Finite Group Databasebeta

← Group #13168596

Character table — Group #13168596

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222222244444444444444444444466888888888888812121212121212121212121212121212121212121212121212181824242424242424242424242424243636363636363654547272727272108
order12223336666666663334666666666121212121212121244366612121212121212121224444661212121212121212121212121212121212124466612121212121212121212124444412124412121212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-111111111-1-11111111111-1-11111-1-11-111-1-1-1-11-1-11-1-1-1-1-11-11-1-1-1
χ31111111111111111111111111111111111111111111111111111-11-111-1-1111111111111111111-1-1-1-1-1-111-11-1-11111-111-1-1-1-1-1-1-1-1-111-1
χ41111111111111111111111111111111111111111111111111111-11-1-1-1-1-1111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-1-11
χ51111111111111111111111111111111111111-1-111111111111111-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111-1-1-11-1-1-1-1
χ61111111111111111111111111111111111111-1-111111111111111-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-111-1-1-1-1-111-1-1-1-111-1-1-1111
χ71111111111111111111111111111111111111-1-11111111111111-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111111-1-11-1-1-1111-11-1-11
χ81111111111111111111111111111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111111-1
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-11-111-1-1-1-11111111111-1-1-1-111111-11-1-1-1-1-111-1-1-11-11-111111-1-11-1-1
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-1-1111-1-1-1-111-1-1111111-1-1-1-1-1-1111-1-11-11-1-1-1-111-1-1111-1-1-1-111-1-111
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-111-11-11111-1-111-1-11-1-1-1-1-1111-11
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1-11-111111-1-1111-11-1-11111-1-11-11-1
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-11-1111111-1-111-1-1-1-1-1-1111111111-11-1-1-1-1-111-1-11-11-1-111-1-1-1-11-111
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1111-1-11-11-1-1-1-11111-1-11-1-111-1111-1-1
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1-111-11-11111-1-1-1-1111-1-11111-1-11-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-11-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-11-111111-1-111-11-11-111-1-11-1-11-11
χ17222222-122-122-1-1222-1-122-12-1-1-1-1-1222-1-1-1-1-1-122-1-1-1-1222-1-1-1-1-1-12220022-1-122-1-10022-1-1-1-1-1-1-1-100-1-1-1-10020-1-10000200200000-10-1000
χ18222222-122-122-1-1222-1-122-12-1-1-1-1-1222-1-1-1-1-1-122-1-1-1-1222-1-1-1-1-1-1-22-200-2-2-1-122-1-10022-1-1-1-1-1-1-1-100111100-20110000-200-200000101000
χ19222222-122-122-1-1222-1-122-12-1-1-1-1-1222-1-1-1-1-1-1-2-2-1-1-1-1222-1-1-1-1-1-12-22002211-2-21100-2-21111111100-1-1-1-10020-1-10000-200-200000101000
χ20222222-122-122-1-1222-1-122-12-1-1-1-1-1222-1-1-1-1-1-1-2-2-1-1-1-1222-1-1-1-1-1-1-2-2-200-2-211-2-21100-2-21111111100111100-20110000200200000-10-1000
χ21222222-122-122-1-1222-1-1-22-12-1-1-1-1-12-2-211111122-1-1-1-1-2-2-21111112-2-2002211-2-2-1-10022-1-1-1-1111100-1-1-1100-20110000-200200000-101000
χ22222222-122-122-1-1222-1-1-22-12-1-1-1-1-12-2-211111122-1-1-1-1-2-2-2111111-2-2200-2-211-2-2-1-10022-1-1-1-1111100111-10020-1-10000200-20000010-1000
χ23222222-122-122-1-1222-1-1-22-12-1-1-1-1-12-2-2111111-2-2-1-1-1-1-2-2-211111122-20022-1-1221100-2-21111-1-1-1-100-1-1-1100-20110000200-20000010-1000
χ24222222-122-122-1-1222-1-1-22-12-1-1-1-1-12-2-2111111-2-2-1-1-1-1-2-2-2111111-22200-2-2-1-1221100-2-21111-1-1-1-100111-10020-1-10000-200200000-101000
χ2522222-12-1222-122-12-12-12-1-1-12-122-1-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-120222-1-1000000-1-10000000000222-1-1222-1-1-1-1-1-1-1-100002-1-1000-10000
χ2622222-12-1222-122-12-12-12-1-1-12-122-1-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-1202-2-2-1-1000000110000000000-2-22-1-12-2-2-11-1-111110000-21100010000
χ2722222-12-1222-122-12-12-12-1-1-12-122-1-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-1-20-22211000000-1-10000000000-2-2-211-2221-111-1-1-1-10000-21100010000
χ2822222-12-1222-122-12-12-12-1-1-12-122-1-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-1-20-2-2-21100000011000000000022-211-2-2-21111111100002-1-1000-10000
χ2922222-12-1222-122-12-12-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-200-1-1-1-111111111120-22-2-1-1000000-1-10000000000222-1-1-22-21111-1-1110000-2-1-100010000
χ3022222-12-1222-122-12-12-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-200-1-1-1-111111111120-2-22-1-1000000110000000000-2-22-1-1-2-221-11111-1-10000211000-10000
χ3122222-12-1222-122-12-12-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-200-1-1-1-1111111111-2022-211000000-1-10000000000-2-2-21122-2-11-1-1-1-1110000211000-10000
χ3222222-12-1222-122-12-12-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-200-1-1-1-1111111111-202-221100000011000000000022-2112-22-1-1-1-111-1-10000-2-1-100010000
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χ342222-1222-12-12222-1-1-122-12-1-12-1-12-1-1-122-1-1-1-122-1-1-1-12-1-122-1-1-1-1020-2-20022-1-122-2-2-1-1-1-1-1-1-1-1-1-1000000110-20011110-2-2000000000110
χ352222-1222-12-12222-1-1-122-12-1-12-1-12-1-1-122-1-1-1-1-2-2-1-1-1-12-1-122-1-1-1-10-202200-2-211-2-2221111111111000000-1-10200-1-1-1-10-2-2000000000110
χ362222-1222-12-12222-1-1-122-12-1-12-1-12-1-1-122-1-1-1-1-2-2-1-1-1-12-1-122-1-1-1-10-20-2-200-2-211-2-2-2-21111111111000000110-2001111022000000000-1-10
χ372222-1222-12-12222-1-1-12-2-12-1-12-1-12-111-2-2111122-1-1-1-1-211-2-211110-202-200-2-2112222-1-1-1-1-1-11111000000-110-200-1-11102-2000000000-110
χ382222-1222-12-12222-1-1-12-2-12-1-12-1-12-111-2-2111122-1-1-1-1-211-2-211110-20-2200-2-21122-2-2-1-1-1-1-1-111110000001-1020011-1-10-220000000001-10
χ392222-1222-12-12222-1-1-12-2-12-1-12-1-12-111-2-21111-2-2-1-1-1-1-211-2-211110202-20022-1-1-2-222111111-1-1-1-1000000-110-200-1-1110-220000000001-10
χ402222-1222-12-12222-1-1-12-2-12-1-12-1-12-111-2-21111-2-2-1-1-1-1-211-2-21111020-220022-1-1-2-2-2-2111111-1-1-1-10000001-1020011-1-102-2000000000-110
χ412-2-22222-2-222-2-2-22-22220-2-2-2-2-22-222000000002i−2i22-2-2000000000000000000002i−2i002i−2i2i2i−2i−2i00002-200000000000000000002-22i−2i000000
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χ432-2-22222-2-222-2-2-22-22220-2-2-2-2-22-22200000000−2i2i22-2-200000000000000000000−2i2i00−2i2i−2i−2i2i2i00002-200000000000000000002-2−2i2i000000
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χ494444-24-24-2-2-24-2-24-2-21-24-2-2-21-211-2-2-2-2-2-211114411114-2-2-2-211110400000-2-2-2-2-2-200-2-2111111110000000000000000000000000000000
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χ524444-24-24-2-2-24-2-24-2-21-2-4-2-2-21-211-2-22222-1-1-1-1-4-41111-42222-1-1-1-10400000-2-2-2-2220022-1-1-1-111110000000000000000000000000000000
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χ934-4-44-24-2-42-2-2-42242-21-20222-121-1-2-200003i−3i−3i3i4i−4i11-1-1000003i−3i−3i3i00000000000−2i2i00−2i2iii−i−i-333-30000000000000000000000000000000
χ944-4-44-24-2-42-2-2-42242-21-20222-121-1-2-200003i−3i−3i3i−4i4i11-1-1000003i−3i−3i3i000000000002i−2i002i−2i−i−iii3-3-330000000000000000000000000000000
χ954-4-44-24-2-42-2-2-42242-21-20222-121-1-2-20000−3i3i3i−3i4i−4i11-1-100000−3i3i3i−3i00000000000−2i2i00−2i2iii−i−i3-3-330000000000000000000000000000000
χ964-4-44-24-2-42-2-2-42242-21-20222-121-1-2-20000−3i3i3i−3i−4i4i11-1-100000−3i3i3i−3i000000000002i−2i002i−2i−i−iii-333-30000000000000000000000000000000
χ978888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4-4-4222200-1-1-1-1-42222-1-1-1-100000000000000000000000000000000000000000000000000000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224444-2-2-2-200-1-1-1-14-2-2-2-2111100000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-48-44-844-884-42-4-402-4-2444-44-200000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-4-444444-44-4222022-2-2-2-22-2-20043−43−23−23232300-11-11000−232333−3−300000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-4-444444-44-4222022-2-2-2-22-2-200−43432323−23−2300-11-1100023−23−3−33300000000000000000000000000000000000000000000000000000000
χ1028-88-88-4-4484-8-4-444-8-4-4204-2-4-4244-2400000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-44-444-4-44442220-2-2222-2-2-2-2−4i34i3002i3−2i32i3−2i300-111-102i3−2i300−i3i3−i3i300000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-44-444-4-44442220-2-2222-2-2-2-24i3−4i300−2i32i3−2i32i300-111-10−2i32i300i3−i3i3−i300000000000000000000000000000000000000000000000000000000
χ1058-8-888-4-44-8-48444-4-8-4-4204-244-2-442-4000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-48448-44-8-8-442-4-40-24-244-44-42000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-444-4-4444-442220-2-2-2-2-22-22200006i−6i−6i6i00-1-11100000−3i3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-444-4-4444-442220-2-2-2-2-22-2220000−6i6i6i−6i00-1-111000003i−3i−3i3i00000000000000000000000000000000000000000000000000000000

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