Finite Group Databasebeta

← Group #13155397

Character table — Group #13155397

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222222244444444444444444444448888888888881212121212121212121212121212121212121212121224242424242424242424242424242424363636363636363636365454545472727272
order12223334466666666633366666666612121212121212121212366612121212121212122244882424242424242424242424242424242466666666121212121212121244448824242424224412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111111111111111111111111111-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111
χ61111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ81111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111
χ91-1-111111-1-1-1-111-1-1-11111-1-1-1-1-1111-111111-1-1-1-1-11-1-1111-1-111-1-11-1i−ii−iiiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1ii−i−iii−i−ii−i1-1i−iii−i−i1-11-1i−i1-1
χ101-1-111111-1-1-1-111-1-1-11111-1-1-1-1-1111-111111-1-1-1-1-11-1-1111-1-111-1-11-1i−i−ii−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1ii−i−iii−i−i−ii-11i−iii−i−i-11-11−ii-11
χ111-1-111111-1-1-1-111-1-1-11111-1-1-1-1-1111-111111-1-1-1-1-11-1-1111-1-111-1-11-1−iii−iiiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1−i−iii−i−iiii−i-11−ii−i−iii-11-11i−i-11
χ121-1-111111-1-1-1-111-1-1-11111-1-1-1-1-1111-111111-1-1-1-1-11-1-1111-1-111-1-11-1−ii−ii−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−iii−i−iii−ii1-1−ii−i−iii1-11-1−ii1-1
χ131-1-111111-1-1-1-111-1-1-11111-1-1-1-1-1111-111111-1-1-1-1-11-1-1111-1-111-1-1-11i−ii−iiiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111ii−i−iii−i−i−ii1-1−ii−i−iii-11-11−ii1-1
χ141-1-111111-1-1-1-111-1-1-11111-1-1-1-1-1111-111111-1-1-1-1-11-1-1111-1-111-1-1-11i−i−ii−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111ii−i−iii−i−ii−i-11−ii−i−iii1-11-1i−i-11
χ151-1-111111-1-1-1-111-1-1-11111-1-1-1-1-1111-111111-1-1-1-1-11-1-1111-1-111-1-1-11−iii−iiiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111−i−iii−i−iii−ii-11i−iii−i−i1-11-1−ii-11
χ161-1-111111-1-1-1-111-1-1-11111-1-1-1-1-1111-111111-1-1-1-1-11-1-1111-1-111-1-1-11−ii−ii−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111−i−iii−i−iiii−i1-1i−iii−i−i-11-11i−i1-1
χ172222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000000022-2-20000
χ182222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000-2-2220000
χ19222222-12222-12-122-122-1-12-1-1-1-12-1-122-12-1-1-12-1-12-1-1-1-12-12-1-1-1-1-122002222-1-1-1-1-1-122-1-1-1-1-1-12-12-1-1-1-1-10000000022000000000000-1-100
χ20222222-12222-12-122-122-1-12-1-1-1-12-1-122-12-1-1-12-1-12-1-1-1-12-12-1-1-1-1-12200-2-2-2-2111111-2-21111112-12-1-1-1-1-100000000-2-20000000000001100
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χ22222222-12222-12-122-122-1-12-1-1-1-12-1-122-12-1-1-12-1-12-1-1-1-12-12-1-1-1-1-1-2-200-2-2-2-2111111-2-2111111-21-2111110000000022000000000000-1-100
χ2322222-12222-12-122-122-12-1-122-1-1-12-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-12222000000000000000000-12-12-1-1-1-12-12-1-1-1-1-1000022-1-1-1-100000000
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χ2622222-12222-12-122-122-12-1-122-1-1-12-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000000000000000001-21-21111-21-211111000022-1-1-1-100000000
χ272222-12222-12222-122-1-1-12-1-1-122-1-12-122-1-1-12-1-1-12-1-1-1-1-12-12-1-1-1-1002222-1-122-1-1-1-1-1-122-1-1-1-100000000-12-12-1-1-1-10022000000000000-1-1
χ282222-12222-12222-122-1-1-12-1-1-122-1-12-122-1-1-12-1-1-12-1-1-1-1-12-12-1-1-1-10022-2-211-2-2111111-2-2111100000000-12-12-1-1-1-100-2-200000000000011
χ292222-12222-12222-122-1-1-12-1-1-122-1-12-122-1-1-12-1-1-12-1-1-1-1-12-12-1-1-1-100-2-222-1-122-1-1-1-1-1-122-1-1-1-1000000001-21-2111100-2-200000000000011
χ302222-12222-12222-122-1-1-12-1-1-122-1-12-122-1-1-12-1-1-12-1-1-1-1-12-12-1-1-1-100-2-2-2-211-2-2111111-2-21111000000001-21-211110022000000000000-1-1
χ312-2-22222-22-2-2-222-2-2-22222-2-2-2-2-2222-2-2-2-2-2-2222222-2-22-2-222-2-2220000000000000000000000000000000000000000000000002-2-220000
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χ342-2-2222-12-2-2-212-1-2-2122-1-1-211112-1-1-22-12-1-11-211-2-111-12-1-21-1-1112-200−2i2i−2i−2iiiiiii2i2i−i−i−i−i−i−i2-1-21-1-11100000000−2i2i000000000000i−i00
χ352-2-2222-12-2-2-212-1-2-2122-1-1-211112-1-1-22-12-1-11-211-2-111-12-1-21-1-111-22002i−2i2i2i−i−i−i−i−i−i−2i−2iiiiiii-212-111-1-100000000−2i2i000000000000i−i00
χ362-2-2222-12-2-2-212-1-2-2122-1-1-211112-1-1-22-12-1-11-211-2-111-12-1-21-1-111-2200−2i2i−2i−2iiiiiii2i2i−i−i−i−i−i−i-212-111-1-1000000002i−2i000000000000−ii00
χ372-2-222-122-2-21-2-12-21-22-12-11-2-211-12-11-12222-2-2-2-21-111-1-1-111-1-1112-22i−2i000000000000000000-121-2-1-1112i−i−2ii−i−iii00002i−2i−i−iii00000000
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χ392-2-222-122-2-21-2-12-21-22-12-11-2-211-12-11-12222-2-2-2-21-111-1-1-111-1-111-222i−2i0000000000000000001-2-1211-1-12i−i−2ii−i−iii0000−2i2iii−i−i00000000
χ402-2-222-122-2-21-2-12-21-22-12-11-2-211-12-11-12222-2-2-2-21-111-1-1-111-1-111-22−2i2i0000000000000000001-2-1211-1-1−2ii2i−iii−i−i00002i−2i−i−iii00000000
χ412-2-22-1222-21-2-2221-2-2-1-1-12111-2-2-1-12122-1-1-1-2111-2-111-1-121-2-1-111002i−2i2i−2i−i−i2i2i−i−i−i−iii−2i−2iiiii00000000−i2ii−2i−i−iii002-2000000000000-11
χ422-2-22-1222-21-2-2221-2-2-1-1-12111-2-2-1-12122-1-1-1-2111-2-111-1-121-2-1-111002i−2i−2i2iii−2i−2iiiii−i−i2i2i−i−i−i−i00000000−i2ii−2i−i−iii00-220000000000001-1
χ432-2-22-1222-21-2-2221-2-2-1-1-12111-2-2-1-12122-1-1-1-2111-2-111-1-121-2-1-11100−2i2i2i−2i−i−i2i2i−i−i−i−iii−2i−2iiiii00000000i−2i−i2iii−i−i00-220000000000001-1
χ442-2-22-1222-21-2-2221-2-2-1-1-12111-2-2-1-12122-1-1-1-2111-2-111-1-121-2-1-11100−2i2i−2i2iii−2i−2iiiii−i−i2i2i−i−i−i−i00000000i−2i−i2iii−i−i002-2000000000000-11
χ45444444-2-4-444-24-244-244-2-24-2-2-2-24-2-24-42-4222-422-4-2-2-2-2-42-42222200000000000000000000000000000000000000000000000000000000
χ4644444-24-4-44-24-244-244-24-2-244-2-2-24-2-22-4-4-4-4-4-4-4-42-2-2-2-22222222200000000000000000000000000000000000000000000000000000000
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χ544444-24-2-4-4-24-24-2-24-2-2-21-2-211-2-2-21-2-2-422-1-122-1-1-411112222-1-1-1-100000000003i3i−3i−3i00003i3i−3i−3i0000000000000000000000000000000000
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χ564444-2-2444-2-24-24-2-24-21-2-21-2-2-2-21-2-21-24-2-2-24-2-2-2-211111-21-21111004400000000000000000000000000-2-2-2-21111000000000000000000
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χ884-4-44-244-442-4-4442-4-4-2-2-24222-4-4-2-242-4-42224-2-2-24-222-22-4-2422-2-200000000000000000000000000000000000000000000000000000000
χ894-4-44-24-24-42-424-22-42-2-21-22-1-122-21-224-2-21122-1-1-41-1-11-2-22211-1-100004i−4i−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i0000000000000000000000000000000000
χ904-4-44-24-24-42-424-22-42-2-21-22-1-122-21-224-2-21122-1-1-41-1-11-2-22211-1-10000−4i4i2i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii0000000000000000000000000000000000
χ914-4-44-24-2-442-424-22-42-2-21-22-1-122-21-22-422-1-1-2-21141-1-1122-2-2-1-111000000000033-3-30000-3-3330000000000000000000000000000000000
χ924-4-44-24-2-442-424-22-42-2-21-22-1-122-21-22-422-1-1-2-21141-1-1122-2-2-1-1110000000000-3-333000033-3-30000000000000000000000000000000000
χ934-4-44-2-244-422-4-2422-4-21-2-2-122221-2-2-1-24-2-2-2-422221-1-111-2-1211-1-1004i−4i00000000000000000000000000−2i−2i2i2iii−i−i000000000000000000
χ944-4-44-2-244-422-4-2422-4-21-2-2-122221-2-2-1-24-2-2-2-422221-1-111-2-1211-1-100−4i4i000000000000000000000000002i2i−2i−2i−i−iii000000000000000000
χ954-4-44-2-24-4422-4-2422-4-21-2-2-122221-2-2-12-42224-2-2-2-21-1-11-121-2-1-11100000000000000000000000000000000003i−3i−3i3i000000000000000000
χ964-4-44-2-24-4422-4-2422-4-21-2-2-122221-2-2-12-42224-2-2-2-21-1-11-121-2-1-1110000000000000000000000000000000000−3i3i3i−3i000000000000000000
χ978888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-422-4-422-4-1-1-1-12222-1-1-1-100000000000000000000000000000000000000000000000000000000
χ988888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444-2-244-2-24-1-1-1-1-2-2-2-2111100000000000000000000000000000000000000000000000000000000
χ9988-8-88-4-4008-4-444-844-8-4-42-4-442-244-24000000000022-2-20000000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4800-4-484-844-842-4-42-44-44-244-2000000000022-2-20000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-400-4-4-444444422222-22-2-2-2-2-20006i−6i006i−6i0-1-1110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-400-4-4-444444422222-22-2-2-2-2-2000−6i6i00−6i6i0-1-11100003i−3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1038-88-88-4-400-844448-4-4-8-4-4244-4-2244-2-400000000002-22-20000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-480044-84-8-4-4842-4-4-24-44-4-244200000000002-22-20000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-40044444-4-4-44222-2-22-22-2-2-220006i−6i00−6i6i0-11-110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-40044444-4-4-44222-2-22-22-2-2-22000−6i6i006i−6i0-11-1100003i−3i−3i3i00000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-48-8444-4-4444-4222-2-2-2-2-2222-2-4-4-42244-2-24-111-122-2-2-1-11100000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4-88444-4-4444-4222-2-2-2-2-2222-2444-2-2-4-422-4-111-1-2-22211-1-100000000000000000000000000000000000000000000000000000000

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