Finite Group Databasebeta

← Group #13155416

Character table — Group #13155416

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222224444444444444444444444888888888888121212121212121212121212121212121212121212121212121212121212181818181818181824242424242424242424242436363636363672727272108108
order12223334466666666633366666666612121212121212121212366612121212121212124444881212121212121212242424242424242424242424242424242244121212121212121212121212121212124444661212121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111
χ51111111111111111111111111111111111111111111111111111-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-1
χ61111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-111
χ71111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ81111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ91-1-111111-1-1-1-1-1-1-1111111-1-1-1-1111-1-11-11111-1-1-1-11-1-1111-1-111-1-1i−ii−ii−iii−i−iii−i−iiiiiiiii−i−i−i−i−i−i−i−i1-11-111-1-1i−ii−iii−i−iii−i−i1-11-11-11-11-1i−i
χ101-1-111111-1-1-1-1-1-1-1111111-1-1-1-1111-1-11-11111-1-1-1-11-1-1111-1-111-1-1i−ii−i−iiii−i−iii−i−i−i−i−i−i−i−i−i−iiiiiiiii1-11-111-1-1i−ii−iii−i−iii−i−i-11-111-1-11-11−ii
χ111-1-111111-1-1-1-1-1-1-1111111-1-1-1-1111-1-11-11111-1-1-1-11-1-1111-1-111-1-1i−i−iii−iii−i−i−i−iiiiiiiiiii−i−i−i−i−i−i−i−i-11-11-1-111i−i−iiii−i−i−i−iii1-1-11-111-1-11−ii
χ121-1-111111-1-1-1-1-1-1-1111111-1-1-1-1111-1-11-11111-1-1-1-11-1-1111-1-111-1-1i−i−ii−iiii−i−i−i−iii−i−i−i−i−i−i−i−iiiiiiiii-11-11-1-111i−i−iiii−i−i−i−iii-111-1-11-111-1i−i
χ131-1-111111-1-1-1-1-1-1-1111111-1-1-1-1111-1-11-11111-1-1-1-11-1-1111-1-111-1-1−iii−ii−i−i−iiiii−i−iiiiiiiii−i−i−i−i−i−i−i−i-11-11-1-111−iii−i−i−iiiii−i−i-111-1-11-111-1−ii
χ141-1-111111-1-1-1-1-1-1-1111111-1-1-1-1111-1-11-11111-1-1-1-11-1-1111-1-111-1-1−iii−i−ii−i−iiiii−i−i−i−i−i−i−i−i−i−iiiiiiiii-11-11-1-111−iii−i−i−iiiii−i−i1-1-11-111-1-11i−i
χ151-1-111111-1-1-1-1-1-1-1111111-1-1-1-1111-1-11-11111-1-1-1-11-1-1111-1-111-1-1−ii−iii−i−i−iii−i−iiiiiiiiiii−i−i−i−i−i−i−i−i1-11-111-1-1−ii−ii−i−iii−i−iii-11-111-1-11-11i−i
χ161-1-111111-1-1-1-1-1-1-1111111-1-1-1-1111-1-11-11111-1-1-1-11-1-1111-1-111-1-1−ii−ii−ii−i−iii−i−iii−i−i−i−i−i−i−i−iiiiiiiii1-11-111-1-1−ii−ii−i−iii−i−iii1-11-11-11-11-1−ii
χ172222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000022-2-2-2-2-2-2000000000000000022000000
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χ19222222-1222222-1-1-1222-1-122-1-12-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1222200-1-1-1-1-1-1-1-100000000000000002222-1-1-1-12222-1-1-1-1-1-1-1-10000-1-1000000
χ20222222-1222222-1-1-1222-1-122-1-12-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-2-200-1-1-1-111110000000000000000-2-2-2-2111122-2-2-1-1-1-11111000011000000
χ21222222-1222222-1-1-1222-1-122-1-12-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-2-222001111-1-1-1-10000000000000000-2-2-2-21111-2-2221111-1-1-1-1000011000000
χ22222222-1222222-1-1-1222-1-122-1-12-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2001111111100000000000000002222-1-1-1-1-2-2-2-2111111110000-1-1000000
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χ25222222-1-2-22222-1-1-1222-1-122-1-12-1-1-1-111-2-2-2-2-2-2-2-2-1-1-1-111111111000000i3−i3i3−i3−i3i3−i3i30000000000000000-2-222-1-1-1-10000i3−i3i3−i3−i3i3−i3i3000011000000
χ26222222-1-2-22222-1-1-1222-1-122-1-12-1-1-1-111-2-2-2-2-2-2-2-2-1-1-1-111111111000000i3−i3i3−i3i3−i3i3−i3000000000000000022-2-211110000i3−i3i3−i3i3−i3i3−i30000-1-1000000
χ2722222-12222-12-12222-1-12-1-1-12-1-12-12-1222-1-1-12-1-1-1-1-1-1-12-12-1-1-1-1-10022220000222222-1-1-1-1-1-122-1-1-1-1-1-10000000000-1-10000-1-1-1-100220000-1-100
χ2822222-12222-12-12222-1-12-1-1-12-1-12-12-1222-1-1-12-1-1-1-1-1-1-12-12-1-1-1-1-10022-2-200002222-2-2111111-2-21111110000000000-1-10000-1-1-1-100-2-200001100
χ2922222-12222-12-12222-1-12-1-1-12-1-12-12-1222-1-1-12-1-1-1-1-1-1-12-12-1-1-1-1-100-2-2220000-2-2-2-222-1-1-1-1-1-122-1-1-1-1-1-10000000000110000111100-2-200001100
χ3022222-12222-12-12222-1-12-1-1-12-1-12-12-1222-1-1-12-1-1-1-1-1-1-12-12-1-1-1-1-100-2-2-2-20000-2-2-2-2-2-2111111-2-21111110000000000110000111100220000-1-100
χ312222-12222-12-12222-12-1-12-1-1-12-1-12-1222-12-1-1-12-1-1-1-1-1-1-12-12-1-1-1-122002222220000-1-122-1-1-1-1-1-122-1-1-1-100000000-1-100-1-1-1-10000220000-1-10000
χ322222-12222-12-12222-12-1-12-1-1-12-1-12-1222-12-1-1-12-1-1-1-1-1-1-12-12-1-1-1-12200-2-22222000011-2-2111111-2-2111100000000-1-100-1-1-1-10000-2-20000110000
χ332222-12222-12-12222-12-1-12-1-1-12-1-12-1222-12-1-1-12-1-1-1-1-1-1-12-12-1-1-1-1-2-20022-2-2-2-20000-1-122-1-1-1-1-1-122-1-1-1-100000000110011110000-2-20000110000
χ342222-12222-12-12222-12-1-12-1-1-12-1-12-1222-12-1-1-12-1-1-1-1-1-1-12-12-1-1-1-1-2-200-2-2-2-2-2-2000011-2-2111111-2-2111100000000110011110000220000-1-10000
χ352-2-22222-22-2-2-2-2-2-2222222-2-2-2-2222-2-2-22-2-2-2-222222-2-22-2-222-2-2220000000000000000000000000000002-2-22-2-22200000000000000002-2000000
χ362-2-22222-22-2-2-2-2-2-2222222-2-2-2-2222-2-2-22-2-2-2-222222-2-22-2-222-2-222000000000000000000000000000000-222-222-2-20000000000000000-22000000
χ372-2-2222-12-2-2-2-2-211-1222-1-1-2-2112-1-111-112222-2-2-2-2-111-1-1-111-1-1112i−2i2i−2i00−i−iii−i−iii00000000000000002-22-2-1-1112i−2i2i−2i−i−iii−i−iii0000-11000000
χ382-2-2222-12-2-2-2-2-211-1222-1-1-2-2112-1-111-112222-2-2-2-2-111-1-1-111-1-1112i−2i−2i2i00−i−iiiii−i−i0000000000000000-22-2211-1-12i−2i−2i2i−i−iiiii−i−i00001-1000000
χ392-2-2222-12-2-2-2-2-211-1222-1-1-2-2112-1-111-112222-2-2-2-2-111-1-1-111-1-111−2i2i2i−2i00ii−i−i−i−iii0000000000000000-22-2211-1-1−2i2i2i−2iii−i−i−i−iii00001-1000000
χ402-2-2222-12-2-2-2-2-211-1222-1-1-2-2112-1-111-112222-2-2-2-2-111-1-1-111-1-111−2i2i−2i2i00ii−i−iii−i−i00000000000000002-22-2-1-111−2i2i−2i2iii−i−iii−i−i0000-11000000
χ412-2-2222-1-22-2-2-2-211-1222-1-1-2-2112-1-1111-1-2-2-2-22222-111-111-1-111-1-10000003−3−333−3−3300000000000000002-2-2211-1-100003−3−333−3−330000-11000000
χ422-2-2222-1-22-2-2-2-211-1222-1-1-2-2112-1-1111-1-2-2-2-22222-111-111-1-111-1-10000003−3−33−333−30000000000000000-222-2-1-11100003−3−33−333−300001-1000000
χ432-2-2222-1-22-2-2-2-211-1222-1-1-2-2112-1-1111-1-2-2-2-22222-111-111-1-111-1-1000000−333−33−3−330000000000000000-222-2-1-1110000−333−33−3−3300001-1000000
χ442-2-2222-1-22-2-2-2-211-1222-1-1-2-2112-1-1111-1-2-2-2-22222-111-111-1-111-1-1000000−333−3−333−300000000000000002-2-2211-1-10000−333−3−333−30000-11000000
χ452-2-222-122-2-21-21-2-222-1-12-111-21-12-1-212-22-1-1-1-2111-111-12-1-21-1-111002i−2i2i−2i00002i2i−2i−2i2i2i−i−i−i−i−i−i−2i−2iiiiiii0000000000−ii0000−i−iii002-20000-1100
χ462-2-222-122-2-21-21-2-222-1-12-111-21-12-1-212-22-1-1-1-2111-111-12-1-21-1-111002i−2i−2i2i00002i2i−2i−2i−2i−2iiiiiii2i2i−i−i−i−i−i−i0000000000−ii0000−i−iii00-2200001-100
χ472-2-222-122-2-21-21-2-222-1-12-111-21-12-1-212-22-1-1-1-2111-111-12-1-21-1-11100−2i2i2i−2i0000−2i−2i2i2i2i2i−i−i−i−i−i−i−2i−2iiiiiii0000000000i−i0000ii−i−i00-2200001-100
χ482-2-222-122-2-21-21-2-222-1-12-111-21-12-1-212-22-1-1-1-2111-111-12-1-21-1-11100−2i2i−2i2i0000−2i−2i2i2i−2i−2iiiiiii2i2i−i−i−i−i−i−i0000000000i−i0000ii−i−i002-20000-1100
χ492-2-22-1222-21-21-2-2-22-12-1-12111-2-1-121-22-2-12-1-11-211-111-1-121-2-1-1112i−2i002i−2i2i2i−2i−2i0000−i−i2i2i−i−i−i−iii−2i−2iiiii00000000−ii00−i−iii00002-20000-110000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.