Finite Group Databasebeta

← Group #13172268

Character table — Group #13172268

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222222244444444444444466888888888888888812121212121212121212121212181818181818181824242424242424242424242424242424242424243636363636363636363654547272108
order12223336666666662333666666666664436666666666666664444412121212121212124444444412121212121212121212121212121212121212124412121212121212124412122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-11-1111111-1-111-1-1-1-1-1-111-1-1111-111111111-1-1-1-11-111-1-1-1-1-1-1-1-11-1-1
χ311111111111111111111111111111111111111111111111111-11-111111-1-111-1-111-1-1-1-1-1-11111-111111-1-1-1-11111-11-1-111-1-1-1-1-1-1-11-1
χ411111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11
χ51111111111111111111111111111111-1-11111111111111111-11111-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1
χ61111111111111111111111111111111-1-11111111111111111-11-11-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-11-1-1-1-1-11111-1-1-1-1-11-1-111-1-1-1-111-111
χ71111111111111111111111111111111-1-11111111111111111-1-11-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-11-1-1-1-1-1-1-1-111111-111-1-1-1-1-1-1111-11
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
χ91111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-11-11-1-1-11111-1-111-1-111-1-111-1-1-1-111-1-1-1-1111
χ101111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-1-111111-1-111-1-111-1-1111-1-11-1-11-111-1-111-1-1-1-1111-1-1-111-1-111111-1-1
χ111111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1111111-1-111-1-1-1-111-111-1-1-1-1111-1-1-1-11111-1-1-1111-1-1-1-11111-11-1
χ121111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-11111111111111111-1-1-11-11-1-1-1-111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-11
χ131111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1111111-1-11-11-11111-1-11111-1-111-1-1-1-1111111-1-111-1-1-1
χ141111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-111-1-11-1-1-1-1-1-11111-1-1-1-1111-1-11111-1-1-11111-1-1-1-111-1111-1-1-1-111-1-1-111
χ151111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-111-1-1-1-1-111-1-1-1-111-1-111-111-111-11-1-111-1-11111-1-11-1-1-111-1-111-1-11-11
χ161111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-1-111-1-1-1-11111-1-1-1-111-1-1-11-1111-1-1-1-111-1-111-1-11111-1-1-1-111-1-11111-1
χ17222222-1222-122-1-1222-1-1222-1-122-1-1-1-122-12-122-1-1-1-1-1-1-1-1-1-1-12020222-1-100-1-10022000000-122-102-1-1-1-10000-1-1-1-10200-1-10000000-10
χ18222222-1222-122-1-1222-1-1222-1-122-1-1-1-122-12-122-1-1-1-1-1-1-1-1-1-1-120-20-222-1-1001100-2-20000001-22-10-2-1-1-1-1000011110-20011000000010
χ19222222-1222-122-1-1222-1-1222-1-122-1-1-1-1-2-2-12-122-1-1-1-1-1-1-1-1-1-1-1-20202-2-21100-1-100-2-2000000-12-210211110000-1-1-1-10-20011000000010
χ20222222-1222-122-1-1222-1-1222-1-122-1-1-1-1-2-2-12-122-1-1-1-1-1-1-1-1-1-1-1-20-20-2-2-211001100220000001-2-210-21111000011110200-1-10000000-10
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χ24222222-1222-122-1-12-22-1-1-2-22-1-122-1-1-1-1-2-2-1-21-2-21111-1-1-1111120-202-2-21100-1-100-2-2000000122-10-211-1-1000011-1-10200110000000-10
χ2522222-1222-12-1-12222-12-122-12-1-1-122-1-122-1-12-1-122-1-1-1-1-1-1-1-1-122020-1-122-1-10022000000-1200-1220-1-1-1-1-1-1-1-1000020-1-100000000-100
χ2622222-1222-12-1-12222-12-122-12-1-1-122-1-122-1-12-1-122-1-1-1-1-1-1-1-1-12-20-20-1-1221100-2-20000001-200-12-20-1-1-1-111110000-201100000000100
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χ2822222-1222-12-1-12222-12-122-12-1-1-122-1-1-2-2-1-12-1-122-1-1-1-1-1-1-1-1-1-2-20-2011-2-21100220000001-2001-2-2011111111000020-1-100000000-100
χ2922222-1222-12-1-1222-2-12-1-2-2-12-1-1-122-1-122-11-211-2-211-1-1-11111-220-20-1-1221100-2-2000000-1-2001-220-1-111-1-1110000201100000000-100
χ3022222-1222-12-1-1222-2-12-1-2-2-12-1-1-122-1-122-11-211-2-211-1-1-11111-2-2020-1-122-1-1002200000012001-2-20-1-11111-1-10000-20-1-100000000100
χ3122222-1222-12-1-1222-2-12-1-2-2-12-1-1-122-1-1-2-2-11-211-2-211-1-1-11111220-2011-2-2110022000000-1-200-122011-1-1-1-1110000-20-1-100000000100
χ3222222-1222-12-1-1222-2-12-1-2-2-12-1-1-122-1-1-2-2-11-211-2-211-1-1-111112-202011-2-2-1-100-2-20000001200-12-2011-1-111-1-10000201100000000-100
χ332222-122-1-1222222-12-1-12-1-1-1-12-1-1-1-12200-122-1-1-1-122-1-1-1-1-1-1-10222200002222000022222-12-100-1-10000-1-1-1-1-1-1-1-1000000-1-1-1-100000
χ342222-122-1-1222222-12-1-12-1-1-1-12-1-1-1-12200-122-1-1-1-122-1-1-1-1-1-1-102-22-2000022-2-20000-2-2-2-22-1-2100-110000-1-1-1-11111000000111100000
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χ362222-122-1-1222222-12-1-12-1-1-1-12-1-1-1-12200-122-1-1-1-122-1-1-1-1-1-1-10-2-2-2-20000-2-2-2-200002222-21-210011000011111111000000-1-1-1-100000
χ372222-122-1-1222222-1-2-1-1211-1-12-1-1-1-12200-1-2-21111-2-2-1-1-11111022-2-20000-2-2-2-2000022-2-2212100-1-10000-1-111-1-111000000-1-11100000
χ382222-122-1-1222222-1-2-1-1211-1-12-1-1-1-12200-1-2-21111-2-2-1-1-1111102-2-220000-2-2220000-2-22221-2-100-110000-1-11111-1-100000011-1-100000
χ392222-122-1-1222222-1-2-1-1211-1-12-1-1-1-12200-1-2-21111-2-2-1-1-111110-222-2000022-2-20000-2-222-2-121001-1000011-1-1-1-11100000011-1-100000
χ402222-122-1-1222222-1-2-1-1211-1-12-1-1-1-12200-1-2-21111-2-2-1-1-111110-2-22200002222000022-2-2-2-1-2-10011000011-1-111-1-1000000-1-11100000
χ412-22-2222-2-222-2-2-2-22022200-2-2-22-22-22-2002000000002-2-2000000000000000002i−2i2i−2i2-20000000000000000000000002i−2i2i−2i2-20000000
χ422-22-2222-2-222-2-2-2-22022200-2-2-22-22-22-2002000000002-2-2000000000000000002i−2i−2i2i-220000000000000000000000002i−2i−2i2i-220000000
χ432-22-2222-2-222-2-2-2-22022200-2-2-22-22-22-2002000000002-2-200000000000000000−2i2i2i−2i-22000000000000000000000000−2i2i2i−2i-220000000
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χ452-2-22222-22-2-22-22-2-2022200-2-22-22-22-2-22i−2i200000000-22-20000000002i−2i2i−2i00000000002i−2i000000002i−2i0000000000000000002i−2i2-2000
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χ1008-88-8-4-4-444-4-44444-4022200-2-2-22-22-22-200-100000000-111−3i33i33i3−3i300000000000000000000000000000000000000000000000000000000
χ1018-88-8-4-4-444-4-44444-4022200-2-2-22-22-22-200-100000000-1113i3−3i3−3i33i300000000000000000000000000000000000000000000000000000000
χ1028-8-88-48-44-4-848-8-4440-42-4004-2-44-4-224400200000000-22-2000000000000000000000000000000000000000000000000000000000000
χ1038-8-88-4-484-44-8-448-8402-4-400-24-4-224-44400200000000-22-2000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-44-444-44-444022200-2-22-22-22-2-200-10000006-61-11-33-3300000000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-44-444-44-444022200-2-22-22-22-2-200-1000000-661-113-33-300000000000000000000000000000000000000000000000000000000

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