Finite Group Databasebeta

← Group #13172105

Character table — Group #13172105

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222222244444444444444444444466888888888888812121212121212121212121212121212121212121212121212181824242424242424242424242424243636363636363654547272727272108
order1222333666666666233366666666666666666443666666666666224441212121212121212121212121212121212121212446666666612121212121222444121244661212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-111-111-1-11111111111111111-1-11-11-111-1-11-111-1-1-1-111-1-1-1-1-1-1-111-1-1
χ31111111111111111111111111111111111111111111111111111-111-11-1-1111111111111111111-1-1-11-11-1-111-11-1-1111-1-1-11-1-1-1-11-1-1-11-1
χ41111111111111111111111111111111111111111111111111111-1-11-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-11-1-1-11
χ51111111111111111111111111111111111111-1-1111111111111111-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-11-1-1-111-1-1-11-1-1-1-1
χ61111111111111111111111111111111111111-1-111111111111111-1-11-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-11-111-1-11-1-1-11-1-1111-1-1-111
χ71111111111111111111111111111111111111-1-11111111111111-11-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-11-1-111-1-111-1-1-111-1-111-11
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
χ91111111111111111-1111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1111111-1-11-11-1
χ101111111111111111-1111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1111-1-1-1-11-1-1-11-1-11111-1-111-1-11111-1-1-1-1-1-11-11-111-1-1-11-1-11111-11-1-1-1-1-1111-1-11
χ111111111111111111-1111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1111-1-1-1-1-11-11-111-1-111-1-111-1-11111-1-1-1-1-1-1-11-11-1-1111-111-1-1-111-11-1-1-1-1-11-1111
χ121111111111111111-1111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1111-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111-11-1-111111-1-11-1-1
χ131111111111111111-1111-1-1-1-111-1-1-1-11111111-1-11-1-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111111111-1-1-1-1-1-11-11-1-111-1-11-1-11-11
χ141111111111111111-1111-1-1-1-111-1-1-1-11111111-1-11-1-1-1-1-1111-1-1-1-11-11-11-1-111-1-111-1-111-1-1-1-11111-1-11-11-111-1-1-11-1-111-111-11-1-111-11-111-1
χ151111111111111111-1111-1-1-1-111-1-1-1-11111111-1-11-1-1-1-1-1111-1-1-1-1-1111-111-1-1-1-111-1-111-1-1-1-11111-1-1-11-11-1-1111-111-1-111-11-1-1-111111-1-1-1
χ161111111111111111-1111-1-1-1-111-1-1-1-11111111-1-11-1-1-1-1-1111-1-1-1-1-1-11111111-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-11-111
χ17222222-12-1-12222-1222-1-12222222222-1-1-1-1-1-1200-1-1-1-1-1-1-1-1-1-1-1-1-122022-1-1-1-100000000000000002222-1-1-1-1-1-122-1-1-1-102000-1-1000-10000
χ18222222-12-1-12222-1222-1-12222222222-1-1-1-1-1-1200-1-1-1-1-1-1-1-1-1-1-1-1-12-202-2-1-1110000000000000000-2-22-2-11-1-1112-2-1-1110-20001100010000
χ19222222-12-1-12222-1222-1-12222222222-1-1-1-1-1-1200-1-1-1-1-1-1-1-1-1-1-1-1-1-220-2211-1-10000000000000000-2-2-221-111-1-1-2211-1-10-20001100010000
χ20222222-12-1-12222-1222-1-12222222222-1-1-1-1-1-1200-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20-2-21111000000000000000022-2-2111111-2-2111102000-1-1000-10000
χ21222222-12-1-12222-12-22-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1200-111111-1-1-11111220-2-2111100000000000000002222-1-1-1-1-1-1-2-211110-2000-1-100010000
χ22222222-12-1-12222-12-22-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1200-111111-1-1-111112-20-2211-1-10000000000000000-2-22-2-11-1-111-2211-1-10200011000-10000
χ23222222-12-1-12222-12-22-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1200-111111-1-1-11111-2202-2-1-1110000000000000000-2-2-221-111-1-12-2-1-1110200011000-10000
χ24222222-12-1-12222-12-22-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1200-111111-1-1-11111-2-2022-1-1-1-1000000000000000022-2-211111122-1-1-1-10-2000-1-100010000
χ2522222-12-122-12222-12-12-122-1-1-1-1-1-1-1-122-1-12-1-122-1222-1-1-1-1-1-1-1-1-1022020022-1-1-1-12222-1-1-1-1-1-1-1-1000-10200-1-10-100-1-1200020000-1000-10
χ2622222-12-122-12222-12-12-122-1-1-1-1-1-1-1-122-1-12-1-122-1222-1-1-1-1-1-1-1-1-10-220-200-2-2-1-1-1-12222-1-1-1-1-1-1-1-100010-20011010011-2000-20000100010
χ2722222-12-122-12222-12-12-122-1-1-1-1-1-1-1-122-1-12-1-1-2-2-1222-1-1-1-1-1-1-1-1-102-20200221111-2-2-2-211111111000-10200-1-10-100-1-1-2000-20000100010
χ2822222-12-122-12222-12-12-122-1-1-1-1-1-1-1-122-1-12-1-1-2-2-1222-1-1-1-1-1-1-1-1-10-2-20-200-2-21111-2-2-2-21111111100010-20011010011200020000-1000-10
χ2922222-12-122-12222-1-2-12-1-2-211-1-1111122-1-12-1-122-1-2-2-211-1-1-1111102-20-200-2-2-1-11122-2-2-1-1-1-11111000-10200-1-1010011-2000200001000-10
χ3022222-12-122-12222-1-2-12-1-2-211-1-1111122-1-12-1-122-1-2-2-211-1-1-111110-2-2020022-1-11122-2-2-1-1-1-1111100010-200110-100-1-12000-20000-100010
χ3122222-12-122-12222-1-2-12-1-2-211-1-1111122-1-12-1-1-2-2-1-2-2-211-1-1-111110220-200-2-211-1-1-2-2221111-1-1-1-1000-10200-1-10100112000-20000-100010
χ3222222-12-122-12222-1-2-12-1-2-211-1-1111122-1-12-1-1-2-2-1-2-2-211-1-1-111110-2202002211-1-1-2-2221111-1-1-1-100010-200110-100-1-1-2000200001000-10
χ332222-1222222-1-1-1222-1-12-1-122-1-1-1-1-1-1-1-122-12-122-12-1-122-1-1-1-1-1-1-12022022002222-1-1-1-1-1-1-1-1-1-1-1-100-1020-1-100-10-1-10000220000000-1-100
χ342222-1222222-1-1-1222-1-12-1-122-1-1-1-1-1-1-1-122-12-122-12-1-122-1-1-1-1-1-1-1-202-20-2-2002222-1-1-1-1-1-1-1-1-1-1-1-10010-20110010110000-2-200000001100
χ352222-1222222-1-1-1222-1-12-1-122-1-1-1-1-1-1-1-122-12-1-2-2-12-1-122-1-1-1-1-1-1-120-2202200-2-2-2-211111111111100-1020-1-100-10-1-10000-2-200000001100
χ362222-1222222-1-1-1222-1-12-1-122-1-1-1-1-1-1-1-122-12-1-2-2-12-1-122-1-1-1-1-1-1-1-20-2-20-2-200-2-2-2-21111111111110010-20110010110000220000000-1-100
χ372222-1222222-1-1-122-2-1-1211-2-2-1-11111-1-122-12-122-1-211-2-2-1-1-1111120-2-20-2-20022-2-2-1-111-1-1-1-1111100-1020-1-10010110000-220000000-1100
χ382222-1222222-1-1-122-2-1-1211-2-2-1-11111-1-122-12-122-1-211-2-2-1-1-11111-20-220220022-2-2-1-111-1-1-1-111110010-201100-10-1-100002-200000001-100
χ392222-1222222-1-1-122-2-1-1211-2-2-1-11111-1-122-12-1-2-2-1-211-2-2-1-1-11111202-20-2-200-2-22211-1-11111-1-1-1-100-1020-1-100101100002-200000001-100
χ402222-1222222-1-1-122-2-1-1211-2-2-1-11111-1-122-12-1-2-2-1-211-2-2-1-1-11111-202202200-2-22211-1-11111-1-1-1-10010-201100-10-1-10000-220000000-1100
χ4122-2-22222-2-2-22-2-22-2022200002-200002-22-2-2-2-22i−2i2000002-2-200000000000002i−2i002i−2i002i2i−2i−2i00002-200000000000000000002-22i−2i000000
χ4222-2-22222-2-2-22-2-22-2022200002-200002-22-2-2-2-22i−2i2000002-2-200000000000002i−2i002i−2i002i2i−2i−2i0000-220000000000000000000-22−2i2i000000
χ4322-2-22222-2-2-22-2-22-2022200002-200002-22-2-2-2-2−2i2i2000002-2-20000000000000−2i2i00−2i2i00−2i−2i2i2i00002-200000000000000000002-2−2i2i000000
χ4422-2-22222-2-2-22-2-22-2022200002-200002-22-2-2-2-2−2i2i2000002-2-20000000000000−2i2i00−2i2i00−2i−2i2i2i0000-220000000000000000000-222i−2i000000
χ4544444-2-2-2-2-2-2444-2-24-2-2144-2-2-2-2-2-2-2-2-2-211-21-2001-2-2-21111111110400400-2-20000000000000000000-20-200110-20011000000000000000
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χ4744444-2-2-2-2-2-2444-2-2-4-2-21-4-422-2-22222-2-211-21-2001222-1-1111-1-1-1-10400-400220000000000000000000-20-200110200-1-1000000000000000
χ4844444-2-2-2-2-2-2444-2-2-4-2-21-4-422-2-22222-2-211-21-2001222-1-1111-1-1-1-10-400400-2-2000000000000000000020200-1-10-20011000000000000000
χ494444-24-24-2-24-2-2-2-244-21-2-2-244-2-2-2-2-2-211-2-21-2-2001-211-2-2111111140040-2-200000000000000000000-20-201100-201100000000000000000
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χ514444-24-24-2-24-2-2-2-24-4-21-222-4-4-2-2222211-2-21-2-20012-1-122111-1-1-1-1400-402200000000000000000000-20-20110020-1-100000000000000000
χ524444-24-24-2-24-2-2-2-24-4-21-222-4-4-2-2222211-2-21-2-20012-1-122111-1-1-1-1-40040-2-2000000000000000000002020-1-100-201100000000000000000
χ534444-2-24-244-2-2-2-24-241-2-2-2-2-2-2111111-2-2-2-2-2-214414-2-2-2-21111111004000000-2-2-2-2-2-2-2-2111111110000000000000000000000000000000
χ544444-2-24-244-2-2-2-24-241-2-2-2-2-2-2111111-2-2-2-2-2-21-4-414-2-2-2-2111111100-400000022222222-1-1-1-1-1-1-1-10000000000000000000000000000000
χ554444-2-24-244-2-2-2-24-2-41-2-2222211-1-1-1-1-2-2-2-2-2-21441-42222111-1-1-1-100-4000000-2-222-2-2221111-1-1-1-10000000000000000000000000000000
χ564444-2-24-244-2-2-2-24-2-41-2-2222211-1-1-1-1-2-2-2-2-2-21-4-41-42222111-1-1-1-100400000022-2-222-2-2-1-1-1-111110000000000000000000000000000000
χ5744-4-444-2422-44-4-4-2-404-2-200004-40000-22-2222-400-200000-222000000000000000000000000000004-40000000000000000000-2200000000
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χ904-4-444-2-222-22-4-442-20-2-21002i3−2i32-22i3−2i3−2i32i32-2-1-1212001000−i3i3-1-11−i3i3i3−i300000002i3−2i30000000000000000000000003-30000−i3i3000000000000000
χ914-4-44-244-4-44-422-2-440-2-2400002-200002-2-4-424200-20000022-2000000000000000000023−23000023−23−23230000000000000000000000000000000
χ924-4-44-244-4-44-422-2-440-2-2400002-200002-2-4-424200-20000022-20000000000000000000−23230000−232323−230000000000000000000000000000000
χ934-4-44-2-242-44222-2-4-201-2-200−2i32i3-11i3−i3−i3i32-2222-2-1001000−2i32i3-1-11i3−i3−i3i300000000000000023−233i−3i−3i3i−333−30000000000000000000000000000000
χ944-4-44-2-242-44222-2-4-201-2-200−2i32i3-11i3−i3−i3i32-2222-2-1001000−2i32i3-1-11i3−i3−i3i3000000000000000−2323−3i3i3i−3i3−3−330000000000000000000000000000000
χ954-4-44-2-242-44222-2-4-201-2-2002i3−2i3-11−i3i3i3−i32-2222-2-10010002i3−2i3-1-11−i3i3i3−i300000000000000023−23−3i3i3i−3i−333−30000000000000000000000000000000
χ964-4-44-2-242-44222-2-4-201-2-2002i3−2i3-11−i3i3i3−i32-2222-2-10010002i3−2i3-1-11−i3i3i3−i3000000000000000−23233i−3i−3i3i3−3−330000000000000000000000000000000
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
χ988888-4-4-4-4-4-4-4-4-4-4-4-4-8222444422-2-2-2-2222222200-14-2-2-2-2-1-1-1111100000000000000000000000000000000000000000000000000000000
χ9988-8-88-4-4-44448-8-8-440-4-420000-440000-442-24-24002000002-2-2000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-48-4844-8-444-4-80-42-40000-4400002-2-44-244002000002-2-2000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-4-4444-444-44022200002-266-6-62-22-2-2-2-200-100000-111-3-33300000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-4-4444-444-44022200002-2-6-6662-22-2-2-2-200-100000-11133-3-300000000000000000000000000000000000000000000000000000000
χ1038-88-88-4-44-44-4-88-8440-4-42000044000044-22-4-2-400200000-22-2000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-44-44-44-44440222−4i34i300-2-22i3−2i32i3−2i3-2-2-222-2200-102i3−2i3001-11−i3i3−i3i300000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-44-44-44-444402224i3−4i300-2-2−2i32i3−2i32i3-2-2-222-2200-10−2i32i3001-11i3−i3i3−i300000000000000000000000000000000000000000000000000000000
χ1068-8-88-48-4-84-4-844-4480-42-400004-40000-2244-2-4400200000-2-22000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-444-4444-44-4022200−4i34i3-222i3−2i3−2i32i3-22-2-2-22-200-10002i3−2i311-1−i3i3i3−i300000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-444-4444-44-40222004i3−4i3-22−2i32i32i3−2i3-22-2-2-22-200-1000−2i32i311-1i3−i3−i3i300000000000000000000000000000000000000000000000000000000

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