Finite Group Databasebeta

← Group #13139968

Character table — Group #13139968

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
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χ61-1-1111-1-1-1111-1-111-1-1-11-111-1-111-11-111-1-1ii−i−iiiii−i−i−i−i−ii-11−i−iii-1-1111-1-1111-1-1-1111-1-111-1-1-11-111-1-111-11-111-1-1ii−i−iiiii−i−i−i−i−ii-11−i−iii-1-111
χ71-1-1111-1-1-1111-1-111-1-1-11-111-1-111-11-111-1-1−i−iii−i−i−i−iiiiii−i-11ii−i−i-1-1111-1-1111-1-1-1111-1-111-1-1-11-111-1-111-11-111-1-1−i−iii−i−i−i−iiiiii−i-11ii−i−i-1-111
χ81-1-1111-1-1-1111-1-111-1-1-11-111-1-111-11-111-1-1−i−iii−i−i−i−iiiii−ii1-1−i−iii11-1-11-1-1111-1-1-1111-1-111-1-1-11-111-1-111-11-111-1-1−i−iii−i−i−i−iiiii−ii1-1−i−iii11-1-1
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χ10222222222222222-122-1-1-12-1-1-1-1-1-122-1-1-1-1000000000000-2-20011110000222222222222222-122-1-1-12-1-1-1-1-1-122-1-1-1-1000000000000-2-20011110000
χ1122222222222222-12-1-1222-1-1-1-1-122-1-1-1-1-1-100000000000000220000-1-1-1-122222222222222-12-1-1222-1-1-1-1-122-1-1-1-1-1-100000000000000220000-1-1-1-1
χ1222222222222222-12-1-1222-1-1-1-1-122-1-1-1-1-1-100000000000000-2-20000111122222222222222-12-1-1222-1-1-1-1-122-1-1-1-1-1-100000000000000-2-200001111
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χ252-2-2222-2-2-2222-2-2-1211-22-2-1-111-12-2-11-1-11100000000000000-22000011-1-12-2-2222-2-2-2222-2-2-1211-22-2-1-111-12-2-11-1-11100000000000000-22000011-1-1
χ262-2-222-22-2-22-2-22222-2-2-22-222-2-22-22-22-2-2220000000000000000000000002-2-222-22-2-22-2-22222-2-2-22-222-2-22-22-22-2-222000000000000000000000000
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χ282-2-222-22-2-22-2-2222-1-2-21-112-111-11-1-2211-1-10000000000000000−333−300002-2-222-22-2-22-2-2222-1-2-21-112-111-11-1-2211-1-10000000000000000−333−30000
χ292-2-222-22-2-22-2-222-1211-22-2-1-111-1-221-111-1-100000000000000000000−i3i3i3−i32-2-222-22-2-22-2-222-1211-22-2-1-111-1-221-111-1-100000000000000000000−i3i3i3−i3
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χ424-4-444-44-4-44-4-444-2-2222-22-21-1-112-22-2-1-1110000000000000000000000004-4-444-44-4-44-4-444-2-2222-22-21-1-112-22-2-1-111000000000000000000000000
χ436666-366-3-3-3-3-3-3-3000000000000000000002222-1-1-1-1-1-1-1-10000000000006666-366-3-3-3-3-3-3-3000000000000000000002222-1-1-1-1-1-1-1-1000000000000
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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
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χ4766-6-6-300-33333−3333−33000000000000000000002−22−2ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ2300000000000066-6-6-300-33333−3333−33000000000000000000002−22−2ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000000000
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χ4966-6-6-300-333−3333−3333000000000000000000002−22−2ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ700000000000066-6-6-300-333−3333−3333000000000000000000002−22−2ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000000000
χ5066-6-6-300-333−3333−333300000000000000000000−22−22−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ700000000000066-6-6-300-333−3333−333300000000000000000000−22−22−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7000000000000
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χ536-66-6-3003-33−333333−3300000000000000000000−i2i2i2−i2ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ230000000000006-66-6-3003-33−333333−3300000000000000000000−i2i2i2−i2ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000000000
χ546-66-6-3003-33−333333−3300000000000000000000i2−i2−i2i2−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ230000000000006-66-6-3003-33−333333−3300000000000000000000i2−i2−i2i2−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000000000
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χ591111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
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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χ802-2-2222-2-2-2222-2-22-1-2-21-112-111-1-112-2-1-1110000000000002i−2i00−i−iii0000-222-2-2-2222-2-2-222-2122-11-1-21-1-111-1-2211-1-1000000000000−2i2i00ii−i−i0000
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χ822-2-2222-2-2-2222-2-2-1211-22-2-1-111-12-2-11-1-111000000000000002-20000-1-111-222-2-2-2222-2-2-2221-2-1-12-2211-1-11-221-111-1-100000000000000-22000011-1-1
χ832-2-2222-2-2-2222-2-2-1211-22-2-1-111-12-2-11-1-11100000000000000-22000011-1-1-222-2-2-2222-2-2-2221-2-1-12-2211-1-11-221-111-1-1000000000000002-20000-1-111
χ842-2-222-22-2-22-2-22222-2-2-22-222-2-22-22-22-2-222000000000000000000000000-222-2-22-222-222-2-2-2-2222-22-2-222-22-22-222-2-2000000000000000000000000
χ852-2-222-22-2-22-2-2222-1-2-21-112-111-11-1-2211-1-100000000000000003−3−330000-222-2-22-222-222-2-2-2122-11-1-21-1-11-112-2-1-1110000000000000000−333−30000
χ862-2-222-22-2-22-2-2222-1-2-21-112-111-11-1-2211-1-10000000000000000−333−30000-222-2-22-222-222-2-2-2122-11-1-21-1-11-112-2-1-11100000000000000003−3−330000
χ872-2-222-22-2-22-2-222-1211-22-2-1-111-1-221-111-1-100000000000000000000−i3i3i3−i3-222-2-22-222-222-2-21-2-1-12-2211-1-112-2-11-1-11100000000000000000000i3−i3−i3i3
χ882-2-222-22-2-22-2-222-1211-22-2-1-111-1-221-111-1-100000000000000000000i3−i3−i3i3-222-2-22-222-222-2-21-2-1-12-2211-1-112-2-11-1-11100000000000000000000−i3i3i3−i3
χ8944444444444444-2-2-2-2-2-2-2-21111-2-2-2-21111000000000000000000000000-4-4-4-4-4-4-4-4-4-4-4-4-4-422222222-1-1-1-12222-1-1-1-1000000000000000000000000
χ9044444-4-4444-4-4-4-4-2-2-2-2-2-2-2-211112222-1-1-1-1000000000000000000000000-4-4-4-4-444-4-4-4444422222222-1-1-1-1-2-2-2-21111000000000000000000000000
χ9144-4-44004-4-400004-24-4-222-4-2-22200000000000000000000000000000000-4-444-400-4440000-42-442-2-2422-2-200000000000000000000000000000000
χ9244-4-44004-4-40000-24-224-4-42-2-22200000000000000000000000000000000-4-444-400-44400002-42-2-444-222-2-200000000000000000000000000000000
χ9344-4-44004-4-40000-2-2-22-222211-1-100003i−3i3i−3i000000000000000000000000-4-444-400-4440000222-22-2-2-2-1-1110000−3i3i−3i3i000000000000000000000000
χ9444-4-44004-4-40000-2-2-22-222211-1-10000−3i3i−3i3i000000000000000000000000-4-444-400-4440000222-22-2-2-2-1-11100003i−3i3i−3i000000000000000000000000
χ954-44-4400-44-400004-2-4422-2-4-22-2200000000000000000000000000000000-44-44-4004-440000-424-4-2-2242-22-200000000000000000000000000000000
χ964-44-4400-44-40000-242-2-4-442-22-2200000000000000000000000000000000-44-44-4004-4400002-4-2244-4-22-22-200000000000000000000000000000000
χ974-44-4400-44-40000-2-22-222-221-11-100003i−3i−3i3i000000000000000000000000-44-44-4004-44000022-22-2-22-2-11-110000−3i3i3i−3i000000000000000000000000
χ984-44-4400-44-40000-2-22-222-221-11-10000−3i3i3i−3i000000000000000000000000-44-44-4004-44000022-22-2-22-2-11-1100003i−3i−3i3i000000000000000000000000
χ994-4-4444-4-4-4444-4-4-2-2222-22-21-1-11-22-2211-1-1000000000000000000000000-444-4-4-4444-4-4-44422-2-2-22-22-111-12-22-2-1-111000000000000000000000000
χ1004-4-444-44-4-44-4-444-2-2222-22-21-1-112-22-2-1-111000000000000000000000000-444-4-44-444-444-4-422-2-2-22-22-111-1-22-2211-1-1000000000000000000000000
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
χ1026666-366-3-3-3-3-3-3-300000000000000000000-2-2-2-211111111000000000000-6-6-6-63-6-63333333000000000000000000002222-1-1-1-1-1-1-1-1000000000000
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
χ10566-6-6-300-33333−3333−33000000000000000000002−22−2ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000000000-6-6663003-3-3−3333−333300000000000000000000−22−22−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23000000000000
χ10666-6-6-300-33333−3333−3300000000000000000000−22−22−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23000000000000-6-6663003-3-3−3333−3333000000000000000000002−22−2ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000000000
χ10766-6-6-300-333−3333−3333000000000000000000002−22−2ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000000000-6-6663003-3-333−3333−3300000000000000000000−22−22−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7000000000000
χ10866-6-6-300-333−3333−333300000000000000000000−22−22−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7000000000000-6-6663003-3-333−3333−33000000000000000000002−22−2ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000000000
χ1096-66-6-3003-3333−33−333300000000000000000000−i2i2i2−i2ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000000000-66-66300-33-3−333333−3300000000000000000000i2−i2−i2i2−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000000000
χ1106-66-6-3003-3333−33−333300000000000000000000i2−i2−i2i2−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000000000-66-66300-33-3−333333−3300000000000000000000−i2i2i2−i2ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000000000
χ1116-66-6-3003-33−333333−3300000000000000000000−i2i2i2−i2ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000000000-66-66300-33-333−33−333300000000000000000000i2−i2−i2i2−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000000000
χ1126-66-6-3003-33−333333−3300000000000000000000i2−i2−i2i2−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000000000-66-66300-33-333−33−333300000000000000000000−i2i2i2−i2ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000000000
χ1136-6-66-36-633-3-3-333000000000000000000002i2i−2i−2i−i−i−i−iiiii000000000000-666-63-66-3-3333-3-300000000000000000000−2i−2i2i2iiiii−i−i−i−i000000000000
χ1146-6-66-36-633-3-3-33300000000000000000000−2i−2i2i2iiiii−i−i−i−i000000000000-666-63-66-3-3333-3-3000000000000000000002i2i−2i−2i−i−i−i−iiiii000000000000
χ1156-6-66-3-6633-333-3-3000000000000000000000000−i3i3−i3i3i3−i3i3−i3000000000000-666-636-6-3-33-3-333000000000000000000000000i3−i3i3−i3−i3i3−i3i3000000000000
χ1166-6-66-3-6633-333-3-3000000000000000000000000i3−i3i3−i3−i3i3−i3i3000000000000-666-636-6-3-33-3-333000000000000000000000000−i3i3−i3i3i3−i3i3−i3000000000000

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