Finite Group Databasebeta

← Group #13139974

Character table — Group #13139974

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
χ51-11-11-11-1-11-1-11111-1-111-1-11-1-1111-1-111-1-111-1-11111-1-1-1-1i−ii−iii−i−iii−i−i1-11-11-11-1-11-1-11111-1-111-1-11-1-1111-1-111-1-111-1-11111-1-1-1-1i−ii−iii−i−iii−i−i
χ61-11-11-11-1-11-1-11111-1-111-1-11-1-1111-1-111-1-111-1-11111-1-1-1-1−ii−ii−i−iii−i−iii1-11-11-11-1-11-1-11111-1-111-1-11-1-1111-1-111-1-111-1-11111-1-1-1-1−ii−ii−i−iii−i−iii
χ71-11-11-11-1-11-1-11111-1-111-1-11-1-1111-1-111-1-1-1-111-1-1-1-11111i−i−iiii−i−i−i−iii1-11-11-11-1-11-1-11111-1-111-1-11-1-1111-1-111-1-1-1-111-1-1-1-11111i−i−iiii−i−i−i−iii
χ81-11-11-11-1-11-1-11111-1-111-1-11-1-1111-1-111-1-1-1-111-1-1-1-11111−iii−i−i−iiiii−i−i1-11-11-11-1-11-1-11111-1-111-1-11-1-1111-1-111-1-1-1-111-1-1-1-11111−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
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χ282-22-22-22-2-22-2-222-121-2-121-2-111-1-121-2-1-111000000000000−2i2i00ii−i−i00002-22-22-22-2-22-2-222-121-2-121-2-111-1-121-2-1-111000000000000−2i2i00ii−i−i0000
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χ792-22-222-2-2-2222-2-22-1-212-1-21-111-1-212-111-1-1000000000000000000003−3−33-22-22-2-2222-2-2-222-212-1-212-11-1-112-1-21-1-11100000000000000000000−333−3
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χ832-22-22-22-2-22-2-2222-1-212-1-21-111-12-1-21-1-111000000000000002i−2i0000−i−iii-22-22-22-222-222-2-2-212-1-212-11-1-11-212-111-1-100000000000000−2i2i0000ii−i−i
χ842-22-22-22-2-22-2-2222-1-212-1-21-111-12-1-21-1-11100000000000000−2i2i0000ii−i−i-22-22-22-222-222-2-2-212-1-212-11-1-11-212-111-1-1000000000000002i−2i0000−i−iii
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χ882-2-22200-22-2000022-2-2-2-2222-22-200000000−222−2−2−22222−2−2000000000000-222-2-2002-220000-2-22222-2-2-22-22000000002−2−2222−2−2−2−222000000000000
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
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χ9144-4-44004-4-400004-24-2-42-42-2-22200000000000000000000000000000000-4-444-400-4440000-42-424-24-222-2-200000000000000000000000000000000
χ9244-4-44004-4-40000-24-242-42-4-2-22200000000000000000000000000000000-4-444-400-44400002-42-4-24-2422-2-200000000000000000000000000000000
χ9344-4-44004-4-40000-2-2-2-2222211-1-100003i−3i3i−3i000000000000000000000000-4-444-400-44400002222-2-2-2-2-1-1110000−3i3i−3i3i000000000000000000000000
χ9444-4-44004-4-40000-2-2-2-2222211-1-10000−3i3i−3i3i000000000000000000000000-4-444-400-44400002222-2-2-2-2-1-11100003i−3i3i−3i000000000000000000000000
χ954-44-444-4-4-4444-4-4-2-222-2-2221-1-1122-2-2-1-111000000000000000000000000-44-44-4-4444-4-4-44422-2-222-2-2-111-1-2-22211-1-1000000000000000000000000
χ964-44-44-44-4-44-4-444-2-222-2-2221-1-11-2-22211-1-1000000000000000000000000-44-44-44-444-444-4-422-2-222-2-2-111-122-2-2-1-111000000000000000000000000
χ974-4-44400-44-400004-2-42-424-2-22-2200000000000000000000000000000000-444-4-4004-440000-424-24-2-422-22-200000000000000000000000000000000
χ984-4-44400-44-40000-242-42-4-24-22-2200000000000000000000000000000000-444-4-4004-4400002-4-24-242-42-22-200000000000000000000000000000000
χ994-4-44400-44-40000-2-22222-2-21-11-100003i−3i−3i3i000000000000000000000000-444-4-4004-44000022-2-2-2-222-11-110000−3i3i3i−3i000000000000000000000000
χ1004-4-44400-44-40000-2-22222-2-21-11-10000−3i3i3i−3i000000000000000000000000-444-4-4004-44000022-2-2-2-222-11-1100003i−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
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
χ1096-66-6-36-633-3-3-3330000000000000000000000003−33−3−33−33000000000000-66-663-66-3-3333-3-3000000000000000000000000−33−333−33−3000000000000
χ1106-66-6-36-633-3-3-333000000000000000000000000−33−333−33−3000000000000-66-663-66-3-3333-3-30000000000000000000000003−33−3−33−33000000000000
χ1116-66-6-3-6633-333-3-30000000000000000000022-2-2-1-1-1-11111000000000000-66-6636-6-3-33-3-33300000000000000000000-2-2221111-1-1-1-1000000000000
χ1126-66-6-3-6633-333-3-300000000000000000000-2-2221111-1-1-1-1000000000000-66-6636-6-3-33-3-3330000000000000000000022-2-2-1-1-1-11111000000000000
χ1136-6-66-3003-3333−33−3333000000000000000000002−2−22ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7000000000000-666-6300-33-3−333333−3300000000000000000000−222−2−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000000000
χ1146-6-66-3003-3333−33−333300000000000000000000−222−2−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000000000-666-6300-33-3−333333−33000000000000000000002−2−22ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7000000000000
χ1156-6-66-3003-33−333333−33000000000000000000002−2−22ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23000000000000-666-6300-33-333−33−333300000000000000000000−222−2−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000000000
χ1166-6-66-3003-33−333333−3300000000000000000000−222−2−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000000000-666-6300-33-333−33−3333000000000000000000002−2−22ζ5−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.