Finite Group Databasebeta

← Group #13139973

Character table — Group #13139973

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size11112222222222666666661212121212121212121212121818181818181818181818183636363636363636363636361111222222222266666666121212121212121212121212181818181818181818181818363636363636363636363636
order1222344666121212123366666636661212121212121212888824242424242424244444121212121212121222226446661212121266666666666612121212121212128888242424242424242444441212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ511-1-11-11-1-11-1-11111-1-111-1-11-1-1111-1-111-1-111-1-11111-1-1-1-1i−ii−iii−i−iii−i−i11-1-11-11-1-11-1-11111-1-111-1-11-1-1111-1-111-1-111-1-11111-1-1-1-1i−ii−iii−i−iii−i−i
χ611-1-11-11-1-11-1-11111-1-111-1-11-1-1111-1-111-1-111-1-11111-1-1-1-1−ii−ii−i−iii−i−iii11-1-11-11-1-11-1-11111-1-111-1-11-1-1111-1-111-1-111-1-11111-1-1-1-1−ii−ii−i−iii−i−iii
χ711-1-11-11-1-11-1-11111-1-111-1-11-1-1111-1-111-1-1-1-111-1-1-1-11111i−i−iiii−i−i−i−iii11-1-11-11-1-11-1-11111-1-111-1-11-1-1111-1-111-1-1-1-111-1-1-1-11111i−i−iiii−i−i−i−iii
χ811-1-11-11-1-11-1-11111-1-111-1-11-1-1111-1-111-1-1-1-111-1-1-1-11111−iii−i−i−iiiii−i−i11-1-11-11-1-11-1-11111-1-111-1-11-1-1111-1-111-1-1-1-111-1-1-1-11111−iii−i−i−iiiii−i−i
χ9222222222222222-12-12-12-1-1-1-1-12-12-1-1-1-1-100000000000000220000-1-1-1-1222222222222222-12-12-12-1-1-1-1-12-12-1-1-1-1-100000000000000220000-1-1-1-1
χ10222222222222222-12-12-12-1-1-1-1-12-12-1-1-1-1-100000000000000-2-200001111222222222222222-12-12-12-1-1-1-1-12-12-1-1-1-1-100000000000000-2-200001111
χ1122222222222222-12-12-12-12-1-1-1-1-12-12-1-1-1-10000000000002200-1-1-1-1000022222222222222-12-12-12-12-1-1-1-1-12-12-1-1-1-10000000000002200-1-1-1-10000
χ1222222222222222-12-12-12-12-1-1-1-1-12-12-1-1-1-1000000000000-2-2001111000022222222222222-12-12-12-12-1-1-1-1-12-12-1-1-1-1000000000000-2-20011110000
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χ1522222-2-2222-2-2-2-22-12-12-12-1-1-1-1-1-21-21111100000000000000000000i3−i3i3−i322222-2-2222-2-2-2-22-12-12-12-1-1-1-1-1-21-21111100000000000000000000i3−i3i3−i3
χ1622222-2-2222-2-2-2-2-12-12-12-12-1-1-1-11-21-211110000000000000000−i3i3−i3i3000022222-2-2222-2-2-2-2-12-12-12-12-1-1-1-11-21-211110000000000000000−i3i3−i3i30000
χ1722222-2-2222-2-2-2-2-12-12-12-12-1-1-1-11-21-211110000000000000000i3−i3i3−i3000022222-2-2222-2-2-2-2-12-12-12-12-1-1-1-11-21-211110000000000000000i3−i3i3−i30000
χ1822-2-222-2-2-2222-2-222-2-222-2-22-2-22-2-222-2-22200000000000000000000000022-2-222-2-2-2222-2-222-2-222-2-22-2-22-2-222-2-222000000000000000000000000
χ1922-2-222-2-2-2222-2-22-1-212-1-21-111-1-212-111-1-1000000000000000000003−3−3322-2-222-2-2-2222-2-22-1-212-1-21-111-1-212-111-1-1000000000000000000003−3−33
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χ282-22-22002-2-20000222-2-2-2-2222-2-200000000i2−i2i2−i2i2i2−i2−i2i2i2−i2−i20000000000002-22-22002-2-20000222-2-2-2-2222-2-200000000i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2000000000000
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χ3144444444444444-2-2-2-2-2-2-2-21111-2-2-2-2111100000000000000000000000044444444444444-2-2-2-2-2-2-2-21111-2-2-2-21111000000000000000000000000
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χ354-44-44004-4-400004-242-42-4-2-2-222000000000000000000000000000000004-44-44004-4-400004-242-42-4-2-2-22200000000000000000000000000000000
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χ456666-3-6-6-3-3-333330000000000000000000000003−33−33−33−30000000000006666-3-6-6-3-3-333330000000000000000000000003−33−33−33−3000000000000
χ466666-3-6-6-3-3-33333000000000000000000000000−33−33−33−330000000000006666-3-6-6-3-3-33333000000000000000000000000−33−33−33−33000000000000
χ4766-6-6-36-633-3-3-3330000000000000000000000003−33−3−33−3300000000000066-6-6-36-633-3-3-3330000000000000000000000003−33−3−33−33000000000000
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χ4966-6-6-3-6633-333-3-30000000000000000000022-2-2-1-1-1-1111100000000000066-6-6-3-6633-333-3-30000000000000000000022-2-2-1-1-1-11111000000000000
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χ516-66-6-300-33333−3333−3300000000000000000000−i2i2−i2i2ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ230000000000006-66-6-300-33333−3333−3300000000000000000000−i2i2−i2i2ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000000000
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χ536-66-6-300-333−3333−333300000000000000000000−i2i2−i2i2ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ70000000000006-66-6-300-333−3333−333300000000000000000000−i2i2−i2i2ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000000000
χ546-66-6-300-333−3333−333300000000000000000000i2−i2i2−i2−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ70000000000006-66-6-300-333−3333−333300000000000000000000i2−i2i2−i2−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000000000
χ556-6-66-3003-3333−33−333300000000000000000000−i2i2i2−i2ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ70000000000006-6-66-3003-3333−33−333300000000000000000000−i2i2i2−i2ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000000000
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χ601111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ611111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-11111
χ621111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11111-1-1-1-1
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χ7522222-2-2222-2-2-2-2-12-12-12-12-1-1-1-11-21-211110000000000000000i3−i3i3−i30000-2-2-2-2-222-2-2-222221-21-21-21-21111-12-12-1-1-1-10000000000000000−i3i3−i3i30000
χ7622-2-222-2-2-2222-2-222-2-222-2-22-2-22-2-222-2-222000000000000000000000000-2-222-2-2222-2-2-222-2-222-2-222-222-222-2-222-2-2000000000000000000000000
χ7722-2-222-2-2-2222-2-22-1-212-1-21-111-1-212-111-1-1000000000000000000003−3−33-2-222-2-2222-2-2-222-212-1-212-11-1-112-1-21-1-11100000000000000000000−333−3
χ7822-2-222-2-2-2222-2-22-1-212-1-21-111-1-212-111-1-100000000000000000000−333−3-2-222-2-2222-2-2-222-212-1-212-11-1-112-1-21-1-111000000000000000000003−3−33
χ7922-2-222-2-2-2222-2-2-121-2-121-2-111-11-2-1211-1-100000000000000003−3−330000-2-222-2-2222-2-2-2221-2-121-2-121-1-11-121-2-1-1110000000000000000−333−30000
χ8022-2-222-2-2-2222-2-2-121-2-121-2-111-11-2-1211-1-10000000000000000−333−30000-2-222-2-2222-2-2-2221-2-121-2-121-1-11-121-2-1-11100000000000000003−3−330000
χ8122-2-22-22-2-22-2-2222-1-212-1-21-111-12-1-21-1-111000000000000002i−2i0000−i−iii-2-222-22-222-222-2-2-212-1-212-11-1-11-212-111-1-100000000000000−2i2i0000ii−i−i
χ8222-2-22-22-2-22-2-2222-1-212-1-21-111-12-1-21-1-11100000000000000−2i2i0000ii−i−i-2-222-22-222-222-2-2-212-1-212-11-1-11-212-111-1-1000000000000002i−2i0000−i−iii
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χ934-44-44004-4-400004-242-42-4-2-2-22200000000000000000000000000000000-44-44-400-4440000-42-4-24-24222-2-200000000000000000000000000000000
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χ954-44-44004-4-40000-2-2-22222-211-1-100003i−3i3i−3i000000000000000000000000-44-44-400-4440000222-2-2-2-22-1-1110000−3i3i−3i3i000000000000000000000000
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χ994-4-44400-44-40000-2-22-222-221-11-100003i−3i−3i3i000000000000000000000000-444-4-4004-44000022-22-2-22-2-11-110000−3i3i3i−3i000000000000000000000000
χ1004-4-44400-44-40000-2-22-222-221-11-10000−3i3i3i−3i000000000000000000000000-444-4-4004-44000022-22-2-22-2-11-1100003i−3i−3i3i000000000000000000000000
χ1016666-366-3-3-3-3-3-3-3000000000000000000002222-1-1-1-1-1-1-1-1000000000000-6-6-6-63-6-6333333300000000000000000000-2-2-2-211111111000000000000
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χ1036666-3-6-6-3-3-333330000000000000000000000003−33−33−33−3000000000000-6-6-6-6366333-3-3-3-3000000000000000000000000−33−33−33−33000000000000
χ1046666-3-6-6-3-3-33333000000000000000000000000−33−33−33−33000000000000-6-6-6-6366333-3-3-3-30000000000000000000000003−33−33−33−3000000000000
χ10566-6-6-36-633-3-3-3330000000000000000000000003−33−3−33−33000000000000-6-6663-66-3-3333-3-3000000000000000000000000−33−333−33−3000000000000
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χ10766-6-6-3-6633-333-3-30000000000000000000022-2-2-1-1-1-11111000000000000-6-66636-6-3-33-3-33300000000000000000000-2-2221111-1-1-1-1000000000000
χ10866-6-6-3-6633-333-3-300000000000000000000-2-2221111-1-1-1-1000000000000-6-66636-6-3-33-3-3330000000000000000000022-2-2-1-1-1-11111000000000000
χ1096-66-6-300-33333−3333−3300000000000000000000−i2i2−i2i2ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000000000-66-663003-3-3−3333−333300000000000000000000i2−i2i2−i2−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000000000
χ1106-66-6-300-33333−3333−3300000000000000000000i2−i2i2−i2−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000000000-66-663003-3-3−3333−333300000000000000000000−i2i2−i2i2ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000000000
χ1116-66-6-300-333−3333−333300000000000000000000−i2i2−i2i2ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000000000-66-663003-3-333−3333−3300000000000000000000i2−i2i2−i2−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000000000
χ1126-66-6-300-333−3333−333300000000000000000000i2−i2i2−i2−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000000000-66-663003-3-333−3333−3300000000000000000000−i2i2−i2i2ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000000000
χ1136-6-66-3003-3333−33−333300000000000000000000−i2i2i2−i2ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000000000-666-6300-33-3−333333−3300000000000000000000i2−i2−i2i2−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000000000
χ1146-6-66-3003-3333−33−333300000000000000000000i2−i2−i2i2−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000000000-666-6300-33-3−333333−3300000000000000000000−i2i2i2−i2ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000000000
χ1156-6-66-3003-33−333333−3300000000000000000000−i2i2i2−i2ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000000000-666-6300-33-333−33−333300000000000000000000i2−i2−i2i2−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000000000
χ1166-6-66-3003-33−333333−3300000000000000000000i2−i2−i2i2−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000000000-666-6300-33-333−33−333300000000000000000000−i2i2i2−i2ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.