Finite Group Databasebeta

← Group #13161994

Character table — Group #13161994

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size111122222222222222444444444444444444444444448888888888888888888888888888888888888181836363636363636363636363636363636363636363672727272727272
order12223334466666666633333666666666666666121212121212412121212121212121212121212121212121212121212121212121212121212121212121244224448888121212122424242424242424266661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-111
χ511111111111111111111111111111111111111111111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111
χ611111111111111111111111111111111111111111111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-11111111111111111-1-1-1-1-1-1-1
χ711111111111111111111111111111111111111111111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1
χ811111111111111111111111111111111111111111111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111-1-111
χ92222222-2-222222222222222222222222222222-2-2-2-2-2-20000000-2-2-2-2-2-2-2-2-2-2000000000000000000002200-200000022-2-2000000000000000
χ102222222-2-222222222222222222222222222222-2-2-2-2-2-20000000-2-2-2-2-2-2-2-2-2-200000000000000000000-2-2002000000-2-222000000000000000
χ11222222-12222222-1-1-122-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-122-1-12222222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122002000000-1-1-1-1000000002-1-10000
χ12222222-12222222-1-1-122-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-122-1-12222222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2000000111100000000-2110000
χ13222222-12222222-1-1-122-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-122-1-122-2-2-2-2-21122-1-1-1-1-1-1-1-1-2-2-2-2111111111111111122002000000-1-1-1-100000000-2110000
χ14222222-12222222-1-1-122-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-122-1-122-2-2-2-2-21122-1-1-1-1-1-1-1-1-2-2-2-21111111111111111-2-200-20000001111000000002-1-10000
χ15222222-1-2-222222-1-1-122-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-1-2-211-2-200000−i3i3-2-2111111110000−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i32200-2000000-1-111000000000−i3i30000
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χ17222222-1-2-222222-1-1-122-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-1-2-211-2-200000i3−i3-2-2111111110000i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i32200-2000000-1-111000000000i3−i30000
χ18222222-1-2-222222-1-1-122-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-1-2-211-2-200000i3−i3-2-2111111110000i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3-2-200200000011-1-1000000000−i3i30000
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χ252222-12222-122-12222-1-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-1-1222-12-211-2-2-2-2-1-1-1-122-1-1-1-1111111-2-2111111-2-21111000002200-2-200000000111100000-1-1
χ262222-12222-122-12222-1-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-1-1222-12-211-2-2-2-2-1-1-1-122-1-1-1-1111111-2-2111111-2-2111100000-2-2002200000000-1-1-1-10000011
χ2722-2-22222-2-2-2-2222-2-2-222222-2-2-2-2-2-2-2-2-2-222222222-2-2-200000002-22-22-222-2-200000000000000000000000002i−2i0000000000000000000002i−2i
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χ2922-2-2222-22-2-2-2222-2-2-222222-2-2-2-2-2-2-2-2-2-222222-2-2-22220000000-22-22-22-2-22200000000000000000000002-200000000000000000000002-200
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χ3122-2-22-12-22-2112-12-2-2-2-12-1-1-111-2-2111111-12-1-1-1-21-222-1000−i3i3001-1-221-111-1-1−i3−i3i3i300−i3i3−i3−i3i3i300−i3i3−i3−i3i3i3002-200000000000−i3−i3i3i30000000-1100
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χ3622-2-2-1222-21-2-2-122-2-21-1-12-1-11111-2-21111-1-12-1-1-122-21-20−i3i30000-11-112-2-1-111−i3i3−i3i3−i3i300−i3i3−i3i3−i3i300−i3i3−i3i300000−2i2i000000000000−3−33300000i−i
χ3722-2-2-1222-21-2-2-122-2-21-1-12-1-11111-2-21111-1-12-1-1-122-21-20i3−i30000-11-112-2-1-111i3−i3i3−i3i3−i300i3−i3i3−i3i3−i300i3−i3i3−i3000002i−2i000000000000−3−33300000−ii
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χ392-22-22220022-2-2-2-22-2-2222222-22-22-222-2-2-2-2-2-2-200000000000000000000000000000000000000000002i−2i00000−i2i22−22i−2i00−i2i2−i2i22−22−20000000
χ402-22-22220022-2-2-2-22-2-2222222-22-22-222-2-2-2-2-2-2-200000000000000000000000000000000000000000002i−2i00000i2−i2−222i−2i00i2−i2i2−i2−22−220000000
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χ4344444-24-4-44-2-24-24444-24-2-2-2-2-244-2-2-2-2-2-2-24-2-2-2-42-4-4-42000000022-4-422222200000000000000000000000000000000000000000000000000
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χ504444-24-244-244-24-2-2-2-2-21-211-2-211-2-21111-21-211-24-2-2-24-422-4-422-2-211-2-211112222-1-122-1-1-1-1-1-122-1-1-1-1000000000000000000000000000000
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χ7444-4-4-24-24-42-4-4-24-2222-21-21122-1-122-1-1-1-1-21-211-24-222-402i3−2i30000-221-1-2211-1-12i3−2i32i3−2i3−i3i300−i3i3−i3i3−i3i300−i3i3−i3i3000000000000000000000000000000
χ7544-4-4-24-2-442-4-4-24-2222-21-21122-1-122-1-1-1-1-21-2112-42-2-2400000002-2-112-2-1-11100003-3003-33-3-3300-33-33000000000000000000000000000000
χ7644-4-4-24-2-442-4-4-24-2222-21-21122-1-122-1-1-1-1-21-2112-42-2-2400000002-2-112-2-1-1110000-3300-33-333-3003-33-3000000000000000000000000000000
χ7744-4-4-2-244-4222-2-24-4-421-2-211-1-12222-1-1-1-11-2-211-2-24-4220−2i32i300001-1-22-2211-1-1i3−i3i3−i3−2i32i300i3−i3i3−i3−2i32i300i3−i3i3−i3000000000000000000000000000000
χ7844-4-4-2-244-4222-2-24-4-421-2-211-1-12222-1-1-1-11-2-211-2-24-42202i3−2i300001-1-22-2211-1-1−i3i3−i3i32i3−2i300−i3i3−i3i32i3−2i300−i3i3−i3i3000000000000000000000000000000
χ7944-4-4-2-24-44222-2-24-4-421-2-211-1-12222-1-1-1-11-2-21122-44-2-2000−2i32i300-112-22-2-1-111i3i3−i3−i300−2i32i3i3i3−i3−i300−2i32i3i3i3−i3−i3000000000000000000000000000000
χ8044-4-4-2-24-44222-2-24-4-421-2-211-1-12222-1-1-1-11-2-21122-44-2-20002i3−2i300-112-22-2-1-111−i3−i3i3i3002i3−2i3−i3−i3i3i3002i3−2i3−i3−i3i3i3000000000000000000000000000000
χ8144-4-4-2-2-24-4222-2-2-2222111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32111−1−3i32−1+3i32-2-2-22220−2i32i300001-11-11-1−1−3i32−1+3i321+3i321−3i32i3−i3i3−i3i3−i33-3−3−i32−3+i323−i323+i32i3−i3-333−i323+i32−3−i32−3+i32000000000000000000000000000000
χ8244-4-4-2-2-24-4222-2-2-2222111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32111−1−3i32−1+3i32-2-2-222202i3−2i300001-11-11-1−1−3i32−1+3i321+3i321−3i32−i3i3−i3i3−i3i3-333+i323−i32−3+i32−3−i32−i3i33-3−3+i32−3−i323+i323−i32000000000000000000000000000000
χ8344-4-4-2-2-24-4222-2-2-2222111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32111−1+3i32−1−3i32-2-2-22220−2i32i300001-11-11-1−1+3i32−1−3i321−3i321+3i32i3−i3i3−i3i3−i3-333−i323+i32−3−i32−3+i32i3−i33-3−3−i32−3+i323−i323+i32000000000000000000000000000000
χ8444-4-4-2-2-24-4222-2-2-2222111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32111−1+3i32−1−3i32-2-2-222202i3−2i300001-11-11-1−1+3i32−1−3i321−3i321+3i32−i3i3−i3i3−i3i33-3−3+i32−3−i323+i323−i32−i3i3-333+i323−i32−3+i32−3−i32000000000000000000000000000000
χ8544-4-4-2-2-2-44222-2-2-2222111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32111−1−3i32−1+3i32222-2-2-2000−2i32i300-11-11-111+3i321−3i32−1−3i32−1+3i32i3i3−i3−i33-3i3−i3−3−i323−i32−3+i323+i32-33i3−i33−i32−3−i323+i32−3+i32000000000000000000000000000000
χ8644-4-4-2-2-2-44222-2-2-2222111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32111−1−3i32−1+3i32222-2-2-20002i3−2i300-11-11-111+3i321−3i32−1−3i32−1+3i32−i3−i3i3i3-33−i3i33+i32−3+i323−i32−3−i323-3−i3i3−3+i323+i32−3−i323−i32000000000000000000000000000000
χ8744-4-4-2-2-2-44222-2-2-2222111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32111−1+3i32−1−3i32222-2-2-2000−2i32i300-11-11-111−3i321+3i32−1+3i32−1−3i32i3i3−i3−i3-33i3−i33−i32−3−i323+i32−3+i323-3i3−i3−3−i323−i32−3+i323+i32000000000000000000000000000000
χ8844-4-4-2-2-2-44222-2-2-2222111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32111−1+3i32−1−3i32222-2-2-20002i3−2i300-11-11-111−3i321+3i32−1+3i32−1−3i32−i3−i3i3i33-3−i3i3−3+i323+i32−3−i323−i32-33−i3i33+i32−3+i323−i32−3−i32000000000000000000000000000000
χ894-44-444-20044-4-4-42-22-44-2-2-2-24-4-22-22-2-222-4222200000000000000000000000000000000000000000004i−4i000000000−2i2i00000000000000000
χ904-44-444-20044-4-4-42-22-44-2-2-2-24-4-22-22-2-222-422220000000000000000000000000000000000000000000−4i4i0000000002i−2i00000000000000000
χ914-44-44-24004-22-42-44-4-4-24-2-2-2-224-4-22-2-2222-422200000000000000000000000000000000000000000000000000−2i22i2000000i2−i2i2−i200000000000
χ924-44-44-24004-22-42-44-4-4-24-2-2-2-224-4-22-2-2222-4222000000000000000000000000000000000000000000000000002i2−2i2000000−i2i2−i2i200000000000
χ934-44-4-24400-24-42-4-44-42-2-24-2-2-22-224-4-2-22222-422000000000000000000000000000000000000000000000000000022−2200000000−22−220000000
χ944-44-4-24400-24-42-4-44-42-2-24-2-2-22-224-4-2-22222-4220000000000000000000000000000000000000000000000000000−2222000000002−22−20000000
χ954-4-4444400-4-44-4-4-4-44444444-44-44-44-4-444-4-4-4-4-40000000000000000000000000000000000000000000000000000000000000000000000000
χ964-4-4444-200-4-44-4-422-244-2-2-2-2-442-22-222-2-2-422220000000000000000000000000000000000000000000000000000000023−23000000000000000
χ974-4-4444-200-4-44-4-422-244-2-2-2-2-442-22-222-2-2-4222200000000000000000000000000000000000000000000000000000000−2323000000000000000
χ984-4-444-2400-42-2-42-4-444-24-2-2-22-2-442-222-2-22-422200000000000000000000000000000000000000000000000000000000006−6−6600000000000
χ994-4-444-2400-42-2-42-4-444-24-2-2-22-2-442-222-2-22-42220000000000000000000000000000000000000000000000000000000000−666−600000000000
χ1004-4-44-244002-442-4-4-44-2-2-24-2-22-22-2-4422-2-222-422000000000000000000000000000000000000000000000000000000000000006−6−660000000
χ1014-4-44-244002-442-4-4-44-2-2-24-2-22-22-2-4422-2-222-42200000000000000000000000000000000000000000000000000000000000000−666−60000000
χ1028-88-88-4-4008-44-844-44-8-4-4222-44-442-222-2-244-2-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-48-400-48-84-84-444-42-422-442-2-4422-2-24-24-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4800-4-4444-88-842-4-4222-2-44-4422-2-2-244-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-400-4-44444-444222−1−3i3−1+3i32-22-22-2−1−3i3−1+3i31+3i31−3i3-2-2-21+3i31−3i30000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-400-4-44444-444222−1+3i3−1−3i32-22-22-2−1+3i3−1−3i31−3i31+3i3-2-2-21−3i31+3i30000000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-888-4-400-84-4-8444-48-4-42224-44-4-22-2-22244-2-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-8-88-48-4004-884-844-4-4-42-4224-4-224-4-2-2224-24-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-480044-444-8-88-42-4-422-224-44-4-2-222-244-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-40044-44444-4-4222−1−3i3−1+3i3-22-22-221+3i31−3i3−1−3i3−1+3i3-2-2-21+3i31−3i30000000000000000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-40044-44444-4-4222−1+3i3−1−3i3-22-22-221−3i31+3i3−1+3i3−1−3i3-2-2-21−3i31+3i30000000000000000000000000000000000000000000000000000000000000000000000000

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