Finite Group Databasebeta

← Group #13155699

Character table — Group #13155699

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222224444444444444444444444888888888888121212121212121212121212121212121212121212121212121212121212181818181818181824242424242424242424242436363636363672727272108108
order1222333446666666663336666666661212121212121212121236661212121212121212444488121212121212121224242424242424242424242424242424444412121212121212121212121212121212444412121212121288
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
χ3111111111111111111111111111111111111111111111111111111-1-111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-111-1-111
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
χ91-11-11111-1-1-11-11-1-1-11111-1-1-1-1-111-11-11-1-1-1-111111-1-111-11-111-1-1i−i1-11-111-1-1ii−i−i11111111-1-1-1-1-1-1-1-1i−ii−iii−i−ii−i1-1ii−i−i11-1-11-1i−ii−ii−i1-1i−i
χ101-11-11111-1-1-11-11-1-1-11111-1-1-1-1-111-11-11-1-1-1-111111-1-111-11-111-1-1i−i1-1-1111-1-1ii−i−i-1-1-1-1-1-1-1-111111111i−ii−iii−i−ii−i1-1ii−i−i11-1-1-11−iii−i−ii-11−ii
χ111-11-11111-1-1-11-11-1-1-11111-1-1-1-1-111-11-11-1-1-1-111111-1-111-11-111-1-1i−i-111-1-1-111ii−i−i11111111-1-1-1-1-1-1-1-1−ii−ii−i−iiii−i-11ii−i−i-1-111-11i−i−iii−i-11−ii
χ121-11-11111-1-1-11-11-1-1-11111-1-1-1-1-111-11-11-1-1-1-111111-1-111-11-111-1-1i−i-11-11-1-111ii−i−i-1-1-1-1-1-1-1-111111111−ii−ii−i−iiii−i-11ii−i−i-1-1111-1−ii−ii−ii1-1i−i
χ131-11-11111-1-1-11-11-1-1-11111-1-1-1-1-111-11-11-1-1-1-111111-1-111-11-111-1-1−ii1-11-111-1-1−i−iii11111111-1-1-1-1-1-1-1-1−ii−ii−i−iii−ii1-1−i−iii11-1-11-1−ii−ii−ii1-1−ii
χ141-11-11111-1-1-11-11-1-1-11111-1-1-1-1-111-11-11-1-1-1-111111-1-111-11-111-1-1−ii1-1-1111-1-1−i−iii-1-1-1-1-1-1-1-111111111−ii−ii−i−iii−ii1-1−i−iii11-1-1-11i−i−iii−i-11i−i
χ151-11-11111-1-1-11-11-1-1-11111-1-1-1-1-111-11-11-1-1-1-111111-1-111-11-111-1-1−ii-111-1-1-111−i−iii11111111-1-1-1-1-1-1-1-1i−ii−iii−i−i−ii-11−i−iii-1-111-11−iii−i−ii-11i−i
χ161-11-11111-1-1-11-11-1-1-11111-1-1-1-1-111-11-11-1-1-1-111111-1-111-11-111-1-1−ii-11-11-1-111−i−iii-1-1-1-1-1-1-1-111111111i−ii−iii−i−i−ii-11−i−iii-1-1111-1i−ii−ii−i1-1−ii
χ172222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000022-2-2-2-2-2-2000000000000000022000000
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χ22222222-1222222-1-1-1222-1-122-1-1-12-1-1-12-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2001111111100000000000000002222-1-1-1-1-2-2-2-2111111110000-1-1000000
χ23222222-1-2-22222-1-1-1222-1-122-1-1-12-1-1-1-211-2-2-2-2-2-2-2-1-1-1-111111111000000−i3i3−i3i3−i3i3−i3i3000000000000000022-2-211110000−i3i3−i3i3−i3i3−i3i30000-1-1000000
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χ25222222-1-2-22222-1-1-1222-1-122-1-1-12-1-1-1-211-2-2-2-2-2-2-2-1-1-1-111111111000000i3−i3i3−i3−i3i3−i3i30000000000000000-2-222-1-1-1-10000−i3i3−i3i3i3−i3i3−i3000011000000
χ26222222-1-2-22222-1-1-1222-1-122-1-1-12-1-1-1-211-2-2-2-2-2-2-2-1-1-1-111111111000000i3−i3i3−i3i3−i3i3−i3000000000000000022-2-211110000i3−i3i3−i3i3−i3i3−i30000-1-1000000
χ2722222-122222-1-1222-12-12-1-1-122-1-1-1-12-1222-1-1-12-1-1-1-1-1-1-1-122-1-1-1-12200220000222222-1-1-1-1-1-122-1-1-1-1-1-100000000-1-100-1-1-1-10000002200-1-10000
χ2822222-122222-1-1222-12-12-1-1-122-1-1-1-12-1222-1-1-12-1-1-1-1-1-1-1-122-1-1-1-12200-2-200002222-2-2111111-2-211111100000000-1-100-1-1-1-1000000-2-200110000
χ2922222-122222-1-1222-12-12-1-1-122-1-1-1-12-1222-1-1-12-1-1-1-1-1-1-1-122-1-1-1-1-2-200220000-2-2-2-222-1-1-1-1-1-122-1-1-1-1-1-10000000011001111000000-2-200110000
χ3022222-122222-1-1222-12-12-1-1-122-1-1-1-12-1222-1-1-12-1-1-1-1-1-1-1-122-1-1-1-1-2-200-2-20000-2-2-2-2-2-2111111-2-211111100000000110011110000002200-1-10000
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χ322222-12222-1-1222222-1-1-12-1-1-1-12-122-1222-1-1-12-1-1-1-1-1-1-122-1-1-1-1-1-10022-2-22222000011-2-2111111-2-211110000000000-1-10000-1-1-1-1-2-20000001100
χ332222-12222-1-1222222-1-1-12-1-1-1-12-122-1222-1-1-12-1-1-1-1-1-1-122-1-1-1-1-1-100-2-222-2-2-2-20000-1-122-1-1-1-1-1-122-1-1-1-100000000001100001111-2-20000001100
χ342222-12222-1-1222222-1-1-12-1-1-1-12-122-1222-1-1-12-1-1-1-1-1-1-122-1-1-1-1-1-100-2-2-2-2-2-2-2-2000011-2-2111111-2-211110000000000110000111122000000-1-100
χ352-22-2222-22-2-22-22-2-2-22222-2-2-2-2-222-222-22222-2-2-2-22-2-22-22-22-2-2220000000000000000000000000000002i−2i−2i2i−2i−2i2i2i00000000000000002i−2i000000
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χ372-22-222-12-2-2-22-2-111-222-1-1-2-21112-11-1-2-11-2-2-22222-111-1-11-11-1-1112i−2i2-200-1-111−i−iii00000000000000002i−2i2i−2i−i−iii2i−2i2-2−i−iii-1-1110000−ii000000
χ382-22-222-12-2-2-22-2-111-222-1-1-2-21112-11-1-2-11-2-2-22222-111-1-11-11-1-1112i−2i-220011-1-1−i−iii0000000000000000−2i2i−2i2iii−i−i2i−2i-22−i−iii11-1-10000i−i000000
χ392-22-222-12-2-2-22-2-111-222-1-1-2-21112-11-1-2-11-2-2-22222-111-1-11-11-1-111−2i2i2-200-1-111ii−i−i0000000000000000−2i2i−2i2iii−i−i−2i2i2-2ii−i−i-1-1110000i−i000000
χ402-22-222-12-2-2-22-2-111-222-1-1-2-21112-11-1-2-11-2-2-22222-111-1-11-11-1-111−2i2i-220011-1-1ii−i−i00000000000000002i−2i2i−2i−i−iii−2i2i-22ii−i−i11-1-10000−ii000000
χ412-22-222-1-22-2-22-2-111-222-1-1-2-21112-11-121-1222-2-2-2-2-111-11-11-111-1-1000000−i3i3i3−i33−3−3300000000000000002i−2i−2i2iii−i−i00003−3−33−i3i3i3−i30000−ii000000
χ422-22-222-1-22-2-22-2-111-222-1-1-2-21112-11-121-1222-2-2-2-2-111-11-11-111-1-1000000−i3i3i3−i3−333−30000000000000000−2i2i2i−2i−i−iii0000−333−3−i3i3i3−i30000i−i000000
χ432-22-222-1-22-2-22-2-111-222-1-1-2-21112-11-121-1222-2-2-2-2-111-11-11-111-1-1000000i3−i3−i3i33−3−330000000000000000−2i2i2i−2i−i−iii00003−3−33i3−i3−i3i30000i−i000000
χ442-22-222-1-22-2-22-2-111-222-1-1-2-21112-11-121-1222-2-2-2-2-111-11-11-111-1-1000000i3−i3−i3i3−333−300000000000000002i−2i−2i2iii−i−i0000−333−3i3−i3−i3i30000−ii000000
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χ462-22-22-122-2-2-2-112-2-212-12-111-2-21-1-11212-2-211-12-1-1-111-1-112-2-1-1112i−2i00-2200002i2i−2i−2i-2-211111122-1-1-1-1-1-100000000−ii00−i−iii000000−2i2i00i−i0000
χ472-22-22-122-2-2-2-112-2-212-12-111-2-21-1-11212-2-211-12-1-1-111-1-112-2-1-111−2i2i002-20000−2i−2i2i2i22-1-1-1-1-1-1-2-211111100000000i−i00ii−i−i000000−2i2i00i−i0000
χ482-22-22-122-2-2-2-112-2-212-12-111-2-21-1-11212-2-211-12-1-1-111-1-112-2-1-111−2i2i00-220000−2i−2i2i2i-2-211111122-1-1-1-1-1-100000000i−i00ii−i−i0000002i−2i00−ii0000
χ492-22-2-1222-2112-22-2-2-2-1-1-121111-2-12-2-1-22-21112-1-1-1-111-12-2-11-1-111002-22-222-2-20000-1-122-1-1-1-111-2-211110000000000-110000-1-1112-2000000-1100
χ502-22-2-1222-2112-22-2-2-2-1-1-121111-2-12-2-1-22-21112-1-1-1-111-12-2-11-1-111002-2-2222-2-2000011-2-21111-1-122-1-1-1-10000000000-110000-1-111-220000001-100
χ512-22-2-1222-2112-22-2-2-2-1-1-121111-2-12-2-1-22-21112-1-1-1-111-12-2-11-1-11100-222-2-2-2220000-1-122-1-1-1-111-2-2111100000000001-1000011-1-1-220000001-100
χ522-22-2-1222-2112-22-2-2-2-1-1-121111-2-12-2-1-22-21112-1-1-1-111-12-2-11-1-11100-22-22-2-222000011-2-21111-1-122-1-1-1-100000000001-1000011-1-12-2000000-1100
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χ874-44-4-24-2-44224-4-222-4-2-21-222-1-12-2-22142-2-2-2-2-42221-1-112-2-11-1-1110000002i3−2i3−2i32i3000000000000000000000000000000000000−i3i3i3−i3000000000000
χ884-44-4-2-244-422-224-4-42-21-2-2-1-12221-22-224-42-1-1-2-2111-1-11-22-2211-1-100004-400000000-2-2-2-211112222-1-1-1-100000000000000000000000000000000
χ894-44-4-2-244-422-224-4-42-21-2-2-1-12221-22-224-42-1-1-2-2111-1-11-22-2211-1-10000-44000000002222-1-1-1-1-2-2-2-2111100000000000000000000000000000000
χ904-44-4-2-24-4422-224-4-42-21-2-2-1-12221-22-2-2-44-21122-1-11-1-112-22-2-1-1110000000000000000003i3i−3i−3i0000−3i−3i3i3i00000000000000000000000000000000
χ914-44-4-2-24-4422-224-4-42-21-2-2-1-12221-22-2-2-44-21122-1-11-1-112-22-2-1-111000000000000000000−3i−3i3i3i00003i3i−3i−3i00000000000000000000000000000000
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χ934-4-4444-200-44-4-42-224-44-2-2-442-2-2-42220000000000-22-22000000000000000000000000000000000000000000−2i32i32i3−2i3000000000000000000000000
χ944-4-4444-200-44-4-42-224-44-2-2-442-2-2-42220000000000-22-220000000000000000000000000000000000000000002i3−2i3−2i32i3000000000000000000000000
χ954-4-444-2400-4422-44-4-2-4-24-22-2-44-2222-40000000000-22-220000000000000000000000006−66−66−600−66−66−6600000000000000000000000000000000
χ964-4-444-2400-4422-44-4-2-4-24-22-2-44-2222-40000000000-22-22000000000000000000000000−66−66−66006−66−66−600000000000000000000000000000000
χ974-4-44-244002-2-4-4-44-442-2-242-22-242-4-420000000000-22-220000000000000000000000i6−i600i6−i6−i6i6−i6i600−i6i6i6−i600000000000000000000000000000000
χ984-4-44-244002-2-4-4-44-442-2-242-22-242-4-420000000000-22-220000000000000000000000−i6i600−i6i6i6−i6i6−i600i6−i6−i6i600000000000000000000000000000000
χ994-4-44-2-24002-222-44-4-221-2-2-112-2-2-122200003i−3i00−3i3i1-11-10000−3i3i3i−3i00000000000000i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000000000000000000000000000
χ1004-4-44-2-24002-222-44-4-221-2-2-112-2-2-122200003i−3i00−3i3i1-11-10000−3i3i3i−3i00000000000000−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000000000000000000000000000
χ1014-4-44-2-24002-222-44-4-221-2-2-112-2-2-12220000−3i3i003i−3i1-11-100003i−3i−3i3i00000000000000i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000000000000000000000000000
χ1024-4-44-2-24002-222-44-4-221-2-2-112-2-2-12220000−3i3i003i−3i1-11-100003i−3i−3i3i00000000000000−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000000000000000000000000000
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χ1048888-4-4-4-8-8-4-4-4-4-4-4-4-4-42222222222224444-2-244-2-2-1-1-1-1-2-2-2-2111100000000000000000000000000000000000000000000000000000000000000
χ10588-8-88-4-4008-84-444-44-8-4-42-44-44-24-224000000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-48-400-44-8844-4-84-42-4-442-2444-4-2000000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
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χ10888-8-8-4-4-400-444-444-4442222-22-2-2-2-22-20000−6i6i00−6i6i-1-11100003i−3i3i−3i00000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-48-844-44-4444-4222-2-2-2-2-222-224-444-2-2-4-422-111-12-22-2-1-11100000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-4-8844-44-4444-4222-2-2-2-2-222-22-44-4-42244-2-2-111-1-22-2211-1-100000000000000000000000000000000000000000000000000000000000000
χ1118-8-888-4-400-88444-44-4-8-4-424-44-424-2-2400000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-48-4004-4-8-84-4484-42-44-4-22-4444-200000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-4004-4444-44-44222-22-222-2-2-2-200006i−6i00−6i6i-11-1100003i−3i−3i3i00000000000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4004-4444-44-44222-22-222-2-2-2-20000−6i6i006i−6i-11-110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000000000000

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