Finite Group Databasebeta

← Group #13156521

Character table — Group #13156521

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111222222222222224444444444444444444444666688888888888812121212121212121212121212121212181818182424242424242424242424242424242424243636363654545454727272727272
order1222333446666666663336666666661212121212121212121288883666121212121212121224242424242424242424242424242424444444121212121212121212121212121212121212121288884412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-11-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-111
χ51111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ71111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-11111-1-1-1-1-1-1-1-11111-11-1-111
χ81111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-1-1-1-11111-1-1-1-111111-111-1-1
χ92222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-200002222-2-2-2-2-2-2-2-2000000000000000022-2-200000000000000000022-2-20000000000
χ102222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-200002222-2-2-2-2-2-2-2-20000000000000000-2-222000000000000000000-2-2220000000000
χ11222222-12222-122-122-12-1-122-1-12-1-1-1-1-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000
χ12222222-12222-122-122-12-1-122-1-12-1-1-1-1-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-2-2-2-2-2-2111111111111-1-1-1-10000000000
χ13222222-12222-122-122-12-1-122-1-12-1-1-1-1-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-22-222-2-2-1-111-1-1-1-1111111110000000000
χ14222222-12222-122-122-12-1-122-1-12-1-1-1-1-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2-22-2-22211-1-11111-1-1-1-111110000000000
χ15222222-1-2-222-122-122-12-1-122-1-12-1-1-1-111-2-2-2-2-2-2-2-20000-1-1-1-111111111000000000000000022-2-2000000−i3i3−i3i3−i3−i3i3i3−i3−i3i3i3-1-1110000000000
χ16222222-1-2-222-122-122-12-1-122-1-12-1-1-1-111-2-2-2-2-2-2-2-20000-1-1-1-111111111000000000000000022-2-2000000i3−i3i3−i3i3i3−i3−i3i3i3−i3−i3-1-1110000000000
χ17222222-1-2-222-122-122-12-1-122-1-12-1-1-1-111-2-2-2-2-2-2-2-20000-1-1-1-1111111110000000000000000-2-222000000−i3i3i3−i3−i3−i3i3i3i3i3−i3−i311-1-10000000000
χ18222222-1-2-222-122-122-12-1-122-1-12-1-1-1-111-2-2-2-2-2-2-2-20000-1-1-1-1111111110000000000000000-2-222000000i3−i3−i3i3i3i3−i3−i3−i3−i3i3i311-1-10000000000
χ1922222-12222-122-122-12-12-1-1-12-1-12-12-1222-1-1-12-1-1-12222-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000200-1-100220000-1-1-1-1000000000200-1-1
χ2022222-12222-122-122-12-12-1-1-12-1-12-12-1222-1-1-12-1-1-12222-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000-2001100-2-200001111000000000-20011
χ2122222-12222-122-122-12-12-1-1-12-1-12-12-1222-1-1-12-1-1-1-2-2-2-2-1-1-1-122-1-1-1-1-1-1-2-2-2-211111111111100000200-1-100220000-1-1-1-1000000000-20011
χ2222222-12222-122-122-12-12-1-1-12-1-12-12-1222-1-1-12-1-1-1-2-2-2-2-1-1-1-122-1-1-1-1-1-1-2-2-2-211111111111100000-2001100-2-200001111000000000200-1-1
χ232222-12222-122-122-122-1-12-1-1-12-1-12-1222-12-1-1-12-1-12222-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000020-1-1002200-1-1-1-100000000000020-1-100
χ242222-12222-122-122-122-1-12-1-1-12-1-12-1222-12-1-1-12-1-12222-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000-201100-2-2001111000000000000-201100
χ252222-12222-122-122-122-1-12-1-1-12-1-12-1222-12-1-1-12-1-1-2-2-2-2-1-1-1-1-1-122-1-1-1-11111-2-2-2-211111111000020-1-1002200-1-1-1-1000000000000-201100
χ262222-12222-122-122-122-1-12-1-1-12-1-12-1222-12-1-1-12-1-1-2-2-2-2-1-1-1-1-1-122-1-1-1-11111-2-2-2-2111111110000-201100-2-200111100000000000020-1-100
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χ2922-2-22220022-2-2-22-2-2-22222-222-2-2-2-2-20000000000−2−22222-2-200000000−2−222−2−222−2−2−2−222222-2000000000000000000002-200−2−222000000
χ3022-2-22220022-2-2-22-2-2-22222-222-2-2-2-2-20000000000−2−22222-2-200000000−2−222−2−222−2−2−2−22222-2200000000000000000000-220022−2−2000000
χ312-22-222200-2-2-222-2-2-22222-22-2-2-2-2-2220000000000−i2i2−i2i22-22-200000000−i2i2−i2i2−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2002-2000000000000000000002-2−i2i2−i2i2000000
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χ332-22-222200-2-2-222-2-2-22222-22-2-2-2-2-2220000000000i2−i2i2−i22-22-200000000i2−i2i2−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2002-2000000000000000000002-2i2−i2i2−i2000000
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χ372-2-22222-22-2-22-2-2-222-2222-2-2-2-2222-2-2-222222-2-2-2-22i−2i−2i2i2-2-22-22-22-2-2222i−2i−2i2i2i−2i−2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ382-2-22222-22-2-22-2-2-222-2222-2-2-2-2222-2-2-222222-2-2-2-2−2i2i2i−2i2-2-22-22-22-2-222−2i2i2i−2i−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ392-2-222-12-22-212-21-22-1-2-12-111-21-12-1-21-222-1-1-1-21112i−2i−2i2i-111-1-221-111-1-12i−2i−2i2i−iii−i−i−iiiii−i−i000000003−3000000003−33−3000000000000−i3i3
χ402-2-222-12-22-212-21-22-1-2-12-111-21-12-1-21-222-1-1-1-21112i−2i−2i2i-111-1-221-111-1-12i−2i−2i2i−iii−i−i−iiiii−i−i00000000−3300000000−33−33000000000000i3−i3
χ412-2-222-12-22-212-21-22-1-2-12-111-21-12-1-21-222-1-1-1-2111−2i2i2i−2i-111-1-221-111-1-1−2i2i2i−2ii−i−iiii−i−i−i−iii000000003−3000000003−33−3000000000000i3−i3
χ422-2-222-12-22-212-21-22-1-2-12-111-21-12-1-21-222-1-1-1-2111−2i2i2i−2i-111-1-221-111-1-1−2i2i2i−2ii−i−iiii−i−i−i−iii00000000−3300000000−33−33000000000000−i3i3
χ432-2-22-122-221-221-2-2-12-2-1-12111-2-1-121-2-22-12-1-11-2112i−2i−2i2i-111-11-1-2211-1-1−iii−i2i−2i−2i2i−i−iiiii−i−i0000003−30000003−33−300000000000000−i3i300
χ442-2-22-122-221-221-2-2-12-2-1-12111-2-1-121-2-22-12-1-11-2112i−2i−2i2i-111-11-1-2211-1-1−iii−i2i−2i−2i2i−i−iiiii−i−i000000−33000000−33−3300000000000000i3−i300
χ452-2-22-122-221-221-2-2-12-2-1-12111-2-1-121-2-22-12-1-11-211−2i2i2i−2i-111-11-1-2211-1-1i−i−ii−2i2i2i−2iii−i−i−i−iii0000003−30000003−33−300000000000000i3−i300
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χ4744444-24-4-44-244-244-24-24-2-2-24-2-24-24-2-4-4-4222-42220000-2-2-2-2-4-42222220000000000000000000000000000000000000000000000000000
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χ534444-24-244-24-2-24-2-24-2-21-2-2-21-2-21-21-2-2-2-24-2-2-24-2-20000111111-2-211110000000000000000000040-2-200-2-2001111000000000000000000
χ544444-24-244-24-2-24-2-24-2-21-2-2-21-2-21-21-2-2-2-24-2-2-24-2-20000111111-2-2111100000000000000000000-4022002200-1-1-1-1000000000000000000
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χ824-4-4444-2-44-4-4-2-4-424424-2-2-4-4224-2-2222-24444-4-4-4-40000-222-22-22-222-2-20000000000000000000000000000000000000000000000000000
χ834-4-444-244-4-424-42-44-2-4-24-222-42-24-2-424-4-42224-2-2-20000-222-24-4-22-2-2220000000000000000000000000000000000000000000000000000
χ844-4-444-2-24-4-42-2-4224-22-2-21222-1-2-212-1-22-42224-2-2-200001-1-11-221-111-1-100000000000000000000000000000000003i−3i−3i3i00000000000000
χ854-4-444-2-24-4-42-2-4224-22-2-21222-1-2-212-1-22-42224-2-2-200001-1-11-221-111-1-10000000000000000000000000000000000−3i3i3i−3i00000000000000
χ864-4-444-2-2-44-42-2-4224-22-2-21222-1-2-212-12-24-2-2-2-422200001-1-112-2-11-1-11100000000000000000000000023−2300000000−33−3300000000000000
χ874-4-444-2-2-44-42-2-4224-22-2-21222-1-2-212-12-24-2-2-2-422200001-1-112-2-11-1-111000000000000000000000000−2323000000003−33−300000000000000
χ884-4-44-2444-42-442-4-4-24-4-2-24222-4-2-242-44-42-422-24-2-20000-222-2-224-4-2-2220000000000000000000000000000000000000000000000000000
χ894-4-44-24-24-42-4-22-42-242-21-222-12-21-2-12-222-422-24-2-200001-1-111-1-2211-1-10000000000000000000000000000003i−3i−3i3i000000000000000000
χ904-4-44-24-24-42-4-22-42-242-21-222-12-21-2-12-222-422-24-2-200001-1-111-1-2211-1-1000000000000000000000000000000−3i3i3i−3i000000000000000000
χ914-4-44-24-2-442-4-22-42-242-21-222-12-21-2-122-2-24-2-22-42200001-1-11-112-2-1-111000000000000000000000023−23000000−33−33000000000000000000
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χ954-4-44-2-24-4422422-4-2-2-41-2-2-1-1221-2-222-44-2-21122-1-14i−4i−4i4i1-1-112-22-2-1-111−2i2i2i−2i−2i2i2i−2iii−i−i−i−iii000000000000000000000000000000000000
χ964-4-44-2-24-4422422-4-2-2-41-2-2-1-1221-2-222-44-2-21122-1-1−4i4i4i−4i1-1-112-22-2-1-1112i−2i−2i2i2i−2i−2i2i−i−iiiii−i−i000000000000000000000000000000000000
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χ988888-4-4-4-8-8-4-4-4-4-4-4-4-4-42222222222224444-2-244-2-20000-1-1-1-1-2-2-2-211110000000000000000000000000000000000000000000000000000
χ9988-8-88-4-4008-44-84-4-844-4-42-44-4244-24-20000000000000022-2-2000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-48-400-4844-8-44-84-42-4-442-44-24-240000000000000022-2-2000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-400-4-4444-44442222-222-2-2-2-2-200006i−6i006i−6i0000-1-1110000−3i3i−3i3i0000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-400-4-4444-44442222-222-2-2-2-2-20000−6i6i00−6i6i0000-1-11100003i−3i3i−3i0000000000000000000000000000000000000000000000000000
χ1038-88-88-4-400-8448-44-84-4-4-424-44-244-2-42000000000000002-22-2000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-48-4004-84-4844-8-4-42-44-4-244-242-4000000000000002-22-2000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-400444-4-4444-4222-22-2-2-2-2-22200006i−6i00−6i6i0000-11-1100003i−3i−3i3i0000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-400444-4-4444-4222-22-2-2-2-2-2220000−6i6i006i−6i0000-11-110000−3i3i3i−3i0000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-48-844-4444-4-44222-2-2-2-2222-2-2-4444-2-2-4-4220000-111-12-22-2-1-1110000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4-8844-4444-4-44222-2-2-2-2222-2-24-4-4-42244-2-20000-111-1-22-2211-1-10000000000000000000000000000000000000000000000000000

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