Finite Group Databasebeta

← Group #13155724

Character table — Group #13155724

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222224444444444444444444444888888888888121212121212121212121212121212121212121212121212121212121212181818181818181824242424242424242424242436363636363672727272108108
order1222333446666666663336666666661212121212121212121236661212121212121212224466668812121212242424242424242424242424242424244444121212126666661212121212122244121266121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-111
χ51111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1
χ61111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111
χ71111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
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
χ911-1-1111-11-1-1111-1-1-1-1111-1-1-1-1-1111-1111-111-1-1-1-11-1-1111-1-111-1-11-1i−i11-1-1i−iii−i−iiiiiiiii−i−i−i−i−i−i−i−ii−ii−iii−i−i1-111-1-1i−iii−i−i1-1i−ii−i1-1i−i1-1
χ1011-1-1111-11-1-1111-1-1-1-1111-1-1-1-1-1111-1111-111-1-1-1-11-1-1111-1-111-1-11-1i−i11-1-1−iiii−i−i−i−i−i−i−i−i−i−iiiiiiiiii−ii−iii−i−i1-111-1-1i−iii−i−i-11−iii−i-11−ii-11
χ1111-1-1111-11-1-1111-1-1-1-1111-1-1-1-1-1111-1111-111-1-1-1-11-1-1111-1-111-1-11-1−ii11-1-1i−i−i−iiiiiiiiiii−i−i−i−i−i−i−i−i−ii−ii−i−iii1-111-1-1−ii−i−iii-11i−i−ii-11i−i-11
χ1211-1-1111-11-1-1111-1-1-1-1111-1-1-1-1-1111-1111-111-1-1-1-11-1-1111-1-111-1-11-1−ii11-1-1−ii−i−iii−i−i−i−i−i−i−i−iiiiiiiii−ii−ii−i−iii1-111-1-1−ii−i−iii1-1−ii−ii1-1−ii1-1
χ1311-1-1111-11-1-1111-1-1-1-1111-1-1-1-1-1111-1111-111-1-1-1-11-1-1111-1-111-1-1-11i−i-1-111i−iii−i−iiiiiiiii−i−i−i−i−i−i−i−i−ii−ii−i−iii-11-1-111i−iii−i−i1-1−ii−ii1-1−ii-11
χ1411-1-1111-11-1-1111-1-1-1-1111-1-1-1-1-1111-1111-111-1-1-1-11-1-1111-1-111-1-1-11i−i-1-111−iiii−i−i−i−i−i−i−i−i−i−iiiiiiiii−ii−ii−i−iii-11-1-111i−iii−i−i-11i−i−ii-11i−i1-1
χ1511-1-1111-11-1-1111-1-1-1-1111-1-1-1-1-1111-1111-111-1-1-1-11-1-1111-1-111-1-1-11−ii-1-111i−i−i−iiiiiiiiiii−i−i−i−i−i−i−i−ii−ii−iii−i−i-11-1-111−ii−i−iii-11−iii−i-11−ii1-1
χ1611-1-1111-11-1-1111-1-1-1-1111-1-1-1-1-1111-1111-111-1-1-1-11-1-1111-1-111-1-1-11−ii-1-111−ii−i−iii−i−i−i−i−i−i−i−iiiiiiiiii−ii−iii−i−i-11-1-111−ii−i−iii1-1i−ii−i1-1i−i-11
χ172222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000022-2-222220000000000000000-2-2000000
χ182222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000-2-222-2-2-2-2000000000000000022000000
χ19222222-1222-122-1-1222-1-12-1-1-122-1-12-122-12-1-12-1-1-1-1-1-1-12-12-1-1-1-1-10022000022222222-1-1-1-1-1-122-1-1-1-1-1-100000000000000-1-1-1-1-1-1220000-1-10000
χ20222222-1222-122-1-1222-1-12-1-1-122-1-12-122-12-1-12-1-1-1-1-1-1-12-12-1-1-1-1-100220000-2-22222-2-2111111-2-211111100000000000000-1-1-1-1-1-1-2-20000110000
χ21222222-1222-122-1-1222-1-12-1-1-122-1-12-122-12-1-12-1-1-1-1-1-1-12-12-1-1-1-1-100-2-2000022-2-2-2-222-1-1-1-1-1-122-1-1-1-1-1-100000000000000111111-2-20000110000
χ22222222-1222-122-1-1222-1-12-1-1-122-1-12-122-12-1-12-1-1-1-1-1-1-12-12-1-1-1-1-100-2-20000-2-2-2-2-2-2-2-2111111-2-211111100000000000000111111220000-1-10000
χ2322222-1222222-122-1-122-1-122-1-1-12-1-1-12-12-1222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-100-1-1-1-100000000000000002222-1-1-1-122-1-1-1-122-1-1-1-10000-1-1000000
χ2422222-1222222-122-1-122-1-122-1-1-12-1-1-12-12-1222222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-1-1-1-10011110000000000000000-2-2-2-2111122-1-1-1-1-2-21111000011000000
χ2522222-1222222-122-1-122-1-122-1-1-12-1-1-12-12-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-222111100-1-1-1-10000000000000000-2-2-2-21111-2-2111122-1-1-1-1000011000000
χ2622222-1222222-122-1-122-1-122-1-1-12-1-1-12-12-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111100111100000000000000002222-1-1-1-1-2-21111-2-211110000-1-1000000
χ2722222-12-2-2222-122-1-122-1-122-1-1-12-1-1-1-21-21-2-2-2-2-2-2-1-1-1-1111111110000−i3i3−i3i300−i3i3−i3i3000000000000000022-2-2-1-1-1-100−i3i3−i3i300−i3i3−i3i3000011000000
χ2822222-12-2-2222-122-1-122-1-122-1-1-12-1-1-1-21-21-2-2-2-2-2-2-1-1-1-1111111110000−i3i3−i3i300i3−i3i3−i30000000000000000-2-222111100−i3i3−i3i300i3−i3i3−i30000-1-1000000
χ2922222-12-2-2222-122-1-122-1-122-1-1-12-1-1-1-21-21-2-2-2-2-2-2-1-1-1-1111111110000i3−i3i3−i300−i3i3−i3i30000000000000000-2-222111100i3−i3i3−i300−i3i3−i3i30000-1-1000000
χ3022222-12-2-2222-122-1-122-1-122-1-1-12-1-1-1-21-21-2-2-2-2-2-2-1-1-1-1111111110000i3−i3i3−i300i3−i3i3−i3000000000000000022-2-2-1-1-1-100i3−i3i3−i300i3−i3i3−i3000011000000
χ312222-12222-12-122222-1-12-1-1-12-1-1-12-12-1222-1-1-12-1-1-1-1-1-1-12-12-1-1-1-122002222220000-1-122-1-1-1-1-1-122-1-1-1-100000000-1-1-1-1-1-100000000220000-1-100
χ322222-12222-12-122222-1-12-1-1-12-1-1-12-12-1222-1-1-12-1-1-1-1-1-1-12-12-1-1-1-122002222-2-2000011-2-2111111-2-2111100000000-1-1-1-1-1-100000000-2-200001100
χ332222-12222-12-122222-1-12-1-1-12-1-1-12-12-1222-1-1-12-1-1-1-1-1-1-12-12-1-1-1-1-2-200-2-2-2-2220000-1-122-1-1-1-1-1-122-1-1-1-10000000011111100000000-2-200001100
χ342222-12222-12-122222-1-12-1-1-12-1-1-12-12-1222-1-1-12-1-1-1-1-1-1-12-12-1-1-1-1-2-200-2-2-2-2-2-2000011-2-2111111-2-211110000000011111100000000220000-1-100
χ3522-2-22222-2-2-2222-2-2-2-2222-2-2-2-2-2222-2-2-2-22-2-222222-2-22-2-222-2-2220000000000000000000000000000002i−2i−2i2i2i2i−2i−2i0000000000000000−2i2i000000
χ3622-2-22222-2-2-2222-2-2-2-2222-2-2-2-2-2222-2-2-2-22-2-222222-2-22-2-222-2-222000000000000000000000000000000−2i2i2i−2i−2i−2i2i2i00000000000000002i−2i000000
χ3722-2-222-1-22-2122-11-2-2-2-1-12111-2-2-1-12122-1-2-1-1-2111-111-12-1-21-1-111002i−2i00002i−2i2i2i−2i−2i2i2i−i−i−i−i−i−i−2i−2iiiiiii00000000000000−ii−i−iii2-20000-110000
χ3822-2-222-1-22-2122-11-2-2-2-1-12111-2-2-1-12122-1-2-1-1-2111-111-12-1-21-1-111002i−2i0000−2i2i2i2i−2i−2i−2i−2iiiiiii2i2i−i−i−i−i−i−i00000000000000−ii−i−iii-2200001-10000
χ3922-2-222-1-22-2122-11-2-2-2-1-12111-2-2-1-12122-1-2-1-1-2111-111-12-1-21-1-11100−2i2i00002i−2i−2i−2i2i2i2i2i−i−i−i−i−i−i−2i−2iiiiiii00000000000000i−iii−i−i-2200001-10000
χ4022-2-222-1-22-2122-11-2-2-2-1-12111-2-2-1-12122-1-2-1-1-2111-111-12-1-21-1-11100−2i2i0000−2i2i−2i−2i2i2i−2i−2iiiiiii2i2i−i−i−i−i−i−i00000000000000i−iii−i−i2-20000-110000
χ4122-2-22-122-2-2-22-12-211-22-1-1-2-21112-1-11-21-2-1-2-22222-111-111-1-111-1-10000−i3i3i3−i3003−3−3300000000000000002i−2i−2i2i−i−iii00−i3i3i3−i3003−3−330000i−i000000
χ4222-2-22-122-2-2-22-12-211-22-1-1-2-21112-1-11-21-2-1-2-22222-111-111-1-111-1-10000−i3i3i3−i300−333−30000000000000000−2i2i2i−2iii−i−i00−i3i3i3−i300−333−30000−ii000000
χ4322-2-22-122-2-2-22-12-211-22-1-1-2-21112-1-11-21-2-1-2-22222-111-111-1-111-1-10000i3−i3−i3i3003−3−330000000000000000−2i2i2i−2iii−i−i00i3−i3−i3i3003−3−330000−ii000000
χ4422-2-22-122-2-2-22-12-211-22-1-1-2-21112-1-11-21-2-1-2-22222-111-111-1-111-1-10000i3−i3−i3i300−333−300000000000000002i−2i−2i2i−i−iii00i3−i3−i3i300−333−30000i−i000000
χ4522-2-22-12-22-2-22-12-211-22-1-1-2-21112-1-112-12122-2-2-2-2-111-1-1-111-1-1112-22i−2i-1-11100−i−iii00000000000000002i−2i2i−2i−i−iii2-2-1-1112i−2i−i−iii0000−ii000000
χ4622-2-22-12-22-2-22-12-211-22-1-1-2-21112-1-112-12122-2-2-2-2-111-1-1-111-1-1112-2−2i2i-1-11100ii−i−i0000000000000000−2i2i−2i2iii−i−i2-2-1-111−2i2iii−i−i0000i−i000000
χ4722-2-22-12-22-2-22-12-211-22-1-1-2-21112-1-112-12122-2-2-2-2-111-1-1-111-1-111-222i−2i11-1-100−i−iii0000000000000000−2i2i−2i2iii−i−i-2211-1-12i−2i−i−iii0000i−i000000
χ4822-2-22-12-22-2-22-12-211-22-1-1-2-21112-1-112-12122-2-2-2-2-111-1-1-111-1-111-22−2i2i11-1-100ii−i−i00000000000000002i−2i2i−2i−i−iii-2211-1-1−2i2iii−i−i0000−ii000000
χ4922-2-2-122-221-2-122-2-2-21-12-111-211-12-1-2-122-2-1-11-211-111-1-121-2-1-1112-20022-2-22i−2i0000−i−i2i2i−i−i−i−iii−2i−2iiiii00000000-11-1-111000000002i−2i0000−ii00
χ5022-2-2-122-221-2-122-2-2-21-12-111-211-12-1-2-122-2-1-11-211-111-1-121-2-1-1112-20022-2-2−2i2i0000ii−2i−2iiiii−i−i2i2i−i−i−i−i00000000-11-1-11100000000−2i2i0000i−i00
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χ5544444-2-2444-24-2-2-2-2-24-21-2-2-21-2-2-21-214-2-2-2-2-24-2-2-21111-21-21111100-4-4000000222200000000000000000000000000000022-1-1-1-1000000000000
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χ7144-4-44-2-2-44-424-2-2222-4-21-222-122-21-2-14-2-22-2-2-42221-1-11-212-111-1-100−4i4i0000002i2i−2i−2i0000000000000000000000000000002i−2i−i−iii000000000000
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χ7444-4-4-24-24-422-24-22-4-421-2-2-1-12221-2-222-424-1-1-2-2111-1-1122-2-2-1-111000000000000000000-3-333000033-3-300000000000000000000000000000000
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χ994-4-44-24-2002-22-4224-4-21-2-2-11-22-2-122200003i−3i00−3i3i1-11-100003i−3i−3i3i00000000000000i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000000000000000000000000000
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χ1078-88-88-4-40084-844-44-4-8-42-4-44-2-444-242000000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4800-4-844-884-44-4-42-4442-244-2-4000000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
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χ1118-8-888-4-400-8-4-8444-448-42-44-424-44-24-200000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-48004844-8-8-44-4-4-424-4-4-2244-2400000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
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χ1148-8-88-4-4-4004-44444-44-4222-222-22-2-2-2-20000−6i6i006i−6i-11-1100003i−3i−3i3i00000000000000000000000000000000000000000000000000000000000000

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