Finite Group Databasebeta

← Group #13169457

Character table — Group #13169457

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size1111222222222222444444444444466668888888888888888812121212121212121212121212121212181818182424242424242424242424242424242424243636363636363636363654545454727272
order122233366666666633346666666664444366612121212121212121212121212444412121212121212121212121244441212121212121212121212121212121212122444121212121212224461212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-111-1-1-1-1-111111111-1-1-1-11-111-1111-1-111-1-11111-11-1111-1-1-1-1-1-1-1-1-11-1
χ31111111111111111111111111111111-1-11111111111111111111-11111111-1-111-1-111-1-1111-11-1-1-111-1-11111111-1-1-1-1-111-1-1-1-1-1-11-1-1
χ41111111111111111111111111111111-1-111111111111111111-11-1-1-1-1-1-111-1-111-1-1-1-1111-11-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1111111-1-11
χ511111111111111111111111111111-1-111111111111111111111-1111111-1-111-1-111-1-111-11-111111111111-1-1-1-1-1-11-1-1-1-1-111-1-1-1-1-1-11
χ611111111111111111111111111111-1-11111111111111111111-1-11-1-1-1-1-1-1-111-1-11111-1-1-1-1-11-1111-1-111-1-1-1-1-1-11-1-1-1-1-111-1-111111-1-1
χ711111111111111111111111111111-1-1-1-1111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-111-1-111-1-1-1-1-11-1111-1-1-1-11111-11-1
χ811111111111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111
χ91111111111111111111-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-111111111-1-111-1-1-1-11-1-1-11111-1-111-1-111-1-111-1-111-1-1111-1-1
χ101111111111111111111-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111111111-1-1-11-1-1-1-1-1-1-1-1111111-1-1-111-11111-1-111-1-1-1-11
χ111111111111111111111-111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-1-1-1-1-1-1-1-11111111-1-1-1-111-1-11-111-1-1-1-1-1-111-1-1111
χ121111111111111111111-111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-11111-11-11-1111-1-1-1-11111-1-1-1-1-11-1-11111-1-111-11-1
χ131111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-11111111-11-11-1-1-11111-1-1-1-111-1-1-11-1-1111111-1-1-11-1
χ141111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-111-1-1-1-1111-1-1-1-1-1-1-11111-1-1111-111-1-1-1-1-1-1-1-111111
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1-1-1-1-1-1-1-1-111-1-11-111111111-1-1-1-1-1-111-111-11111-1-1-1-111-1-11
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-1111111-1111-1-1-1-111-1-11111-1-111-1-11111-1-11-1-1
χ17222222-12-1-1222-1222-1-122-1-1-12-12-1-12200-1-1-1-1-122-1-122-1-1-1-1-1-1220222-1-1-1-10022002200-1220-1000-1-100-1-1-1-1-1-1200000-1-1000000-100
χ18222222-12-1-1222-1222-1-122-1-1-12-12-1-12200-1-1-1-1-122-1-122-1-1-1-1-1-1-220-2-2-211-1-1002200-2-200-1-2201000110011-1-1-1-1-20000011000000100
χ19222222-12-1-1222-1222-1-122-1-1-12-12-1-1-2-200-1-1-1-1-122-1-122-1-1-1-1-1-12-20222-1-11100-2-200-2-20012-20-1000-1-100-1-11111-20000011000000100
χ20222222-12-1-1222-1222-1-122-1-1-12-12-1-1-2-200-1-1-1-1-122-1-122-1-1-1-1-1-1-2-20-2-2-2111100-2-20022001-2-2010001100111111200000-1-1000000-100
χ21222222-12-1-1222-1222-1-1-22-1-1-12-12-1-12200-1-1-1-11-2-211-2-21111112-20-22211-1-1002200-2-2001-2-20-1000-1-10011-1-11120000011000000-100
χ22222222-12-1-1222-1222-1-1-22-1-1-12-12-1-12200-1-1-1-11-2-211-2-2111111-2-202-2-2-1-1-1-1002200220012-2010001100-1-1-1-111-200000-1-1000000100
χ23222222-12-1-1222-1222-1-1-22-1-1-12-12-1-1-2-200-1-1-1-11-2-211-2-2111111220-222111100-2-2002200-1-220-1000-1-1001111-1-1-200000-1-1000000100
χ24222222-12-1-1222-1222-1-1-22-1-1-12-12-1-1-2-200-1-1-1-11-2-211-2-2111111-2202-2-2-1-11100-2-200-2-200-122010001100-1-111-1-120000011000000-100
χ2522222-122222-1-12-12-12-12-12-1-1-12-12-12222-1-1-1-122-1-1-1-1-122-1-1-1-1022000002222-1-1-1-1000020-1-102-1-100-1-100-1-1-1-10202-1-1000000000-10
χ2622222-122222-1-12-12-12-12-12-1-1-12-12-122-2-2-1-1-1-122-1-1-1-1-122-1-1-1-102-20000022-2-2-1-111000020-110-211001100-1-1-1-10-20-21100000000010
χ2722222-122222-1-12-12-12-12-12-1-1-12-12-1-2-222-1-1-1-122-1-1-1-1-122-1-1-1-10-2200000-2-22211-1-10000-201-102-1-100-1-10011110-20-21100000000010
χ2822222-122222-1-12-12-12-12-12-1-1-12-12-1-2-2-2-2-1-1-1-122-1-1-1-1-122-1-1-1-10-2-200000-2-2-2-211110000-20110-21100110011110202-1-1000000000-10
χ2922222-122222-1-12-12-12-1-2-12-1-1-12-12-12222-1-1-1-1-2-211111-2-211110-2-2000002222-1-1-1-10000-20110-21100-1-100-1-111020-2-1-100000000010
χ3022222-122222-1-12-12-12-1-2-12-1-1-12-12-122-2-2-1-1-1-1-2-211111-2-211110-220000022-2-2-1-1110000-201-102-1-1001100-1-1110-20211000000000-10
χ3122222-122222-1-12-12-12-1-2-12-1-1-12-12-1-2-222-1-1-1-1-2-211111-2-2111102-200000-2-22211-1-1000020-110-21100-1-10011-1-10-20211000000000-10
χ3222222-122222-1-12-12-12-1-2-12-1-1-12-12-1-2-2-2-2-1-1-1-1-2-211111-2-2111102200000-2-2-2-21111000020-1-102-1-100110011-1-1020-2-1-100000000010
χ332222-122-122-12222-1-1-122-1-122-1-1-1-120022-1-1-1-12-1222-1-1-1-1-1-1-1-12022-1-12200-1-1002200220-1022-1-1-1-1-1-1-1-1-1000000200000-1-1000000-1
χ342222-122-122-12222-1-1-122-1-122-1-1-1-120022-1-1-1-12-1222-1-1-1-1-1-1-1-1-202-211-2-200-1-1002200-2-20102-2-1-1-111-1-111000000-200000110000001
χ352222-122-122-12222-1-1-122-1-122-1-1-1-1200-2-2-1-1-1-12-1222-1-1-1-1-1-1-1-120-22-1-122001100-2-200-2-20-10-22111-1-111-1-1000000-200000110000001
χ362222-122-122-12222-1-1-122-1-122-1-1-1-1200-2-2-1-1-1-12-1222-1-1-1-1-1-1-1-1-20-2-211-2-2001100-2-20022010-2-2111111111000000200000-1-1000000-1
χ372222-122-122-12222-1-1-12-2-1-122-1-1-1-120022-1-1-1-1-21-2-2-21111111120-2-2-1-1-2-200-1-100220022010-22111-1-1-1-111000000-200000-1-10000001
χ382222-122-122-12222-1-1-12-2-1-122-1-1-1-120022-1-1-1-1-21-2-2-211111111-20-22112200-1-1002200-2-20-10-2-211111-1-1-1-100000020000011000000-1
χ392222-122-122-12222-1-1-12-2-1-122-1-1-1-1200-2-2-1-1-1-1-21-2-2-211111111202-2-1-1-2-2001100-2-200-2-201022-1-1-1-1-1111100000020000011000000-1
χ402222-122-122-12222-1-1-12-2-1-122-1-1-1-1200-2-2-1-1-1-1-21-2-2-211111111-20221122001100-2-200220-102-2-1-1-11111-1-1000000-200000-1-10000001
χ412-22-2222-2-22-22-2-2-222220-22-2-22-2-2-22002i−2i22-2-2000000000000000000000002i−2i002i−2i2i−2i0000000000002i−2i0000000000002i−2i002-200000
χ422-22-2222-2-22-22-2-2-222220-22-2-22-2-2-22002i−2i22-2-2000000000000000000000002i−2i002i−2i−2i2i0000000000002i−2i000000000000−2i2i00-2200000
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χ452-2-22222-22-22-2-2-22-22220-2-2-22-2-222-22i−2i002-2-220000000000000000000002i−2i002i−2i00002i−2i000000000000002i−2i00000000002i−2i002-2000
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χ5044444-2-24-2-24-2-2-2-24-2-214-2-211-2-2-2-21-4-4001111-24-211-2-2-2-211110-400000022002200000020200000000000-1-1-1-100000000000000000
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χ1018-88-8-4-4-444-44-4444-42220-22-2-22-2-2-220000-1-11100000−6i6i003i−3i3i−3i0000000000000000000000000000000000000000000000000000000
χ1028-8-88-48-44-44-4-8-8484-42-404-24-44-2-42400002-2-2200000000000000000000000000000000000000000000000000000000000000000000
χ1038-8-88-4-4848-8-444-8-442-4-40-244-4-242-4400002-2-2200000000000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-44-44-4444-442220-2-2-22-2-222-20000-111-10006-60000-333-30000000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-44-44-4444-442220-2-2-22-2-222-20000-111-1000-6600003-3-330000000000000000000000000000000000000000000000000000000

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