21-2-2-1-1-1-1-211-2111111000000i3−i3i3−i3−i3i3−i3i3-2-222-1-1-1-100i3−i3i3−i3000000−i3i3−i3i300000000110000000000
χ26222222-1-2-22222-12-12-12-1-12-1-1-12-1-12-1-21-21-2-2-1-1-1-1-211-2111111000000i3−i3i3−i3i3−i3i3−i322-2-2111100i3−i3i3−i3000000i3−i3i3−i300000000-1-10000000000
χ2722222-12222-12-12-1222-12-1-12-1-1-12-1-12-12222-1-1-1-1-1-12-1-12-1-1-1-1-12200222222000000000000-1-1-1-1-1-1-1-100220000-1-1-1-1220000-1-1-1-1000000
χ2822222-12222-12-12-1222-12-1-12-1-1-12-1-12-12222-1-1-1-1-1-12-1-12-1-1-1-1-12200-2-22222000000000000-1-1-1-1-1-11100-2-200001111-2-200001111000000
χ2922222-12222-12-12-1222-12-1-12-1-1-12-1-12-12222-1-1-1-1-1-12-1-12-1-1-1-1-1-2-20022-2-2-2-2000000000000111111-1-100220000-1-1-1-1-2-200001111000000
χ3022222-12222-12-12-1222-12-1-12-1-1-12-1-12-12222-1-1-1-1-1-12-1-12-1-1-1-1-1-2-200-2-2-2-2-2-20000000000001111111100-2-200001111220000-1-1-1-1000000
χ312222-12222-12-12222-12-1-12-1-122-1-12-1-122-12-12-1-1-1-1-1-12-1-12-1-1-1-1002222000022220000000000000022-1-1-1-1-1-1-1-1-1-1-1-10022000000-1-1-1-100
χ322222-12222-12-12222-12-1-12-1-122-1-12-1-122-12-12-1-1-1-1-1-12-1-12-1-1-1-10022-2-20000222200000000000000-2-2-1-111-1-1-1-1111100-2-2000000111100
χ332222-12222-12-12222-12-1-12-1-122-1-12-1-122-12-12-1-1-1-1-1-12-1-12-1-1-1-100-2-2220000-2-2-2-2000000000000002211-1-11111-1-1-1-100-2-2000000111100
χ342222-12222-12-12222-12-1-12-1-122-1-12-1-122-12-12-1-1-1-1-1-12-1-12-1-1-1-100-2-2-2-20000-2-2-2-200000000000000-2-21111111111110022000000-1-1-1-100
χ352-2-22222-22-2-2222-2-2-2-2222-2-2-2-2222-2-2-2-222-222-2-22-2-2-2222-2-222000000000000002i−2i−2i2i−2i−2i2i2i0000000000000000000000002i−2i0000000000
χ362-2-22222-22-2-2222-2-2-2-2222-2-2-2-2222-2-2-2-222-222-2-22-2-2-2222-2-22200000000000000−2i2i2i−2i2i2i−2i−2i000000000000000000000000−2i2i0000000000
χ372-2-2222-12-2-2-222-1-21-212-1-1-21112-1-1-212-1-212-2-111-12-1-1-211-1-1112-22i−2i00-1-111−i−iii2i−2i2i−2i−i−iii2-2-1-111002i−2i00−i−iii00000000−ii0000000000
χ382-2-2222-12-2-2-222-1-21-212-1-1-21112-1-1-212-1-212-2-111-12-1-1-211-1-1112-2−2i2i00-1-111ii−i−i−2i2i−2i2iii−i−i2-2-1-11100−2i2i00ii−i−i00000000i−i0000000000
χ392-2-2222-12-2-2-222-1-21-212-1-1-21112-1-1-212-1-212-2-111-12-1-1-211-1-111-222i−2i0011-1-1−i−iii−2i2i−2i2iii−i−i-2211-1-1002i−2i00−i−iii00000000i−i0000000000
χ402-2-2222-12-2-2-222-1-21-212-1-1-21112-1-1-212-1-212-2-111-12-1-1-211-1-111-22−2i2i0011-1-1ii−i−i2i−2i2i−2i−i−iii-2211-1-100−2i2i00ii−i−i00000000−ii0000000000
χ412-2-2222-1-22-2-222-1-21-212-1-1-21112-1-1-21-212-1-22-111-1-2112-1-111-1-1000000−i3i3i3−i33−3−332i−2i−2i2iii−i−i00−i3i3i3−i30000003−3−3300000000−ii0000000000
χ422-2-2222-1-22-2-222-1-21-212-1-1-21112-1-1-21-212-1-22-111-1-2112-1-111-1-1000000−i3i3i3−i3−333−3−2i2i2i−2i−i−iii00−i3i3i3−i3000000−333−300000000i−i0000000000
χ432-2-2222-1-22-2-222-1-21-212-1-1-21112-1-1-21-212-1-22-111-1-2112-1-111-1-1000000i3−i3−i3i33−3−33−2i2i2i−2i−i−iii00i3−i3−i3i30000003−3−3300000000i−i0000000000
χ442-2-2222-1-22-2-222-1-21-212-1-1-21112-1-1-21-212-1-22-111-1-2112-1-111-1-1000000i3−i3−i3i3−333−32i−2i−2i2iii−i−i00i3−i3−i3i3000000−333−300000000−ii0000000000
χ452-2-222-122-2-212-121-2-2-2-12-11-211-12-11-2-12-2-221-111-1-12-11-21-1-1112-2002i−2i22-2-2000000000000-11-1-111−ii002i−2i0000−i−iii2i−2i0000−i−iii000000
χ462-2-222-122-2-212-121-2-2-2-12-11-211-12-11-2-12-2-221-111-1-12-11-21-1-1112-200−2i2i22-2-2000000000000-11-1-111i−i00−2i2i0000ii−i−i−2i2i0000ii−i−i000000
χ472-2-222-122-2-212-121-2-2-2-12-11-211-12-11-2-12-2-221-111-1-12-11-21-1-111-22002i−2i-2-2220000000000001-111-1-1−ii002i−2i0000−i−iii−2i2i0000ii−i−i000000
χ482-2-222-122-2-212-121-2-2-2-12-11-211-12-11-2-12-2-221-111-1-12-11-21-1-111-2200−2i2i-2-2220000000000001-111-1-1i−i00−2i2i0000ii−i−i2i−2i0000−i−iii000000
χ492-2-22-1222-21-2-122-2-21-2-1-1211-2-2-1-1211221-2-1-2-111-1-1-1211-2-1-111002i−2i2i−2i00002i2i−2i−2i000000000000002i−2i−ii−ii−i−iii−i−iii002-2000000-1-11100
χ502-2-22-1222-21-2-122-2-21-2-1-1211-2-2-1-1211221-2-1-2-111-1-1-1211-2-1-111002i−2i−2i2i00002i2i−2i−2i00000000000000−2i2i−iii−i−i−iiiii−i−i00-2200000011-1-100
χ512-2-22-1222-21-2-122-2-21-2-1-1211-2-2-1-1211221-2-1-2-111-1-1-1211-2-1-11100−2i2i2i−2i0000−2i−2i2i2i000000000000002i−2ii−i−iiii−i−i−i−iii00-2200000011-1-100
χ522-2-22-1222-21-2-122-2-21-2-1-1211-2-2-1-1211221-2-1-2-111-1-1-1211-2-1-11100−2i2i−2i2i0000−2i−2i2i2i00000000000000−2i2ii−ii−iii−i−iii−i−i002-2000000-1-11100
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χ884-4-44-24-24-42-4-24-2-4222-21-22-122-21-22-14-222-2-41-1-11-21-22-1211-1-100−4i4i0000002i2i−2i−2i00000000000000002i−2i00−i−iii00000000000000000000
χ894-4-44-24-2-442-4-24-2-4222-21-22-122-21-22-1-42-2-2241-1-112-12-21-2-1-111000000000023−23−232300000000000000000000−333−300000000000000000000
χ904-4-44-24-2-442-4-24-2-4222-21-22-122-21-22-1-42-2-2241-1-112-12-21-2-1-1110000000000−232323−23000000000000000000003−3−3300000000000000000000
χ914-4-44-2-244-422-2-242-42-41-2-2-12221-2-2-12-242-4-221-1-111-2-2-12211-1-100004i−4i0000000000000000000000−2i2i00−2i2i0000ii−i−i0000000000000000
χ924-4-44-2-244-422-2-242-42-41-2-2-12221-2-2-12-242-4-221-1-111-2-2-12211-1-10000−4i4i00000000000000000000002i−2i002i−2i0000−i−iii0000000000000000
χ934-4-44-2-24-4422-2-242-42-41-2-2-12221-2-2-122-4-242-21-1-11-1221-2-2-1-111000000000000000000000000000000000000003i−3i−3i3i0000000000000000
χ944-4-44-2-24-4422-2-242-42-41-2-2-12221-2-2-122-4-242-21-1-11-1221-2-2-1-11100000000000000000000000000000000000000−3i3i3i−3i0000000000000000
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
χ9788-8-88-4-4008-4-8444-4-84-4-42-4-42-244-24400000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-48-400-484-84-8-444-42-4-42-444-244-200000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4800-4-444-8484-82-4-42-4-44-244-2400000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-400-4-44444-444222222-2-2-2-2-2-2000000-1-11100000033−3333−330000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-400-4-44444-444222222-2-2-2-2-2-2000000-1-111000000−3333−33330000000000000000000000000000000000000000000000000000000000
χ1028-88-88-4-400-84-844-448-4-4-4244-2244-2-4-40000002-22-200000000000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-48-4004-84-8484-4-4-42-44-24-44-24-420000002-22-200000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-48004444-8-4-8-482-4-4-244-4-2442-40000002-22-200000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-40044444-44-4-4222-2-2-22-2-2-222000000-11-1100000033−33−33330000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-40044444-44-4-4222-2-2-22-2-2-222000000-11-11000000−333333−330000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-48-844-4-4-44444222-2-2-2-2222-2-2-4-444-44-111-1222-2-2-2-1-1110000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4-8844-4-4-44444222-2-2-2-2222-2-244-4-44-4-111-1-2-2-222211-1-10000000000000000000000000000000000000000000000000000000000

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