Finite Group Databasebeta

← Group #13155691

Character table — Group #13155691

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222224444444444444444444444888888888888121212121212121212121212121212121212121212121212121212121212181818181818181824242424242424242424242436363636363672727272108108
order12223334466666666633366666666612121212121212121212366612121212121212124444881212121212121212242424242424242424242424242424244444121212121212121212121212121212122244121266121288
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
χ3111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-111
χ51111111111111111111111111111111111111111111111111111-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-111-1-1-1-1
χ61111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111
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
χ911-1-1111-11-1-11-111-1-1-1111-1-1-1-1-111-11111-111-1-1-1-11-1-111-11-111-1-11-1i−ii−i11-1-1ii−i−iiiiiiiii−i−i−i−i−i−i−i−ii−ii−iii−i−ii−i1-1ii−i−i11-1-11-1i−ii−i1-1i−i1-1
χ1011-1-1111-11-1-11-111-1-1-1111-1-1-1-1-111-11111-111-1-1-1-11-1-111-11-111-1-11-1i−i−ii11-1-1ii−i−i−i−i−i−i−i−i−i−iiiiiiiiii−ii−iii−i−ii−i1-1ii−i−i11-1-1-11−iii−i-11−ii-11
χ1111-1-1111-11-1-11-111-1-1-1111-1-1-1-1-111-11111-111-1-1-1-11-1-111-11-111-1-11-1−iii−i11-1-1−i−iiiiiiiiiii−i−i−i−i−i−i−i−i−ii−ii−i−iii−ii1-1−i−iii11-1-1-11i−i−ii-11i−i-11
χ1211-1-1111-11-1-11-111-1-1-1111-1-1-1-1-111-11111-111-1-1-1-11-1-111-11-111-1-11-1−ii−ii11-1-1−i−iii−i−i−i−i−i−i−i−iiiiiiiii−ii−ii−i−iii−ii1-1−i−iii11-1-11-1−ii−ii1-1−ii1-1
χ1311-1-1111-11-1-11-111-1-1-1111-1-1-1-1-111-11111-111-1-1-1-11-1-111-11-111-1-1-11i−ii−i-1-111ii−i−iiiiiiiii−i−i−i−i−i−i−i−i−ii−ii−i−iiii−i-11ii−i−i-1-1111-1−ii−ii1-1−ii-11
χ1411-1-1111-11-1-11-111-1-1-1111-1-1-1-1-111-11111-111-1-1-1-11-1-111-11-111-1-1-11i−i−ii-1-111ii−i−i−i−i−i−i−i−i−i−iiiiiiiii−ii−ii−i−iiii−i-11ii−i−i-1-111-11i−i−ii-11i−i1-1
χ1511-1-1111-11-1-11-111-1-1-1111-1-1-1-1-111-11111-111-1-1-1-11-1-111-11-111-1-1-11−iii−i-1-111−i−iiiiiiiiiii−i−i−i−i−i−i−i−ii−ii−iii−i−i−ii-11−i−iii-1-111-11−iii−i-11−ii1-1
χ1611-1-1111-11-1-11-111-1-1-1111-1-1-1-1-111-11111-111-1-1-1-11-1-111-11-111-1-1-11−ii−ii-1-111−i−iii−i−i−i−i−i−i−i−iiiiiiiiii−ii−iii−i−i−ii-11−i−iii-1-1111-1i−ii−i1-1i−i-11
χ172222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000022-2-222220000000000000000-2-2000000
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χ19222222-1222-1-1-1222222-1-122-1-1-1-1-1-12-1222-1-1-12-1-1-1-1-1-1-1-122-1-1-1-10022220000222222-1-1-1-1-1-122-1-1-1-1-1-100000000-1-100-1-1-1-10000220000-1-10000
χ20222222-1222-1-1-1222222-1-122-1-1-1-1-1-12-1222-1-1-12-1-1-1-1-1-1-1-122-1-1-1-10022-2-200002222-2-2111111-2-211111100000000-1-100-1-1-1-10000-2-20000110000
χ21222222-1222-1-1-1222222-1-122-1-1-1-1-1-12-1222-1-1-12-1-1-1-1-1-1-1-122-1-1-1-100-2-2220000-2-2-2-222-1-1-1-1-1-122-1-1-1-1-1-100000000110011110000-2-20000110000
χ22222222-1222-1-1-1222222-1-122-1-1-1-1-1-12-1222-1-1-12-1-1-1-1-1-1-1-122-1-1-1-100-2-2-2-20000-2-2-2-2-2-2111111-2-211111100000000110011110000220000-1-10000
χ2322222-122222222-1-1-12-12-1-1-122-12-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1222200-1-1-1-1-1-1-1-100000000000000002222-1-1-1-12222-1-1-1-1-1-1-1-10000-1-1000000
χ2422222-122222222-1-1-12-12-1-1-122-12-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122-2-200-1-1-1-111110000000000000000-2-2-2-21111-2-2221111-1-1-1-1000011000000
χ2522222-122222222-1-1-12-12-1-1-122-12-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-222001111-1-1-1-10000000000000000-2-2-2-2111122-2-2-1-1-1-11111000011000000
χ2622222-122222222-1-1-12-12-1-1-122-12-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2001111111100000000000000002222-1-1-1-1-2-2-2-2111111110000-1-1000000
χ2722222-12-2-222222-1-1-12-12-1-1-122-12-1-1-1-2-211-2-2-2-2-2-2-1-1-1-111111111000000−i3i3−i3i3−i3i3−i3i3000000000000000022-2-2-1-1-1-10000−i3i3−i3i3−i3i3−i3i3000011000000
χ2822222-12-2-222222-1-1-12-12-1-1-122-12-1-1-1-2-211-2-2-2-2-2-2-1-1-1-111111111000000−i3i3−i3i3i3−i3i3−i30000000000000000-2-22211110000i3−i3i3−i3−i3i3−i3i30000-1-1000000
χ2922222-12-2-222222-1-1-12-12-1-1-122-12-1-1-1-2-211-2-2-2-2-2-2-1-1-1-111111111000000i3−i3i3−i3−i3i3−i3i30000000000000000-2-22211110000−i3i3−i3i3i3−i3i3−i30000-1-1000000
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χ312222-12222-1222-1222-1-1-12-1-1-1-12-122-12-122-1-12-1-1-1-1-1-1-122-1-1-1-1-1-122002222220000-1-122-1-1-1-1-1-122-1-1-1-10000000000-1-10000-1-1-1-100220000-1-100
χ322222-12222-1222-1222-1-1-12-1-1-1-12-122-12-122-1-12-1-1-1-1-1-1-122-1-1-1-1-1-12200-2-22222000011-2-2111111-2-211110000000000-1-10000-1-1-1-100-2-200001100
χ332222-12222-1222-1222-1-1-12-1-1-1-12-122-12-122-1-12-1-1-1-1-1-1-122-1-1-1-1-1-1-2-20022-2-2-2-20000-1-122-1-1-1-1-1-122-1-1-1-10000000000110000111100-2-200001100
χ342222-12222-1222-1222-1-1-12-1-1-1-12-122-12-122-1-12-1-1-1-1-1-1-122-1-1-1-1-1-1-2-200-2-2-2-2-2-2000011-2-2111111-2-211110000000000110000111100220000-1-100
χ3522-2-22222-2-2-22-222-2-2-2222-2-2-2-2-222-22-2-2-22-2-222222-2-22-22-22-2-2220000000000000000000000000000002i−2i−2i2i2i2i−2i−2i0000000000000000−2i2i000000
χ3622-2-22222-2-2-22-222-2-2-2222-2-2-2-2-222-22-2-2-22-2-222222-2-22-22-22-2-222000000000000000000000000000000−2i2i2i−2i−2i−2i2i2i00000000000000002i−2i000000
χ3722-2-222-1-22-21-1122-2-2-22-1-1-2-2111-1-112-122-2-1-11-211-111-1-112-2-1-111002i−2i2i−2i00002i2i−2i−2i2i2i−i−i−i−i−i−i−2i−2iiiiiii00000000−ii00−i−iii00002-20000-110000
χ3822-2-222-1-22-21-1122-2-2-22-1-1-2-2111-1-112-122-2-1-11-211-111-1-112-2-1-111002i−2i−2i2i00002i2i−2i−2i−2i−2iiiiiii2i2i−i−i−i−i−i−i00000000−ii00−i−iii0000-2200001-10000
χ3922-2-222-1-22-21-1122-2-2-22-1-1-2-2111-1-112-122-2-1-11-211-111-1-112-2-1-11100−2i2i2i−2i0000−2i−2i2i2i2i2i−i−i−i−i−i−i−2i−2iiiiiii00000000i−i00ii−i−i0000-2200001-10000
χ4022-2-222-1-22-21-1122-2-2-22-1-1-2-2111-1-112-122-2-1-11-211-111-1-112-2-1-11100−2i2i−2i2i0000−2i−2i2i2i−2i−2iiiiiii2i2i−i−i−i−i−i−i00000000i−i00ii−i−i00002-20000-110000
χ4122-2-22-122-2-2-22-22-111-2-12-111-2-212-11-1-2-21-1-2-22222-111-11-11-111-1-1000000−i3i3i3−i33−3−3300000000000000002i−2i−2i2i−i−iii00003−3−33−i3i3i3−i30000i−i000000
χ4222-2-22-122-2-2-22-22-111-2-12-111-2-212-11-1-2-21-1-2-22222-111-11-11-111-1-1000000−i3i3i3−i3−333−30000000000000000−2i2i2i−2iii−i−i0000−333−3−i3i3i3−i30000−ii000000
χ4322-2-22-122-2-2-22-22-111-2-12-111-2-212-11-1-2-21-1-2-22222-111-11-11-111-1-1000000i3−i3−i3i33−3−330000000000000000−2i2i2i−2iii−i−i00003−3−33i3−i3−i3i30000−ii000000
χ4422-2-22-122-2-2-22-22-111-2-12-111-2-212-11-1-2-21-1-2-22222-111-11-11-111-1-1000000i3−i3−i3i3−333−300000000000000002i−2i−2i2i−i−iii0000−333−3i3−i3−i3i30000i−i000000
χ4522-2-22-12-22-2-22-22-111-2-12-111-2-212-11-122-1122-2-2-2-2-111-1-11-11-1-1112-22i−2i00-1-111−i−iii00000000000000002i−2i2i−2i−i−iii2i−2i2-2−i−iii-1-1110000−ii000000
χ4622-2-22-12-22-2-22-22-111-2-12-111-2-212-11-122-1122-2-2-2-2-111-1-11-11-1-1112-2−2i2i00-1-111ii−i−i0000000000000000−2i2i−2i2iii−i−i−2i2i2-2ii−i−i-1-1110000i−i000000
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χ4822-2-22-12-22-2-22-22-111-2-12-111-2-212-11-122-1122-2-2-2-2-111-1-11-11-1-111-22−2i2i0011-1-1ii−i−i00000000000000002i−2i2i−2i−i−iii−2i2i-22ii−i−i11-1-10000−ii000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.