Finite Group Databasebeta

← Group #13172309

Character table — Group #13172309

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222222244444444444444444444466888888888888812121212121212121212121212121212121212121212121212181824242424242424242424242424243636363636363654547272727272108
order12223336666666662333666666666666666664436666666666662444412121212121212121212121212121212121212124466661212121212121212121222444121222661212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111111111-1-11111-1-11-111-1-1-1-11-11-1-1-1-1-1-1-111-1-1-1
χ31111111111111111111111111111111111111111111111111111-11-1111111111111-1-111111111-1-1-1-1-1-111-11-1-11111-11-11-1-1-1-1-11-1-11-1-1
χ41111111111111111111111111111111111111111111111111111-11-1-1-1-1-111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111
χ51111111111111111111111111111111111111-1-111111111111111-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111-1-1-1-1-1-11-1
χ61111111111111111111111111111111111111-1-111111111111111-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11-111-1-1-1-1-11-11-1-1-1111-1-11-11
χ71111111111111111111111111111111111111-1-11111111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111111-11-1-1-1-111-111-1-11
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
χ91111111111111111-1111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1111-1-1-1-11-1-11-1-1-111-1-111-1-1-1-11111-1-1-1-11111111-1-11-1-111-1-1-111-1-111111-11-1-1-1
χ101111111111111111-1111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1111-1-1-1-11-1-1-111111-1-111-1-1-1-11111-1-1-1-1-1-11111-11-1-1-1-1-1-111-1-1111-1-1-1-1-1-11111
χ111111111111111111-1111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1111-1-1-1-1-1-111-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11-1111111-1-111-1-11-1-1-1-111-1-111
χ121111111111111111-1111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1111-1-1-1-1-1-11-111111-1-111-1-1111111-1-1-1-111-1-1-1-1-111-111-1-1111-1-11-11111-11-11-1-1
χ131111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-11-1-1-1-1-1111-1-1-1-111-11-1-1-1-1-111-1-111-1-1-1-1-1-111111111111-1-11-1-111-1-11-1-11-111-1-1-11-11-11
χ141111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-11-1-1-1-1-1111-1-1-1-111-1-1111-1-111-1-111-1-1-1-1-1-11111-1-11111-11-1-1-1-1-1-11111-1-11-1-11111-1-11-1
χ151111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-11-1-1-1-1-1111-1-1-1-1-1111-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11-1111111-1-1-1-1111-1-111-1-1111-1
χ161111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-11-1-1-1-1-1111-1-1-1-1-111-1111-1-111-1-11111-1-1-1-1111111-1-1-1-1-111-111-1-111-111-1-111-1-11-11-1-11
χ17222222-1-1222-12-12222-1-122-1-12-1-1-1-1-1-1-1-122-1-122-1222-1-1-1-1-1-1-1-1-12220000-1-1-1-1222222-1-1-1-1-1-1-1-1002-1-1-100-10-1-100002020000000-1-1000
χ18222222-1-1222-12-12222-1-122-1-12-1-1-1-1-1-1-1-122-1-122-1222-1-1-1-1-1-1-1-1-1-22-20000-1-1-1-12222-2-2-1-1-1-1-1-1-1-100-21110010110000-20-2000000011000
χ19222222-1-1222-12-12222-1-122-1-12-1-1-1-1-1-1-1-122-1-1-2-2-1222-1-1-1-1-1-1-1-1-12-2200001111-2-2-2-22211111111002-1-1-100-10-1-10000-20-2000000011000
χ20222222-1-1222-12-12222-1-122-1-12-1-1-1-1-1-1-1-122-1-1-2-2-1222-1-1-1-1-1-1-1-1-1-2-2-200001111-2-2-2-2-2-21111111100-211100101100002020000000-1-1000
χ21222222-1-1222-12-122-22-1-1-2-2112-1-11111-1-122-1-122-1-2-2-211-1-1-111112-2-20000-1-11122-2-2-2-2-1-1-1-11111002-1-1-10010110000-20200000001-1000
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χ23222222-1-1222-12-122-22-1-1-2-2112-1-11111-1-122-1-1-2-2-1-2-2-211-1-1-1111122-2000011-1-1-2-222-2-21111-1-1-1-1002-1-1-1001011000020-20000000-11000
χ24222222-1-1222-12-122-22-1-1-2-2112-1-11111-1-122-1-1-2-2-1-2-2-211-1-1-11111-222000011-1-1-2-222221111-1-1-1-100-211100-10-1-10000-20200000001-1000
χ2522222-1222-1-12222-12-1-12-1-122-1-1-1-1-1-1-122-1-12-122-12-1-122-1-1-1-1-1-1-102022222222-1-1-1-100-1-1-1-1-1-1-1-1000000-1-10200-1-1-1-1020200000-100-100
χ2622222-1222-1-12222-12-1-12-1-122-1-1-1-1-1-1-122-1-12-122-12-1-122-1-1-1-1-1-1-1020-2-2-2-22222-1-1-1-100-1-1-1-1-1-1-1-1000000110-20011110-20-200000100100
χ2722222-1222-1-12222-12-1-12-1-122-1-1-1-1-1-1-122-1-12-1-2-2-12-1-122-1-1-1-1-1-1-10-202222-2-2-2-211110011111111000000-1-10200-1-1-1-10-20-200000100100
χ2822222-1222-1-12222-12-1-12-1-122-1-1-1-1-1-1-122-1-12-1-2-2-12-1-122-1-1-1-1-1-1-10-20-2-2-2-2-2-2-2-211110011111111000000110-2001111020200000-100-100
χ2922222-1222-1-12222-1-2-1-1211-2-2-1-1-1111122-1-12-122-1-211-2-2-1-1-111110-202-2-2-222-2-2-1-11100-1-1-1-11111000000-110200-1-111020-200000-100100
χ3022222-1222-1-12222-1-2-1-1211-2-2-1-1-1111122-1-12-122-1-211-2-2-1-1-111110-20-222222-2-2-1-11100-1-1-1-111110000001-10-20011-1-10-20200000100-100
χ3122222-1222-1-12222-1-2-1-1211-2-2-1-1-1111122-1-12-1-2-2-1-211-2-2-1-1-111110202-2-2-2-2-22211-1-1001111-1-1-1-1000000-110200-1-1110-20200000100-100
χ3222222-1222-1-12222-1-2-1-1211-2-2-1-1-1111122-1-12-1-2-2-1-211-2-2-1-1-11111020-2222-2-22211-1-1001111-1-1-1-10000001-10-20011-1-1020-200000-100100
χ332222-1222-1222-12-122-12-12222-1222222-1-1-1-1-1200-1-1-1-1-1-1-1-1-1-1-1-1-120222-1-100000000-1-10000000022-12-1-1222-1-1-1-1-1-1-100002-1-1000000-10
χ342222-1222-1222-12-122-12-12222-1222222-1-1-1-1-1200-1-1-1-1-1-1-1-1-1-1-1-1-1202-2-21100000000-1-100000000-2-2-12-1-1-2-221-1-111110000-21100000010
χ352222-1222-1222-12-122-12-12222-1222222-1-1-1-1-1200-1-1-1-1-1-1-1-1-1-1-1-1-1-20-222-1-1000000001100000000-2-21-21122-2-111-1-1-1-10000-21100000010
χ362222-1222-1222-12-122-12-12222-1222222-1-1-1-1-1200-1-1-1-1-1-1-1-1-1-1-1-1-1-20-2-2-211000000001100000000221-211-2-2-2111111100002-1-1000000-10
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χ382222-1222-1222-12-12-2-12-1-2-2-2-2-122-2-2-2-2-1-1-1-1-1200-111111-1-1-1111120-2-22-1-1000000001100000000-2-2-12-1-1-22-211111-1-10000211000000-10
χ392222-1222-1222-12-12-2-12-1-2-2-2-2-122-2-2-2-2-1-1-1-1-1200-111111-1-1-11111-2022-21100000000-1-100000000-2-21-2112-22-1-1-1-1-1110000211000000-10
χ402222-1222-1222-12-12-2-12-1-2-2-2-2-122-2-2-2-2-1-1-1-1-1200-111111-1-1-11111-202-22-1-100000000-1-100000000221-211-2221-1-111-1-10000-2-1-100000010
χ412-2-22222222-2-2-2-2-2-202220000-22-200002-22-2-2-22i−2i2000002-2-2000000000002i−2i002i−2i00002i2i−2i−2i00002i−2i00000000000000000002i−2i2-2000000
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χ894-4-444-2444-22-4-4-4-420-2-2400002-2200004-4-22-424i−4i-200000-222000000000004i−4i00−2i2i0000−2i−2i2i2i00000000000000000000000000000000000
χ904-4-444-2444-22-4-4-4-420-2-2400002-2200004-4-22-42−4i4i-200000-22200000000000−4i4i002i−2i00002i2i−2i−2i00000000000000000000000000000000000
χ914-4-444-2-2-24-222-42-420-21-2000021-13-3-33-22-222-14i−4i1000001-1-13-3-330000000−2i2i00−2i2i0000ii−i−i3i−3i−3i3i0000000000000000000000000000000
χ924-4-444-2-2-24-222-42-420-21-2000021-13-3-33-22-222-1−4i4i1000001-1-13-3-3300000002i−2i002i−2i0000−i−iii−3i3i3i−3i0000000000000000000000000000000
χ934-4-444-2-2-24-222-42-420-21-2000021-1-333-3-22-222-14i−4i1000001-1-1-333-30000000−2i2i00−2i2i0000ii−i−i−3i3i3i−3i0000000000000000000000000000000
χ944-4-444-2-2-24-222-42-420-21-2000021-1-333-3-22-222-1−4i4i1000001-1-1-333-300000002i−2i002i−2i0000−i−iii3i−3i−3i3i0000000000000000000000000000000
χ954-4-44-2444-24-4-42-42-40-24-2000024-40000-22-222-400-200000-222000000000000000000000000000004i−4i0000000000000000000−2i2i00000000
χ964-4-44-2444-24-4-42-42-40-24-2000024-40000-22-222-400-200000-22200000000000000000000000000000−4i4i00000000000000000002i−2i00000000
χ978888-4-4-4-4-4-4-4-4-4-4-4-48222-4-4-4-4222222222222200-1-42222-1-1-1-1-1-1-100000000000000000000000000000000000000000000000000000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-4-82224444222-2-2-2-222222200-14-2-2-2-2-1-1-1111100000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-48-844-4-848-4402-4-40000-24-4000044-22-4400200000-22-2000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-4444-444-4-44022200−4i34i3-2-222i32i3−2i3−2i3-2-2-222-200-10002i3−2i31-11−i3−i3i3i300000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-4444-444-4-440222004i3−4i3-2-22−2i3−2i32i32i3-2-2-222-200-1000−2i32i31-11i3i3−i3−i300000000000000000000000000000000000000000000000000000000
χ1028-88-8-48-444-8-8-4-44480-4-420000-4440000-2244-2-400200000-2-22000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-44444-4-444-40222−4i34i3002-2-22i3−2i32i3−2i3-22-2-2-2200-102i3−2i30011-1−i3i3−i3i300000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-44444-4-444-402224i3−4i3002-2-2−2i32i3−2i32i3-22-2-2-2200-10−2i32i30011-1i3−i3i3−i300000000000000000000000000000000000000000000000000000000
χ1058-8-88-48-4-4-48-84444-80-4-4200004-4400002-2-44-24002000002-2-2000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-488-4-44-84-84402-4-40000-2-440000-442-244002000002-2-2000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-4-4-4-444444402220000-22-26-6-662-22-2-2-200-100000-111-333-300000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4-4-4-444444402220000-22-2-666-62-22-2-2-200-100000-1113-3-3300000000000000000000000000000000000000000000000000000000

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