Finite Group Databasebeta

← Group #13145742

Character table — Group #13145742

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size112222222224444444444444444444444444444444888888888888888888888888888888888888363636363636727272727272727272727272727272
order1223336666622333334666666666666666666666121266666666666666666666666612121212121212121212121244121212124444412121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ511111111111-1-111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1i−ii−i-1-1ii−i−iii−i−i
χ611111111111-1-111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1−ii−ii-1-1−i−iii−i−iii
χ711111111111-1-111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11i−i−ii11ii−i−i−i−iii
χ811111111111-1-111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11−iii−i11−i−iiiii−i−i
χ9222222222222-222222-22222222222222222222-2-2-2-222-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000
χ1022222222222-2222222-222222222222222222-2-222-2-2-2-222-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000
χ1122222-122-1-1-1222-1-1-1-122222-1-1-1-1-1-1-1-12-1-1-1-12222-1-12-12-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-120000-1-100000000
χ1222222-122-1-1-1222-1-1-1-122222-1-1-1-1-1-1-1-12-1-1-1-12222-1-12-12-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-21111-200001100000000
χ1322222-122-1-1-12-22-1-1-1-1-22222-1-1-1-1-1-1-1-12-1-1-1-122-2-2112-1-2122-1-1-1-1-1-1-1-1-2-211111111-2-2-2-21111111100−i3−i3i3i300000−i3i300000000
χ1422222-122-1-1-12-22-1-1-1-1-22222-1-1-1-1-1-1-1-12-1-1-1-122-2-2112-1-2122-1-1-1-1-1-1-1-1-2-211111111-2-2-2-21111111100i3i3−i3−i300000i3−i300000000
χ1522222-122-1-1-1-222-1-1-1-1-22222-1-1-1-1-1-1-1-12-1-1-1-1-2-22211-212-1-2-21111111122-1-1-1-1-1-1-1-1-2-2-2-21111111100−i3−i3i3i300000i3−i300000000
χ1622222-122-1-1-1-222-1-1-1-1-22222-1-1-1-1-1-1-1-12-1-1-1-1-2-22211-212-1-2-21111111122-1-1-1-1-1-1-1-1-2-2-2-21111111100i3i3−i3−i300000−i3i300000000
χ1722222-122-1-1-1-2-22-1-1-1-122222-1-1-1-1-1-1-1-12-1-1-1-1-2-2-2-2-1-1-21-21-2-211111111-2-2111111112222-1-1-1-1-1-1-1-122-1-1-1-1-200001100000000
χ1822222-122-1-1-1-2-22-1-1-1-122222-1-1-1-1-1-1-1-12-1-1-1-1-2-2-2-2-1-1-21-21-2-211111111-2-2111111112222-1-1-1-1-1-1-1-1-2-2111120000-1-100000000
χ192222-122-122222-12-1-1-122-1-1-122-1-1-1-1-1-1-12-1-1-122-1-122-1222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12-1-1-122-1-1-1-1-1-100000000022000000-1-1-1-1
χ202222-122-122222-12-1-1-122-1-1-122-1-1-1-1-1-1-12-1-1-122-1-122-1222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12-1-1-122-1-1-1-1-1-1000000000-2-20000001111
χ212222-122-12222-2-12-1-1-1-22-1-1-122-1-1-1-1-1-1-12-1-1-12211-2-2-12-2-2-1-122-1-1-1-1-1-111-2-2111111-2111-2-2111111000000000000000003−33−3
χ222222-122-12222-2-12-1-1-1-22-1-1-122-1-1-1-1-1-1-12-1-1-12211-2-2-12-2-2-1-122-1-1-1-1-1-111-2-2111111-2111-2-211111100000000000000000−33−33
χ232222-122-1222-22-12-1-1-1-22-1-1-122-1-1-1-1-1-1-12-1-1-1-2-2-1-1-2-21-22211-2-2111111-1-122-1-1-1-1-1-1-2111-2-211111100000000000000000−i3i3i3−i3
χ242222-122-1222-22-12-1-1-1-22-1-1-122-1-1-1-1-1-1-12-1-1-1-2-2-1-1-2-21-22211-2-2111111-1-122-1-1-1-1-1-1-2111-2-211111100000000000000000i3−i3−i3i3
χ252222-122-1222-2-2-12-1-1-122-1-1-122-1-1-1-1-1-1-12-1-1-1-2-211221-2-2-211-2-211111111-2-21111112-1-1-122-1-1-1-1-1-10000000002i−2i000000−i−iii
χ262222-122-1222-2-2-12-1-1-122-1-1-122-1-1-1-1-1-1-12-1-1-1-2-211221-2-2-211-2-211111111-2-21111112-1-1-122-1-1-1-1-1-1000000000−2i2i000000ii−i−i
χ27222-122-1222222-1-12-1-12-12-1-1-1-122-1-1-1-1-1-12-1-1-1-1222222-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-12-1-1-1-122-1-1-1-10000000220000-1-1-1-10000
χ28222-122-1222222-1-12-1-12-12-1-1-1-122-1-1-1-1-1-12-1-1-1-1222222-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-12-1-1-1-122-1-1-1-10000000-2-2000011110000
χ29222-122-122222-2-1-12-1-1-2-12-1-1-1-122-1-1-1-1-1-12-1-1-1-1-2-2-2-2221-2-1-1-1-122-1-1-1-11111-2-211111-21111-2-211110000000000000−i3i3−i3i30000
χ30222-122-122222-2-1-12-1-1-2-12-1-1-1-122-1-1-1-1-1-12-1-1-1-1-2-2-2-2221-2-1-1-1-122-1-1-1-11111-2-211111-21111-2-211110000000000000i3−i3i3−i30000
χ31222-122-12222-22-1-12-1-1-2-12-1-1-1-122-1-1-1-1-1-12-1-11122-2-2-2-2-121111-2-21111-1-1-1-122-1-1-1-11-21111-2-2111100000000000003−3−330000
χ32222-122-12222-22-1-12-1-1-2-12-1-1-1-122-1-1-1-1-1-12-1-11122-2-2-2-2-121111-2-21111-1-1-1-122-1-1-1-11-21111-2-211110000000000000−333−30000
χ33222-122-12222-2-2-1-12-1-12-12-1-1-1-122-1-1-1-1-1-12-1-111-2-222-2-21-21111-2-211111111-2-21111-12-1-1-1-122-1-1-1-100000002i−2i0000−i−iii0000
χ34222-122-12222-2-2-1-12-1-12-12-1-1-1-122-1-1-1-1-1-12-1-111-2-222-2-21-21111-2-211111111-2-21111-12-1-1-1-122-1-1-1-10000000−2i2i0000ii−i−i0000
χ354444-2-24-2-2-2-244-2-211144-2-2-2-2-2111111-2-211144-2-2-2-2-2-24-2-2-2-2-2111111-2-2-2-21111114-2-2-2-2-2111111000000000000000000000
χ364444-2-24-2-2-2-24-4-2-2111-44-2-2-2-2-2111111-2-2111442222-2-2-42-2-2-2-21111112222-1-1-1-1-1-1-422222-1-1-1-1-1-1000000000000000000000
χ374444-2-24-2-2-2-2-44-2-2111-44-2-2-2-2-2111111-2-2111-4-4-2-222224-22222-1-1-1-1-1-1-2-2-2-2111111-422222-1-1-1-1-1-1000000000000000000000
χ384444-2-24-2-2-2-2-4-4-2-211144-2-2-2-2-2111111-2-2111-4-422-2-222-422222-1-1-1-1-1-12222-1-1-1-1-1-14-2-2-2-2-2111111000000000000000000000
χ39444-24-2-24-2-2-244-21-2114-24-2-211-2-21111-21-211-2-244-2-24-2-2-2-2-211-2-21111-2-211-2-21111-24-2-211-2-21111000000000000000000000
χ40444-24-2-24-2-2-24-4-21-211-4-24-2-211-2-21111-21-211-2-2-4-4224-222-2-211-2-2111122-1-122-1-1-1-12-422-1-122-1-1-1-1000000000000000000000
χ41444-24-2-24-2-2-2-44-21-211-4-24-2-211-2-21111-21-211224422-42-2-222-1-122-1-1-1-1-2-211-2-211112-422-1-122-1-1-1-1000000000000000000000
χ42444-24-2-24-2-2-2-4-4-21-2114-24-2-211-2-21111-21-21122-4-4-2-2-422222-1-122-1-1-1-122-1-122-1-1-1-1-24-2-211-2-21111000000000000000000000
χ43444-2-24-2-2444441-2-2114-2-211-2-2-2-211111-2-211-2-2-2-244-24-2411-2-2-2-2111111-2-2-2-21111-2-211-2-2-2-21111000000000000000000000
χ44444-2-24-2-24444-41-2-211-4-2-211-2-2-2-211111-2-211-2-222-4-4-242-411-2-2-2-21111-1-12222-1-1-1-122-1-12222-1-1-1-1000000000000000000000
χ45444-2-24-2-2444-441-2-211-4-2-211-2-2-2-211111-2-21122-2-2-4-42-4-24-1-12222-1-1-1-111-2-2-2-2111122-1-12222-1-1-1-1000000000000000000000
χ46444-2-24-2-2444-4-41-2-2114-2-211-2-2-2-211111-2-2112222442-42-4-1-12222-1-1-1-1-1-12222-1-1-1-1-2-211-2-2-2-21111000000000000000000000
χ47444-2-2-2-2-2-2-2-244111−1−3i32−1+3i324-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i32-2-2-2-2-2-2-2-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111111−1−3i32−1−3i32−1+3i32−1+3i32-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32000000000000000000000
χ48444-2-2-2-2-2-2-2-244111−1+3i32−1−3i324-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111−1+3i32−1−3i32-2-2-2-2-2-2-2-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111111−1+3i32−1+3i32−1−3i32−1−3i32-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32000000000000000000000
χ49444-2-2-2-2-2-2-2-24-4111−1−3i32−1+3i32-4-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i32-2-22222-2-222111111−1−3i32−1−3i32−1+3i32−1+3i32-1-1-1-1-1-11+3i321+3i321−3i321−3i3222-1-1-1-1-1-11+3i321+3i321−3i321−3i32000000000000000000000
χ50444-2-2-2-2-2-2-2-24-4111−1+3i32−1−3i32-4-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111−1+3i32−1−3i32-2-22222-2-222111111−1+3i32−1+3i32−1−3i32−1−3i32-1-1-1-1-1-11−3i321−3i321+3i321+3i3222-1-1-1-1-1-11−3i321−3i321+3i321+3i32000000000000000000000
χ51444-2-2-2-2-2-2-2-2-44111−1−3i32−1+3i32-4-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i3222-2-22222-2-2-1-1-1-1-1-11+3i321+3i321−3i321−3i32111111−1−3i32−1−3i32−1+3i32−1+3i3222-1-1-1-1-1-11+3i321+3i321−3i321−3i32000000000000000000000
χ52444-2-2-2-2-2-2-2-2-44111−1+3i32−1−3i32-4-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111−1+3i32−1−3i3222-2-22222-2-2-1-1-1-1-1-11−3i321−3i321+3i321+3i32111111−1+3i32−1+3i32−1−3i32−1−3i3222-1-1-1-1-1-11−3i321−3i321+3i321+3i32000000000000000000000
χ53444-2-2-2-2-2-2-2-2-4-4111−1−3i32−1+3i324-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i322222-2-22222-1-1-1-1-1-11+3i321+3i321−3i321−3i32-1-1-1-1-1-11+3i321+3i321−3i321−3i32-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32000000000000000000000
χ54444-2-2-2-2-2-2-2-2-4-4111−1+3i32−1−3i324-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111−1+3i32−1−3i322222-2-22222-1-1-1-1-1-11−3i321−3i321+3i321+3i32-1-1-1-1-1-11−3i321−3i321+3i321+3i32-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32000000000000000000000
χ5544-444444-4-4400444440-4-4-4-4-4-4-4-4-4-4-4-444444000000000000000000000000000000000000000000000000000000000000000
χ5644-444-24422-2004-2-2-2-20-4-4-4-4222222224-2-2-2-20000−2i32i30000000000000000000000000000−2i32i3−2i32i3−2i32i3−2i32i3000000000000000000000
χ5744-444-24422-2004-2-2-2-20-4-4-4-4222222224-2-2-2-200002i3−2i300000000000000000000000000002i3−2i32i3−2i32i3−2i32i3−2i3000000000000000000000
χ5844-44-244-2-4-4400-24-2-2-20-4222-4-4222222-24-2-2-200−2i32i30000000000000000−2i32i300−2i32i3−2i32i3−2i32i3000000000000000000000000000000000
χ5944-44-244-2-4-4400-24-2-2-20-4222-4-4222222-24-2-2-2002i3−2i300000000000000002i3−2i3002i3−2i32i3−2i32i3−2i3000000000000000000000000000000000
χ6044-44-2-24-222-200-2-21110-422222-1-1-1-1-1-1-2-211100−2i32i3−2i32i3000000003-33-33-3−2i32i300i3−i3i3−i3i3−i30000−2i32i3i3−i3i3−i3i3−i3000000000000000000000
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χ6644-4-24-2-2422-200-21-21102-422-1-122-1-1-1-1-21-211−2i32i300−2i32i30000−2i32i3i3−i300i3−i3−i3i3003-3003-3-330000i3−i3−2i32i3i3−i3i3−i3000000000000000000000
χ6744-4-24-2-2422-200-21-21102-422-1-122-1-1-1-1-21-211−2i32i3002i3−2i30000−2i32i3i3−i300i3−i3−i3i300-3300-333-30000−i3i32i3−2i3−i3i3−i3i3000000000000000000000
χ6844-4-24-2-2422-200-21-21102-422-1-122-1-1-1-1-21-2112i3−2i300−2i32i300002i3−2i3−i3i300−i3i3i3−i300-3300-333-30000i3−i3−2i32i3i3−i3i3−i3000000000000000000000
χ6944-4-24-2-2422-200-21-21102-422-1-122-1-1-1-1-21-2112i3−2i3002i3−2i300002i3−2i3−i3i300−i3i3i3−i3003-3003-3-330000−i3i32i3−2i3−i3i3−i3i3000000000000000000000
χ7044-4-2-24-2-2-4-44001-2-211022-1-12222-1-1-1-11-2-211−2i32i3−2i32i3000000i3−i3−2i32i300i3−i3−i3i3i3−i300−2i32i3i3−i3i3−i3003-300003-3-33000000000000000000000
χ7144-4-2-24-2-2-4-44001-2-211022-1-12222-1-1-1-11-2-211−2i32i32i3−2i3000000i3−i3−2i32i300i3−i3−i3i3−i3i3002i3−2i3−i3i3−i3i300-330000-333-3000000000000000000000
χ7244-4-2-24-2-2-4-44001-2-211022-1-12222-1-1-1-11-2-2112i3−2i3−2i32i3000000−i3i32i3−2i300−i3i3i3−i3i3−i300−2i32i3i3−i3i3−i300-330000-333-3000000000000000000000
χ7344-4-2-24-2-2-4-44001-2-211022-1-12222-1-1-1-11-2-2112i3−2i32i3−2i3000000−i3i32i3−2i300−i3i3i3−i3−i3i3002i3−2i3−i3i3−i3i3003-300003-3-33000000000000000000000
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χ834-40444-4-400-400444440000000000000-4-4-4-4-4000000000000000000000000000000000000000000−2i2i−2i2i−2i2i000000000000000
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χ918-80-4884-800-800-4-48-4-4000000000000044-844000000000000000000000000000000000000000000000000000000000000000
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χ948-80-4-484400-8002-4-4220006-600006-6-66-244-2-2000000000000000000000000000000000000000000000000000000000000000
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χ968-80-4-4-444−4i34i3400222−1−3i3−1+3i30006-62i3−2i32i3−2i3−3−i33+i33−i3−3+i3-2-2-21+3i31−3i3000000000000000000000000000000000000000000000000000000000000000
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χ988-80-4-4-4444i3−4i3400222−1−3i3−1+3i3000-66−2i32i3−2i32i33+i3−3−i3−3+i33−i3-2-2-21+3i31−3i3000000000000000000000000000000000000000000000000000000000000000
χ998-80-4-4-4444i3−4i3400222−1+3i3−1−3i30006-6−2i32i3−2i32i3−3+i33−i33+i3−3−i3-2-2-21−3i31+3i3000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.