Finite Group Databasebeta

← Group #13172156

Character table — Group #13172156

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order122233366666666623336666666666666666644441212121236666666666662444121212121212121212121212121212121212121212122266661212121212121212244446666121212121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-11-111111-1-1111111111111111111-1-1-1-1-111111-1-1-11-1-1-111-1-111-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-111111111111111111111-1-1-1-1-111111111-1-111111111-1-111111-1-1-1-1-111-1-111-1-1-1-1-1-1-111-1-1-1
χ4111111111111111111111111111111111111111-1-111111111111111111-11-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-111-1-1-1-1111
χ51111111111111111111111111111111111111-1-111-1-1-1-111111111111111-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111111-1-1-11-1-111-1-1-1-11-1-1
χ61111111111111111111111111111111111111-1-111-1-1-1-11111111111111-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-111-111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-11-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-111-11-1-1-111-1-111-1-1-111
χ81111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91111111111111111-1111-1-1-1-1111-1-1-1-1111111111111111-1-1-1-1-1111-1-1-1-11-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1111111-1-111-1-1-1-1-1-1-11111-1-1-1-11-111-1
χ101111111111111111-1111-1-1-1-1111-1-1-1-1111111111111111-1-1-1-1-1111-1-1-1-1-1-11-1-1-1111111-1-1-1-1111111-1-1-1-111-1-1-1-11-111-1-1111-11-1-11111-1-1-11-1-11
χ111111111111111111-1111-1-1-1-1111-1-1-1-111111111-1-111111-1-1-1-1-1111-1-1-1-11-1-1111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-11-1-111-1-111-11-1-1-111111-1-1-11
χ121111111111111111-1111-1-1-1-1111-1-1-1-111111111-1-111111-1-1-1-1-1111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-111-11-1-1-1-111-1111-1
χ131111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-111-1-1-1-11-1-1-1-1-1111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-11111-1-111-1-1-1-1-111-11-1-1-1-111-111-11
χ141111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-111-1-1-1-11-1-1-1-1-1111-1-1-1-1-111-1-1-11111-1-1111111-1-1-1-11111-1-1-1-1-1-11-111-1-11111-11-1-1-111111-1-11-1
χ151111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1111-1-1-1-111-1111-1-1-1-1-1-11111-1-1-1-1-1-11111111111-11-1-111-1-11-11-1-11111-1-1-11-11-1
χ161111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1111-1-1-1-1-111111-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-11111-1-1-1-11-11-11
χ17222222-1-12-122222-122-1-1222222-12222-1-1-1-1-1200220000-1-1-1-1-1-1-1-1-1-1-1-1-1202222-1-1-1-10000002200000000002-1-1-12-1-1-1-1-1-1-12000200-1-10000-100
χ18222222-1-12-122222-122-1-1222222-12222-1-1-1-1-1200220000-1-1-1-1-1-1-1-1-1-1-1-1-1-20-2222-1-111000000220000000000-2111-2-1-1-1-1-111-2000-200110000100
χ19222222-1-12-122222-122-1-1222222-12222-1-1-1-1-1200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-1202-2-2-211-1-1000000-2-200000000002-1-1-1211111-1-1-2000-200110000100
χ20222222-1-12-122222-122-1-1222222-12222-1-1-1-1-1200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-1-20-2-2-2-21111000000-2-20000000000-2111-211111112000200-1-10000-100
χ21222222-1-12-122222-1-22-1-1-2-2-2-222-1-2-2-2-2-1-1-1-1-1200220000-111111-1-1-1111120-2-2-2-2-1-1110000002200000000002-1-1-1-21-1-11111-2000200110000-100
χ22222222-1-12-122222-1-22-1-1-2-2-2-222-1-2-2-2-2-1-1-1-1-1200220000-111111-1-1-11111-202-2-2-2-1-1-1-1000000220000000000-211121-1-111-1-12000-200-1-10000100
χ23222222-1-12-122222-1-22-1-1-2-2-2-222-1-2-2-2-2-1-1-1-1-1200-2-20000-111111-1-1-1111120-22221111000000-2-200000000002-1-1-1-2-111-1-1112000-200-1-10000100
χ24222222-1-12-122222-1-22-1-1-2-2-2-222-1-2-2-2-2-1-1-1-1-1200-2-20000-111111-1-1-11111-20222211-1-1000000-2-20000000000-21112-111-1-1-1-1-2000200110000-100
χ2522222-122-12222-1-122-1-1222-1-1-1-1-1-1-1-1-122-1-12-12222-1-1-1-1-12-1-122-1-1-1-1-1-1-10202-1-122002222-1-1-1-1-1-1-1-1-1-1-1-122000002-1-1-1-10002000-1-100-1-100000
χ2622222-122-12222-1-122-1-1222-1-1-1-1-1-1-1-1-122-1-12-122-2-2-1-1-1-1-12-1-122-1-1-1-1-1-1-1020-211-2-2002222-1-111-1-1-1-1-1-1-1-1-2-200000-21111000-200011001100000
χ2722222-122-12222-1-122-1-1222-1-1-1-1-1-1-1-1-122-1-12-1-2-2221111-12-1-122-1-1-1-1-1-1-10-202-1-12200-2-2-2-211-1-111111111-2-2000002-1-1-1-1000-200011001100000
χ2822222-122-12222-1-122-1-1222-1-1-1-1-1-1-1-1-122-1-12-1-2-2-2-21111-12-1-122-1-1-1-1-1-1-10-20-211-2-200-2-2-2-21111111111112200000-211110002000-1-100-1-100000
χ2922222-122-12222-1-12-2-1-12-2-211-1-1-1111122-1-12-12222-1-1-1-1-1-211-2-2-1-1-111110-20-211220022-2-211-1-1-1-1-1-111112200000-2-1-111000-2000-1-1001100000
χ3022222-122-12222-1-12-2-1-12-2-211-1-1-1111122-1-12-122-2-2-1-1-1-1-1-211-2-2-1-1-111110-202-1-1-2-20022-2-21111-1-1-1-11111-2-200000211-1-100020001100-1-100000
χ3122222-122-12222-1-12-2-1-12-2-211-1-1-1111122-1-12-1-2-2221111-1-211-2-2-1-1-11111020-2112200-2-222-1-1-1-11111-1-1-1-1-2-200000-2-1-11100020001100-1-100000
χ3222222-122-12222-1-12-2-1-12-2-211-1-1-1111122-1-12-1-2-2-2-21111-1-211-2-2-1-1-111110202-1-1-2-200-2-222-1-1111111-1-1-1-12200000211-1-1000-2000-1-1001100000
χ332222-122222-1-1-12222-12-1-1-122-1-12-1-1-1-1-1-122-1-122002222-1222-1-1-1-1-1-1-1-1-12220000022-1-1-1-12200-1-1-1-1-1-1-1-100-12-1-1-100000-1-100220000000-1-1000
χ342222-122222-1-1-12222-12-1-1-122-1-12-1-1-1-1-1-122-1-122002222-1222-1-1-1-1-1-1-1-1-1-22-200000-2-2-1-1-1-12200-1-1-1-1-1-1-1-1001-2111000001100-2-2000000011000
χ352222-122222-1-1-12222-12-1-1-122-1-12-1-1-1-1-1-122-1-1-2-200-2-2-2-2-1222-1-1-1-1-1-1-1-1-12-2200000221111-2-2001111111100-12-1-1-100000-1-100-2-2000000011000
χ362222-122222-1-1-12222-12-1-1-122-1-12-1-1-1-1-1-122-1-1-2-200-2-2-2-2-1222-1-1-1-1-1-1-1-1-1-2-2-200000-2-21111-2-20011111111001-2111000001100220000000-1-1000
χ372222-122222-1-1-1222-2-12-111-2-2-1-121111-1-122-1-122002222-1-2-2-211-1-1-111112-2-200000-2-2-1-111-2-200-1-1-1-1111100-12-1-11000001100-220000000-11000
χ382222-122222-1-1-1222-2-12-111-2-2-1-121111-1-122-1-122002222-1-2-2-211-1-1-11111-2-220000022-1-111-2-200-1-1-1-11111001-211-100000-1-1002-200000001-1000
χ392222-122222-1-1-1222-2-12-111-2-2-1-121111-1-122-1-1-2-200-2-2-2-2-1-2-2-211-1-1-1111122-200000-2-211-1-122001111-1-1-1-100-12-1-110000011002-200000001-1000
χ402222-122222-1-1-1222-2-12-111-2-2-1-121111-1-122-1-1-2-200-2-2-2-2-1-2-2-211-1-1-11111-222000002211-1-122001111-1-1-1-1001-211-100000-1-100-220000000-11000
χ412-22-22222-2-22-2-22-2-2022200002-2200002-2-2-2-2-22i−2i2i−2i2i2i−2i−2i2000002-2-200000000002i−2i002i−2i00002i−2i2i2i−2i−2i00002-20000002i−2i0000000002-2000000000
χ422-22-22222-2-22-2-22-2-2022200002-2200002-2-2-2-2-22i−2i−2i2i2i2i−2i−2i2000002-2-20000000000−2i2i002i−2i0000−2i2i2i2i−2i−2i0000-22000000−2i2i000000000-22000000000
χ432-22-22222-2-22-2-22-2-2022200002-2200002-2-2-2-2-2−2i2i2i−2i−2i−2i2i2i2000002-2-200000000002i−2i00−2i2i00002i−2i−2i−2i2i2i0000-220000002i−2i000000000-22000000000
χ442-22-22222-2-22-2-22-2-2022200002-2200002-2-2-2-2-2−2i2i−2i2i−2i−2i2i2i2000002-2-20000000000−2i2i00−2i2i0000−2i2i−2i−2i2i2i00002-2000000−2i2i0000000002-2000000000
χ452-22-22-1221-22-2-2-11-20-1-1200−i3i3-11-1−i3−i3i3i32-211-212i−2i2i−2i−i−iii-10−i3i300-111−i3−i3i3i300003−32i−2i002i−2i003−3−ii−i−iii33−3−32-2000000−ii3−30000000-1100−i3i300000
χ462-22-22-1221-22-2-2-11-20-1-1200−i3i3-11-1−i3−i3i3i32-211-212i−2i−2i2i−i−iii-10−i3i300-111−i3−i3i3i30000−33−2i2i002i−2i003−3i−i−i−iii33−3−3-22000000i−i−3300000001-100i3−i300000
χ472-22-22-1221-22-2-2-11-20-1-1200−i3i3-11-1−i3−i3i3i32-211-21−2i2i2i−2iii−i−i-10−i3i300-111−i3−i3i3i300003−32i−2i00−2i2i00−33−iiii−i−i−3−333-22000000−ii3−300000001-100i3−i300000
χ482-22-22-1221-22-2-2-11-20-1-1200−i3i3-11-1−i3−i3i3i32-211-21−2i2i−2i2iii−i−i-10−i3i300-111−i3−i3i3i30000−33−2i2i00−2i2i00−33i−iii−i−i−3−3332-2000000i−i−330000000-1100−i3i300000
χ492-22-22-1221-22-2-2-11-20-1-1200i3−i3-11-1i3i3−i3−i32-211-212i−2i2i−2i−i−iii-10i3−i300-111i3i3−i3−i30000−332i−2i002i−2i00−33−ii−i−iii−3−3332-2000000−ii−330000000-1100i3−i300000
χ502-22-22-1221-22-2-2-11-20-1-1200i3−i3-11-1i3i3−i3−i32-211-212i−2i−2i2i−i−iii-10i3−i300-111i3i3−i3−i300003−3−2i2i002i−2i00−33i−i−i−iii−3−333-22000000i−i3−300000001-100−i3i300000
χ512-22-22-1221-22-2-2-11-20-1-1200i3−i3-11-1i3i3−i3−i32-211-21−2i2i2i−2iii−i−i-10i3−i300-111i3i3−i3−i30000−332i−2i00−2i2i003−3−iiii−i−i33−3−3-22000000−ii−3300000001-100−i3i300000
χ522-22-22-1221-22-2-2-11-20-1-1200i3−i3-11-1i3i3−i3−i32-211-21−2i2i−2i2iii−i−i-10i3−i300-111i3i3−i3−i300003−3−2i2i00−2i2i003−3i−iii−i−i33−3−32-2000000i−i3−30000000-1100i3−i300000
χ5344444-2-2-2-2-2444-2-2-24-21-244-2-2-2-21-2-2-2-2-2-211-2-2004400001-211-2-211111110004-2-2-2-200000000-2-2000000000000000-21111000000000000000000
χ5444444-2-2-2-2-2444-2-2-24-21-244-2-2-2-21-2-2-2-2-2-211-2-200-4-400001-211-2-21111111000-4222200000000220000000000000002-1-1-1-1000000000000000000
χ5544444-2-2-2-2-2444-2-2-2-4-21-2-4-422-2-212222-2-211-2-20044000012-1-122111-1-1-1-1000-422-2-200000000-2-2000000000000000211-1-1000000000000000000
χ5644444-2-2-2-2-2444-2-2-2-4-21-2-4-422-2-212222-2-211-2-200-4-4000012-1-122111-1-1-1-10004-2-2220000000022000000000000000-2-1-111000000000000000000
χ574444-24-2-24-2-2-2-244-24-2-21-2-244-2-2-2-2-2-2-211-2-21-2000000001-2-2-211111111140400000-2-2000000000000000000-2-211-200000110000000000000000
χ584444-24-2-24-2-2-2-244-24-2-21-2-244-2-2-2-2-2-2-211-2-21-2000000001-2-2-2111111111-40-4000002200000000000000000022-1-1200000-1-10000000000000000
χ594444-24-2-24-2-2-2-244-2-4-2-2122-4-4-2-2-2222211-2-21-2000000001222-1-1111-1-1-1-140-40000022000000000000000000-2-211200000-1-10000000000000000
χ604444-24-2-24-2-2-2-244-2-4-2-2122-4-4-2-2-2222211-2-21-2000000001222-1-1111-1-1-1-1-40400000-2-200000000000000000022-1-1-200000110000000000000000
χ614444-2-244-24-2-2-2-2-2441-2-2-2-2-2-211-21111-2-2-2-2-214400-2-2-2-214-2-2-2-211111110400000000-2-2-2-2-2-20011111111000000000000000000000000000000
χ624444-2-244-24-2-2-2-2-2441-2-2-2-2-2-211-21111-2-2-2-2-21-4-400222214-2-2-2-211111110-40000000022222200-1-1-1-1-1-1-1-1000000000000000000000000000000
χ634444-2-244-24-2-2-2-2-24-41-2-2222211-2-1-1-1-1-2-2-2-2-214400-2-2-2-21-42222111-1-1-1-10-400000000-2-22222001111-1-1-1-1000000000000000000000000000000
χ644444-2-244-24-2-2-2-2-24-41-2-2222211-2-1-1-1-1-2-2-2-2-21-4-40022221-42222111-1-1-1-1040000000022-2-2-2-200-1-1-1-11111000000000000000000000000000000
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χ6944-4-44-24-424-44-42-2-40-2-2400002220000-4-4-224-200002i3−2i32i3−2i3-2000002-2200000000000000000000002i3−2i32i3−2i30000000000000000000000000000000000
χ7044-4-4-244-4-442-22-44-40-24-2−2i32i30022-4−2i32i3−2i32i3224-4-2-200000000-2000−2i32i32-22−2i32i3−2i32i300000000000000000000000000000000000000000000000000000000
χ7144-4-4-244-4-442-22-44-40-24-22i3−2i30022-42i3−2i32i3−2i3224-4-2-200000000-20002i3−2i32-222i3−2i32i3−2i300000000000000000000000000000000000000000000000000000000
χ7244-4-4-24-22-4-22-22-4420-2-21−2i32i300222−2i32i3−2i32i3-1-1-221-2000000001000i3−i3-11-1i3−i3i3−i300000000−2i32i3000000000000000000003-3000000i3−i30000000000000000
χ7344-4-4-24-22-4-22-22-4420-2-21−2i32i300222−2i32i3−2i32i3-1-1-221-2000000001000i3−i3-11-1i3−i3i3−i3000000002i3−2i300000000000000000000-33000000−i3i30000000000000000
χ7444-4-4-24-22-4-22-22-4420-2-212i3−2i3002222i3−2i32i3−2i3-1-1-221-2000000001000−i3i3-11-1−i3i3−i3i300000000−2i32i300000000000000000000-33000000i3−i30000000000000000
χ7544-4-4-24-22-4-22-22-4420-2-212i3−2i3002222i3−2i32i3−2i3-1-1-221-2000000001000−i3i3-11-1−i3i3−i3i3000000002i3−2i3000000000000000000003-3000000−i3i30000000000000000
χ7644-4-4-2-24-4242-222-2-401-2-2−2i32i300-1-12i3−i3i3−i322-22-210000−2i32i3−2i32i31000−2i32i3-11-1i3−i3i3−i3000000000000000000i3−i3i3−i33-33-3000000000000000000000000000000
χ7744-4-4-2-24-4242-222-2-401-2-2−2i32i300-1-12i3−i3i3−i322-22-2100002i3−2i32i3−2i31000−2i32i3-11-1i3−i3i3−i3000000000000000000−i3i3−i3i3-33-33000000000000000000000000000000
χ7844-4-4-2-24-4242-222-2-401-2-22i3−2i300-1-12−i3i3−i3i322-22-210000−2i32i3−2i32i310002i3−2i3-11-1−i3i3−i3i3000000000000000000i3−i3i3−i3-33-33000000000000000000000000000000
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χ804-44-444-2-2-424-4-44-4204-2-200004-4-20000-22222-4004i−4i0000-200000-2220000000000−2i2i000000004i−4i0000000000000000−2i2i00000000000000000000
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χ874-44-4-2444-4-4-2224-4-40-24-20000-2240000-22-4-422−4i4i00−4i−4i4i4i-200000-222000000000000002i−2i0000002i2i−2i−2i0000000000000000000000000000000000
χ884-44-4-2-2442-4-222-22-401-2-200−2i32i31-1-2i3i3−i3−i3-22222-14i−4i00−2i−2i2i2i10−2i32i3001-1-1i3i3−i3−i30000000000−2i2i0023−2300ii−i−i−3−333000000000000000000000000000000
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χ984-4-44-244-44-422-2-4-440-24-200002-2-400002-2-442200000000-20000022-20000000000000000−232300000000−232323−23000000000000000000000000000000
χ994-4-44-2-24-4-2-422-222401-2-20000-1123-3-332-22-22-1000023−23−2323100000-1-113-3-3300000000000023−230000−333−3−333−3000000000000000000000000000000
χ1004-4-44-2-24-4-2-422-222401-2-20000-1123-3-332-22-22-10000−232323−23100000-1-113-3-33000000000000−232300003−3−333−3−33000000000000000000000000000000
χ1014-4-44-2-24-4-2-422-222401-2-20000-112-333-32-22-22-1000023−23−2323100000-1-11-333-3000000000000−23230000−333−33−3−33000000000000000000000000000000
χ1024-4-44-2-24-4-2-422-222401-2-20000-112-333-32-22-22-10000−232323−23100000-1-11-333-300000000000023−2300003−3−33−333−3000000000000000000000000000000
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χ10688-8-8-4-4-444-44-444-440222−4i34i300-2-2-22i3−2i32i3−2i3-2-22-22200000000-10002i3−2i31-11−i3i3−i3i300000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-444-44-444-4402224i3−4i300-2-2-2−2i32i3−2i32i3-2-22-22200000000-1000−2i32i31-11i3−i3i3−i300000000000000000000000000000000000000000000000000000000
χ1088-88-8-48-4-4-84-4448-840-4-420000-44-400002-244-24000000002000002-2-2000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-4-444-444-444022200−4i34i32-222i32i3−2i3−2i32-2-2-2-2-200000000-102i3−2i300-111−i3−i3i3i300000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-4-444-444-4440222004i3−4i32-22−2i3−2i32i32i32-2-2-2-2-200000000-10−2i32i300-111i3i3−i3−i300000000000000000000000000000000000000000000000000000000
χ1118-8-888-4-44-44-8-8844-40-42-400004-4-200004-4-224400000000200000-2-22000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-48-448444-4-8-8-40-4-4200004-440000-224-4-2400000000200000-2-22000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-44-4444-444-402220000-22-26-6-66-22-22-2-200000000-10000011-1-333-300000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-44-4444-444-402220000-22-2-666-6-22-22-2-200000000-10000011-13-3-3300000000000000000000000000000000000000000000000000000000

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