Finite Group Databasebeta

← Group #13172741

Character table — Group #13172741

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222222244444444444444466888888888888888812121212121212121212121212181818181818181824242424242424242424242424242424242424243636363636363636363654547272108
order12223336666666662333666666666664436666666666666662244412121212121212122222444466666666121212121212121212121212446666121212122212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-11-11111111-1-111-1-1-1-1-1-11-11-111-1-11-111111111-1-11-111-1-1-1-1-1-1-1-11-1-1
χ31111111111111111111111111111111111111111111111111-11-1111111-1-111-1-111-1-1-1-1-11-11-1-111-11111111-1-111-11-1-111-1-1-1-1-1-1-11-1
χ41111111111111111111111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-11
χ51111111111111111111111111111111-1-111111111111111111111-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1
χ61111111111111111111111111111111-1-111111111111111111-11-1-1-1-1-1-111-1-1-1-111-1-1-1-11-11-111-1-11-1-1-1-1-1-1-111-1-1-11-1-111-1-1-1-111-111
χ71111111111111111111111111111111-1-11111111111111111-11-11-1-1-1-1-1-1-11111-1-1-1-1-1-1-11-11-1-111-11-1-1-1-1-1-1-1-1111-111-1-1-1-1-1-1111-11
χ81111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1
χ91111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-1111
χ101111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-11-11111-1-111-1-111-1-1111-11-111-1-1-11-1-111-1-1-1-1111-1-1-111-1-111111-1-1
χ111111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-1111111-1-111-1-1-1-111-11-11-1-1111-1-1-111-1-111-1-1-1111-1-1-1-11111-11-1
χ121111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1111111-1-1-1-1-1-11
χ131111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-111-1-11-1-1-1-1-1-1-1-1111111-1-111111111-1-111-1-111-1-1-1-1-1-1111111-1-111-1-1-1
χ141111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-1-111-1-1-1-1-1-11111-1-1-1-1111-11-111-1-1-1111-1-111-1-111-1111-1-1-1-111-1-1-111
χ151111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-111-11-1-1-1-111-1-1-1-111-1-111-11-11-1-1111-111-1-11111-1-11-1-1-111-1-111-1-11-11
χ161111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-111-1-11111-1
χ17222222-122-122-12-122-12-122-122-1-1-1-12-122-12-1-1-122-1-1-1-1-1-1-1-1-10202222-1-100-1-100220000020-100-1-1022-1-1-1-1-100-1-10200-1-10000000-10
χ18222222-122-122-12-122-12-122-122-1-1-1-12-122-12-1-1-122-1-1-1-1-1-1-1-1-10-20-2222-1-1001100-2-200000-20100110-22-1-1-1-1-100110-20011000000010
χ19222222-122-122-12-122-12-122-122-1-1-1-12-1-2-2-12-1-1-122-1-1-1-1-1-1-1-1-10202-2-2-21100-1-100-2-20000020-100-1-102-21111100-1-10-20011000000010
χ20222222-122-122-12-122-12-122-122-1-1-1-12-1-2-2-12-1-1-122-1-1-1-1-1-1-1-1-10-20-2-2-2-2110011002200000-20100110-2-21111100110200-1-10000000-10
χ21222222-122-122-12-12-2-12-1-2-2-122-1-1-1-12-122-1-2111-2-211-1-1-11111020-2-222-1-1001100-2-20000020-100-1-10-2-21-1-11100110200110000000-10
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χ23222222-122-122-12-12-2-12-1-2-2-122-1-1-1-12-1-2-2-1-2111-2-211-1-1-11111020-22-2-211001100220000020-100-1-10-22-111-1-100110-200-1-1000000010
χ24222222-122-122-12-12-2-12-1-2-2-122-1-1-1-12-1-2-2-1-2111-2-211-1-1-111110-2022-2-21100-1-100-2-200000-2010011022-111-1-100-1-10200110000000-10
χ2522222-122-122-12-1222-1-1222-1-1-122-1-1-1222-1-12-1-1-1-122-1-1-1-1-1-1-120202-1-122-1-1002200000020-10-1-10020-12-1-1-1-1-1-10020-1-100000000-100
χ2622222-122-122-12-1222-1-1222-1-1-122-1-1-1222-1-12-1-1-1-122-1-1-1-1-1-1-1-20-202-1-1221100-2-2000000-20101100-20-12-1-1-1-11100-201100000000100
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χ2822222-122-122-12-1222-1-1222-1-1-122-1-1-12-2-2-1-12-1-1-1-122-1-1-1-1-1-1-1-20-20-211-2-2110022000000-20101100-201-21111110020-1-100000000-100
χ2922222-122-122-12-122-2-1-12-2-2-1-1-122-1-1-1222-11-21111-2-2-1-1-1111120-20-2-1-1221100-2-200000020-10-1-100-201-2-1-1111100201100000000-100
χ3022222-122-122-12-122-2-1-12-2-2-1-1-122-1-1-1222-11-21111-2-2-1-1-11111-2020-2-1-122-1-10022000000-20101100201-2-1-111-1-100-20-1-100000000100
χ3122222-122-122-12-122-2-1-12-2-2-1-1-122-1-1-12-2-2-11-21111-2-2-1-1-1111120-20211-2-211002200000020-10-1-100-20-1211-1-11100-20-1-100000000100
χ3222222-122-122-12-122-2-1-12-2-2-1-1-122-1-1-12-2-2-11-21111-2-2-1-1-11111-2020211-2-2-1-100-2-2000000-2010110020-1211-1-1-1-100201100000000-100
χ332222-122-122-12222-122-1-1-1-12-1-1-1-122-1-100-12222-1-1-1-1-1-1-1-1-1-1-1222200000222200002222-1-122-1-1-1-1-1-1000000-1-1-1-1000000-1-1-1-100000
χ342222-122-122-12222-122-1-1-1-12-1-1-1-122-1-100-12222-1-1-1-1-1-1-1-1-1-1-12-22-20000022-2-20000-2-2-2-2-112-2-1-111-11000000-1-111000000111100000
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χ362222-122-122-12222-122-1-1-1-12-1-1-1-122-1-100-12222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000-2-2-2-20000222211-2-21111110000001111000000-1-1-1-100000
χ372222-122-122-12222-1-22-1-1112-1-1-1-122-1-100-1-2-2-2-21111-1-1-1111122-2-200000-2-2-2-2000022-2-2-1-122-1-1-1-1110000001111000000-1-11100000
χ382222-122-122-12222-1-22-1-1112-1-1-1-122-1-100-1-2-2-2-21111-1-1-111112-2-2200000-2-2220000-2-222-112-2-1-1111-100000011-1-100000011-1-100000
χ392222-122-122-12222-1-22-1-1112-1-1-1-122-1-100-1-2-2-2-21111-1-1-11111-222-20000022-2-20000-2-2221-1-2211-1-1-11000000-1-11100000011-1-100000
χ402222-122-122-12222-1-22-1-1112-1-1-1-122-1-100-1-2-2-2-21111-1-1-11111-2-222000002222000022-2-211-2-21111-1-1000000-1-1-1-1000000-1-11100000
χ412-22-2222222-2-2-2-2-2-202220022-22-2-2-2-2-22i−2i2000000002-2-20000000002i−2i2i−2i00000000002i−2i0000000000002i−2i000000000000002i−2i2-2000
χ422-22-2222222-2-2-2-2-2-202220022-22-2-2-2-2-22i−2i2000000002-2-20000000002i−2i2i−2i0000000000−2i2i0000000000002i−2i00000000000000−2i2i-22000
χ432-22-2222222-2-2-2-2-2-202220022-22-2-2-2-2-2−2i2i2000000002-2-2000000000−2i2i−2i2i00000000002i−2i000000000000−2i2i000000000000002i−2i-22000
χ442-22-2222222-2-2-2-2-2-202220022-22-2-2-2-2-2−2i2i2000000002-2-2000000000−2i2i−2i2i0000000000−2i2i000000000000−2i2i00000000000000−2i2i2-2000
χ452-2-22222-2-2-2-2-2-2222022200-2-22-222-2-2-200200000000-22-2000000000000000002-22-22-20000000000000000000000002-22-22-20000000
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χ534444-24-2-24-2-24-24-2-24-2-21-2-2-2-2-211-2-2-210014-2-2-2-2-211111111104040000000-2-2000000000-20-200110-20000000011000000000000000
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χ1018-8-888-4-4-844-844-4-4802-4-400-24-44-42-24400200000000-22-2000000000000000000000000000000000000000000000000000000000000
χ1028-8-88-48-44-844-848-4-40-4-420044-4-22-444-200200000000-22-2000000000000000000000000000000000000000000000000000000000000
χ1038-8-88-4-4844-844-8-48-40-42-4004-224-4-44-2400200000000-22-2000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-4444444-4-4-4022200-2-22-222-2-2-200-1000000001-11−3i33i33i3−3i300000000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-4444444-4-4-4022200-2-22-222-2-2-200-1000000001-113i3−3i3−3i33i300000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).