Finite Group Databasebeta

← Group #13156557

Character table — Group #13156557

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11112222222222222222224444444444444444444444448888888888121212121212121212121212121212121212121212121212121212121212121212121212242424242424242424363636363636727272727272216
order12223334466666666612121212333666666666121212121212121212121212366612121212121288882424242424242424242424242424242424242424242424242424242424242424412121212121212124412121212246612124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11-111-1-1-1
χ41111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111
χ511111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-11-1-111-1
χ611111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11
χ711111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-11
χ811111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-20000000000000000000000000000000000000000000002-222-2-20000000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2000000000000000000000000000000000000000000000-22-2-2220000000
χ11222222-1222-12-12-122222222-1-122-1-1-12-1-1-1-1222-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1220022220000-1-1-1-1-1-1-1-1-1-1-1-1000000000000222-1-1-1-1-1-100000020-1-1000
χ12222222-1222-12-12-122222222-1-122-1-1-12-1-1-1-1222-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1220022220000-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-2-2111111000000-2011000
χ13222222-1222-12-12-122222222-1-122-1-1-12-1-1-1-1222-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2-2-2-20000111111111111000000000000222-1-1-1-1-1-1000000-2011000
χ14222222-1222-12-12-122222222-1-122-1-1-12-1-1-1-1222-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2-2-2-20000111111111111000000000000-2-2-211111100000020-1-1000
χ1522222-122222-1222-1-12-1-1-1-1-12-1-1-12-1-1-12-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000022-1-1-1-10000000
χ1622222-122222-1222-1-12-1-1-1-1-12-1-1-12-1-1-12-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-122-2-2-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2-2-211111111000000000-2-211110000000
χ1722222-122222-1222-1-12-1-1-1-1-12-1-1-12-1-1-12-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2221111-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1000000000-2-211110000000
χ1822222-122222-1222-1-12-1-1-1-1-12-1-1-12-1-1-12-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2-2-21111111100000000022-1-1-1-10000000
χ1922222-12-2-222-1222-1-121111-12-1-1-12-1-1-12-12-2-21111-2-21111-1-1-1-1-2-21111000033−3−333−3−300003333−3−3−3−300003333−3−3−3−30000000002-2-1-1110000000
χ2022222-12-2-222-1222-1-121111-12-1-1-12-1-1-12-12-2-21111-2-21111-1-1-1-1-2-21111000033−3−3−3−33300003333−3−3−3−30000−3−3−3−33333000000000-2211-1-10000000
χ2122222-12-2-222-1222-1-121111-12-1-1-12-1-1-12-12-2-21111-2-21111-1-1-1-1-2-211110000−3−33333−3−30000−3−3−3−3333300003333−3−3−3−3000000000-2211-1-10000000
χ2222222-12-2-222-1222-1-121111-12-1-1-12-1-1-12-12-2-21111-2-21111-1-1-1-1-2-211110000−3−333−3−3330000−3−3−3−333330000−3−3−3−333330000000002-2-1-1110000000
χ232222-12222-1222-1222-12222-1-12-1-1-122-1-12-12-1-1-1222-1-1-122-1-1-1-1-1-1-1-1-1-1002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-12-1-122-1-1-1-10000000200-1-10
χ242222-12222-1222-1222-12222-1-12-1-1-122-1-12-12-1-1-1222-1-1-122-1-1-1-1-1-1-1-1-1-1002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-1-211-2-211110000000-200110
χ252222-12222-1222-1222-12222-1-12-1-1-122-1-12-12-1-1-1222-1-1-122-1-1-1-1-1-1-1-1-1-100-2-20000-2-2-2-20000000000001111111111112-1-122-1-1-1-10000000-200110
χ262222-12222-1222-1222-12222-1-12-1-1-122-1-12-12-1-1-1222-1-1-122-1-1-1-1-1-1-1-1-1-100-2-20000-2-2-2-2000000000000111111111111-211-2-211110000000200-1-10
χ272-22-22222-2-2-222-2-2-2-2222-2-2222-2-2-2-2-2222-22-2-2-222-2222-2-22-2-222-222-2-22i−2i002i−2i2i−2i00002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000
χ282-22-22222-2-2-222-2-2-2-2222-2-2222-2-2-2-2-2222-22-2-2-222-2222-2-22-2-222-222-2-2−2i2i00−2i2i−2i2i0000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000
χ292-22-2222-22-2-222-2-2-2-22-2-222222-2-2-2-2-2222-2-2222-2-22-2-2-2222-2-22-22-2-222002i−2i00002i−2i2i−2i0000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000
χ302-22-2222-22-2-222-2-2-2-22-2-222222-2-2-2-2-2222-2-2222-2-22-2-2-2222-2-22-22-2-22200−2i2i0000−2i2i−2i2i000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000
χ312-22-222-12-2-212-1-21-2-2222-2-22-1-1-2-21112-1-11-1-2-2-2-1-1122211-111-1-11-1-1112i−2i002i−2i2i−2i0000−i−iii−i−iii−i−iii0000000000000003−333−3−300000000−i3i3000
χ322-22-222-12-2-212-1-21-2-2222-2-22-1-1-2-21112-1-11-1-2-2-2-1-1122211-111-1-11-1-1112i−2i002i−2i2i−2i0000−i−iii−i−iii−i−iii000000000000000−33−3−33300000000i3−i3000
χ332-22-222-12-2-212-1-21-2-2222-2-22-1-1-2-21112-1-11-1-2-2-2-1-1122211-111-1-11-1-111−2i2i00−2i2i−2i2i0000ii−i−iii−i−iii−i−i0000000000000003−333−3−300000000i3−i3000
χ342-22-222-12-2-212-1-21-2-2222-2-22-1-1-2-21112-1-11-1-2-2-2-1-1122211-111-1-11-1-111−2i2i00−2i2i−2i2i0000ii−i−iii−i−iii−i−i000000000000000−33−3−33300000000−i3i3000
χ352-22-22-122-2-2-2-12-2-2112-1-111-12-111-211-12-1-22-211-1-1-22-1-111-111-12-2-1-1112i−2i00−ii−ii−i3i3i3−i32i2i−2i−2i−i−iii−i−iii0000−i3−i3i3i3i3i3−i3−i3000000000003−33−30000000
χ362-22-22-122-2-2-2-12-2-2112-1-111-12-111-211-12-1-22-211-1-1-22-1-111-111-12-2-1-1112i−2i00−ii−iii3−i3−i3i32i2i−2i−2i−i−iii−i−iii0000i3i3−i3−i3−i3−i3i3i300000000000−33−330000000
χ372-22-22-122-2-2-2-12-2-2112-1-111-12-111-211-12-1-22-211-1-1-22-1-111-111-12-2-1-111−2i2i00i−ii−i−i3i3i3−i3−2i−2i2i2iii−i−iii−i−i0000−i3−i3i3i3i3i3−i3−i300000000000−33−330000000
χ382-22-22-122-2-2-2-12-2-2112-1-111-12-111-211-12-1-22-211-1-1-22-1-111-111-12-2-1-111−2i2i00i−ii−ii3−i3−i3i3−2i−2i2i2iii−i−iii−i−i0000i3i3−i3−i3−i3−i3i3i3000000000003−33−30000000
χ392-22-22-12-22-2-2-12-2-211211-1-1-12-111-211-12-1-2-22-1-1112-211-1-1-111-1-2211-1-1002i−2i−i3i3i3−i3−ii−ii0000−i3−i3i3i3i3i3−i3−i32i2i−2i−2i−i−iii−i−iii00000000000−333−30000000
χ402-22-22-12-22-2-2-12-2-211211-1-1-12-111-211-12-1-2-22-1-1112-211-1-1-111-1-2211-1-1002i−2ii3−i3−i3i3−ii−ii0000i3i3−i3−i3−i3−i3i3i32i2i−2i−2i−i−iii−i−iii000000000003−3−330000000
χ412-22-22-12-22-2-2-12-2-211211-1-1-12-111-211-12-1-2-22-1-1112-211-1-1-111-1-2211-1-100−2i2i−i3i3i3−i3i−ii−i0000−i3−i3i3i3i3i3−i3−i3−2i−2i2i2iii−i−iii−i−i000000000003−3−330000000
χ422-22-22-12-22-2-2-12-2-211211-1-1-12-111-211-12-1-2-22-1-1112-211-1-1-111-1-2211-1-100−2i2ii3−i3−i3i3i−ii−i0000i3i3−i3−i3−i3−i3i3i3−2i−2i2i2iii−i−iii−i−i00000000000−333−30000000
χ432-22-2-122-221-2221-2-2-2-1-2-222-1-12111-2-2-1-121-2-1-1-1-2-2211122-111-11-111-1-1002i−2i00002i−2i2i−2i000000000000−i−iii−i−iii−i−iii03−3003−33−30000000000−i3i30
χ442-22-2-122-221-2221-2-2-2-1-2-222-1-12111-2-2-1-121-2-1-1-1-2-2211122-111-11-111-1-1002i−2i00002i−2i2i−2i000000000000−i−iii−i−iii−i−iii0−3300−33−330000000000i3−i30
χ452-22-2-122-221-2221-2-2-2-1-2-222-1-12111-2-2-1-121-2-1-1-1-2-2211122-111-11-111-1-100−2i2i0000−2i2i−2i2i000000000000ii−i−iii−i−iii−i−i03−3003−33−30000000000i3−i30
χ462-22-2-122-221-2221-2-2-2-1-2-222-1-12111-2-2-1-121-2-1-1-1-2-2211122-111-11-111-1-100−2i2i0000−2i2i−2i2i000000000000ii−i−iii−i−iii−i−i0−3300−33−330000000000−i3i30
χ47444444-2-4-44-24-24-2444-4-4-4-44-2-244-2-2-24-2-2-22-4-4-4222-4-4-422-2-2-2-22222220000000000000000000000000000000000000000000000000000000000
χ4844444-2-2444-2-2-24-2-2-24-2-2-2-2-2-21-2-2-211-2-21-2-24-2-211-24-2-2111111-2-211114400-2-2-2-20000-2-2-2-2111111110000000000000000000000000000000000
χ4944444-2-2444-2-2-24-2-2-24-2-2-2-2-2-21-2-2-211-2-21-2-24-2-211-24-2-2111111-2-21111-4-400222200002222-1-1-1-1-1-1-1-10000000000000000000000000000000000
χ5044444-2-2-4-44-2-2-24-2-2-242222-2-21-2-2-211-2-21-22-422-1-12-422-1-1111122-1-1-1-100002323−23−2300000000−3−3−3−333330000000000000000000000000000000000
χ5144444-2-2-4-44-2-2-24-2-2-242222-2-21-2-2-211-2-21-22-422-1-12-422-1-1111122-1-1-1-10000−23−232323000000003333−3−3−3−30000000000000000000000000000000000
χ524444-244-4-4-2444-2444-2-4-4-4-4-2-24-2-2-244-2-24-2-4222-4-4-4222-4-4-2-2-2-22222220000000000000000000000000000000000000000000000000000000000
χ534444-24-244-2-24-2-2-244-24444-21-2-2-21-2-2-21-21-2-2-2-2-2-2-2-2-2-2-2-211111111110000000000000000000000000000000000004-2-2-2-211110000000000000
χ544444-24-244-2-24-2-2-244-24444-21-2-2-21-2-2-21-21-2-2-2-2-2-2-2-2-2-2-2-21111111111000000000000000000000000000000000000-42222-1-1-1-10000000000000
χ554444-24-2-4-4-2-24-2-2-244-2-4-4-4-4-21-2-2-21-2-2-21-212222222222221111-1-1-1-1-1-1000000000000000000000000000000000000000003-3-330000000000000
χ564444-24-2-4-4-2-24-2-2-244-2-4-4-4-4-21-2-2-21-2-2-21-212222222222221111-1-1-1-1-1-100000000000000000000000000000000000000000-333-30000000000000
χ574444-2-2444-24-24-24-2-2-2-2-2-2-21-2-211-2-2-21-2-2-24-211-2-24-211-2-21111-2-2111100440000-2-2-2-2000000000000-2-2-2-2111111110000000000000000000000
χ584444-2-2444-24-24-24-2-2-2-2-2-2-21-2-211-2-2-21-2-2-24-211-2-24-211-2-21111-2-2111100-4-4000022220000000000002222-1-1-1-1-1-1-1-10000000000000000000000
χ594444-2-24-4-4-24-24-24-2-2-222221-2-211-2-2-21-2-2-2-42-1-122-42-1-122111122-1-1-1-1000000002323−23−230000000000000000−3−3−3−333330000000000000000000000
χ604444-2-24-4-4-24-24-24-2-2-222221-2-211-2-2-21-2-2-2-42-1-122-42-1-122111122-1-1-1-100000000−23−23232300000000000000003333−3−3−3−30000000000000000000000
χ6144-4-44440044-4-4-4-44-4-400004444-444-4-4-4-4-400000000000044-4-40000000000000000000000000000000000000000000000000000000000000000
χ6244-4-444-2004-2-42-424-4-400004-2-24-4-2-22-4222000000000000-2-2220000000000000000006−66−66−66−66−66−60000000000000000000000000000000000
χ6344-4-444-2004-2-42-424-4-400004-2-24-4-2-22-4222000000000000-2-222000000000000000000−66−66−66−66−66−660000000000000000000000000000000000
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χ6644-4-44-2-2004-222-42-22-423−2323−23-2-21-22-21-122-120023−23−330023−23−3311-1-100−33−330000000000006−66−6−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ230000000000000000000000000000000000
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χ6844-4-44-2-2004-222-42-22-4−2323−2323-2-21-22-21-122-1200−23233−300−23233−311-1-1003−33−30000000000006−66−6ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ230000000000000000000000000000000000
χ6944-4-44-2-2004-222-42-22-4−2323−2323-2-21-22-21-122-1200−23233−300−23233−311-1-1003−33−3000000000000−66−66−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ232ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ230000000000000000000000000000000000
χ7044-4-4-24400-24-4-42-44-420000-2-24-22-24-422-42000000000000-2-222000000000000000000000000000000i6−i6i6−i6i6−i6i6−i6i6−i6i6−i60000000000000000000000
χ7144-4-4-24400-24-4-42-44-420000-2-24-22-24-422-42000000000000-2-222000000000000000000000000000000−i6i6−i6i6−i6i6−i6i6−i6i6−i6i60000000000000000000000
χ7244-4-4-2-2400-242-42-4-22223−2323−231-2-21-1-2-22-122200−3323−2300−3323−2311-1-100−33−33000000000000000000000000i6−i6i6−i6ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ230000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.