Finite Group Databasebeta

← Group #13172338

Character table — Group #13172338

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order122233366666666623336666666666666666644441212121236666666666662444661212121212121212121212121212121212121212446661212121212121212122244466121212126121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-111-1-1-11111111111111111111111-1-1-11-1-11111-1-11-1-1-1-11111-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-11111111111111111111-1111-1-1111111-1-1-1-111111111-1-1111-111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111111-1-111111111111111111-11-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1111-1-111
χ51111111111111111111111111111111111111-1-111-1-1-1-111111111111111-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-11-1-11-1-1-1-1111-1-1-1-1
χ61111111111111111111111111111111111111-1-111-1-1-1-11111111111111-1-11-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-1-1-1111-1-1-1-11111-1-1-1-1-111
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
χ91111111111111111-1111-1-1-1-1111-1-1-1-1111111111111111-1-1-1-1-1111-1-1-1-11-1-1-1111111-1-1-1-1-1-1111111-1-1-1-111111-1-1-111-1-1-1-1-1-1-111-1-11111-11-11-1
χ101111111111111111-1111-1-1-1-1111-1-1-1-1111111111111111-1-1-1-1-1111-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-111-111-1-1-1-111-1-11-11-11
χ111111111111111111-1111-1-1-1-1111-1-1-1-111111111-1-111111-1-1-1-1-1111-1-1-1-11-11-111-1-111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111-11-111-1-1-1-111-1-11
χ121111111111111111-1111-1-1-1-1111-1-1-1-111111111-1-111111-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1111-1-111111-11-1111-1-111-1-111-1
χ131111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-111-1-1-1-11-1-1-1-1-1111-1-1-1-111-1-11111-1-11111-1-111-1-1-1-11111-1-1111-1-1-111-1-1-1-11-11-1111-1-111-1-11-11
χ141111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-111-1-1-1-11-1-1-1-1-1111-1-1-1-1-11-11-1-111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-11111-11-111-1-1-1-111-11-1
χ151111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1111-1-1-1-1111-111-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-111-1-1-111-1-1-1-111-1-11-111-1
χ161111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1111-1-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1111-1-11111-1-1-111-1-11111-11-1-11
χ17222222-1-12-122222-122-1-1222222-12222-1-1-1-1-1200220000-1-1-1-1-1-1-1-1-1-1-1-1-12022-1-12200000022-1-100000000002-1-1-1-12-1-1-1-1-1-1020020000-1-1-10000
χ18222222-1-12-122222-122-1-1222222-12222-1-1-1-1-1200220000-1-1-1-1-1-1-1-1-1-1-1-1-1-202-2112200000022-1-10000000000-211-11-2-1-1-1-1110-200-200001110000
χ19222222-1-12-122222-122-1-1222222-12222-1-1-1-1-1200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-120-22-1-1-2-2000000-2-21100000000002-1-11-121111-1-10-200-200001110000
χ20222222-1-12-122222-122-1-1222222-12222-1-1-1-1-1200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-1-20-2-211-2-2000000-2-2110000000000-21111-2111111020020000-1-1-10000
χ21222222-1-12-122222-1-22-1-1-2-2-2-222-1-2-2-2-2-1-1-1-1-1200220000-111111-1-1-1111120-2-2-1-122000000-2-2-1-100000000002-1-111-2-1-111110-20020000-1-110000
χ22222222-1-12-122222-1-22-1-1-2-2-2-222-1-2-2-2-2-1-1-1-1-1200220000-111111-1-1-11111-20-221122000000-2-2-1-10000000000-2111-12-1-111-1-10200-2000011-10000
χ23222222-1-12-122222-1-22-1-1-2-2-2-222-1-2-2-2-2-1-1-1-1-1200-2-20000-111111-1-1-11111202-2-1-1-2-2000000221100000000002-1-1-11-211-1-1110200-2000011-10000
χ24222222-1-12-122222-1-22-1-1-2-2-2-222-1-2-2-2-2-1-1-1-1-1200-2-20000-111111-1-1-11111-202211-2-200000022110000000000-211-1-1211-1-1-1-10-20020000-1-110000
χ2522222-122-12222-1-122-1-1222-1-1-1-1-1-1-1-1-122-1-12-12222-1-1-1-1-12-1-122-1-1-1-1-1-1-1022000-1-12222-1-1-1-122-1-1-1-1-1-1-1-122000200-1-1-1-10020000-1-1-1-10000000
χ2622222-122-12222-1-122-1-1222-1-1-1-1-1-1-1-1-122-1-12-122-2-2-1-1-1-1-12-1-122-1-1-1-1-1-1-102-2000112222-1-111-2-2-1-1-1-1-1-1-1-1-2-2000-200111100-2000011110000000
χ2722222-122-12222-1-122-1-1222-1-1-1-1-1-1-1-1-122-1-12-1-2-2221111-12-1-122-1-1-1-1-1-1-10-22000-1-1-2-2-2-211-1-12211111111-2-2000200-1-1-1-100-2000011110000000
χ2822222-122-12222-1-122-1-1222-1-1-1-1-1-1-1-1-122-1-12-1-2-2-2-21111-12-1-122-1-1-1-1-1-1-10-2-200011-2-2-2-21111-2-21111111122000-20011110020000-1-1-1-10000000
χ2922222-122-12222-1-12-2-1-12-2-211-1-1-1111122-1-12-12222-1-1-1-1-1-211-2-2-1-1-111110-2-2000-1-122-2-2111122-1-1-1-1111122000-200-1-11100-2000011-1-10000000
χ3022222-122-12222-1-12-2-1-12-2-211-1-1-1111122-1-12-122-2-2-1-1-1-1-1-211-2-2-1-1-111110-220001122-2-211-1-1-2-2-1-1-1-11111-2-200020011-1-10020000-1-1110000000
χ3122222-122-12222-1-12-2-1-12-2-211-1-1-1111122-1-12-1-2-2221111-1-211-2-2-1-1-1111102-2000-1-1-2-222-1-111221111-1-1-1-1-2-2000-200-1-1110020000-1-1110000000
χ3222222-122-12222-1-12-2-1-12-2-211-1-1-1111122-1-12-1-2-2-2-21111-1-211-2-2-1-1-1111102200011-2-222-1-1-1-1-2-21111-1-1-1-12200020011-1-100-2000011-1-10000000
χ332222-122222-1-1-12222-12-1-1-122-1-12-1-1-1-1-1-122-1-122002222-1222-1-1-1-1-1-1-1-1-122022200-1-1-1-1220000-1-1-1-1-1-1-1-100-1-1-102-10000-1-1002200000000-1-100
χ342222-122222-1-1-12222-12-1-1-122-1-12-1-1-1-1-1-122-1-122002222-1222-1-1-1-1-1-1-1-1-1-220-2-2-200-1-1-1-1220000-1-1-1-1-1-1-1-1001110-2100001100-2-2000000001100
χ352222-122222-1-1-12222-12-1-1-122-1-12-1-1-1-1-1-122-1-1-2-200-2-2-2-2-1222-1-1-1-1-1-1-1-1-12-20222001111-2-200001111111100-1-1-102-10000-1-100-2-2000000001100
χ362222-122222-1-1-12222-12-1-1-122-1-12-1-1-1-1-1-122-1-1-2-200-2-2-2-2-1222-1-1-1-1-1-1-1-1-1-2-20-2-2-2001111-2-2000011111111001110-21000011002200000000-1-100
χ372222-122222-1-1-1222-2-12-111-2-2-1-121111-1-122-1-122002222-1-2-2-211-1-1-111112-20-22200-1-111-2-20000-1-1-1-1111100-1-1-10-2100001100-2200000000-1100
χ382222-122222-1-1-1222-2-12-111-2-2-1-121111-1-122-1-122002222-1-2-2-211-1-1-11111-2-202-2-200-1-111-2-20000-1-1-1-111110011102-10000-1-1002-2000000001-100
χ392222-122222-1-1-1222-2-12-111-2-2-1-121111-1-122-1-1-2-200-2-2-2-2-1-2-2-211-1-1-11111220-2220011-1-12200001111-1-1-1-100-1-1-10-21000011002-2000000001-100
χ402222-122222-1-1-1222-2-12-111-2-2-1-121111-1-122-1-1-2-200-2-2-2-2-1-2-2-211-1-1-11111-2202-2-20011-1-12200001111-1-1-1-10011102-10000-1-100-2200000000-1100
χ412-22-22222-2-22-2-22-2-2022200002-2200002-2-2-2-2-22i−2i2i−2i2i2i−2i−2i2000002-2-200000000002i−2i2i−2i0000002i−2i2i2i−2i−2i00002-20000002i−2i000000000002-20000000
χ422-22-22222-2-22-2-22-2-2022200002-2200002-2-2-2-2-22i−2i−2i2i2i2i−2i−2i2000002-2-20000000000−2i2i2i−2i000000−2i2i2i2i−2i−2i0000-22000000−2i2i00000000000-220000000
χ432-22-22222-2-22-2-22-2-2022200002-2200002-2-2-2-2-2−2i2i2i−2i−2i−2i2i2i2000002-2-200000000002i−2i−2i2i0000002i−2i−2i−2i2i2i0000-220000002i−2i00000000000-220000000
χ442-22-22222-2-22-2-22-2-2022200002-2200002-2-2-2-2-2−2i2i−2i2i−2i−2i2i2i2000002-2-20000000000−2i2i−2i2i000000−2i2i−2i−2i2i2i00002-2000000−2i2i000000000002-20000000
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−i3i3i3000000−ii2i−2i003−33−32i−2i−i−iii33−3−32-2000000−ii3−30000000−i3i3-110000000
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−i3i3i3000000i−i2i−2i003−3−33−2i2i−i−iii33−3−3-22000000i−i−330000000i3−i31-10000000
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−i3i3i3000000−ii−2i2i00−333−32i−2iii−i−i−3−333-22000000−ii3−30000000i3−i31-10000000
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−i3i3i3000000i−i−2i2i00−33−33−2i2iii−i−i−3−3332-2000000i−i−330000000−i3i3-110000000
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−i3000000−ii2i−2i00−33−332i−2i−i−iii−3−3332-2000000−ii−330000000i3−i3-110000000
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−i3000000i−i2i−2i00−333−3−2i2i−i−iii−3−333-22000000i−i3−30000000−i3i31-10000000
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−i3000000−ii−2i2i003−3−332i−2iii−i−i33−3−3-22000000−ii−330000000−i3i31-10000000
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−i3000000i−i−2i2i003−33−3−2i2iii−i−i33−3−32-2000000i−i3−30000000i3−i3-110000000
χ5344444-2-2-2-2-2444-2-2-24-21-244-2-2-2-21-2-2-2-2-2-211-2-2004400001-211-2-21111111004000-2-2000000-2-2-2-20000000000000-2001111000000000000000000
χ5444444-2-2-2-2-2444-2-2-24-21-244-2-2-2-21-2-2-2-2-2-211-2-200-4-400001-211-2-2111111100-40002200000022220000000000000200-1-1-1-1000000000000000000
χ5544444-2-2-2-2-2444-2-2-2-4-21-2-4-422-2-212222-2-211-2-20044000012-1-122111-1-1-1-100-4000-2-200000022-2-2000000000000020011-1-1000000000000000000
χ5644444-2-2-2-2-2444-2-2-2-4-21-2-4-422-2-212222-2-211-2-200-4-4000012-1-122111-1-1-1-100400022000000-2-2220000000000000-200-1-111000000000000000000
χ574444-24-2-24-2-2-2-244-24-2-21-2-244-2-2-2-2-2-2-211-2-21-2000000001-2-2-21111111114004-2-20000000000000000000000-2110-2-20000110000000000000000
χ584444-24-2-24-2-2-2-244-24-2-21-2-244-2-2-2-2-2-2-211-2-21-2000000001-2-2-2111111111-400-42200000000000000000000002-1-10220000-1-10000000000000000
χ594444-24-2-24-2-2-2-244-2-4-2-2122-4-4-2-2-2222211-2-21-2000000001222-1-1111-1-1-1-1400-4-2-20000000000000000000000-2110220000-1-10000000000000000
χ604444-24-2-24-2-2-2-244-2-4-2-2122-4-4-2-2-2222211-2-21-2000000001222-1-1111-1-1-1-1-40042200000000000000000000002-1-10-2-20000110000000000000000
χ614444-2-244-24-2-2-2-2-2441-2-2-2-2-2-211-21111-2-2-2-2-214400-2-2-2-214-2-2-2-2111111104000000-2-2-2-2-2-2000011111111000000000000000000000000000000
χ624444-2-244-24-2-2-2-2-2441-2-2-2-2-2-211-21111-2-2-2-2-21-4-400222214-2-2-2-211111110-40000002222220000-1-1-1-1-1-1-1-1000000000000000000000000000000
χ634444-2-244-24-2-2-2-2-24-41-2-2222211-2-1-1-1-1-2-2-2-2-214400-2-2-2-21-42222111-1-1-1-10-4000000-2-2222200001111-1-1-1-1000000000000000000000000000000
χ644444-2-244-24-2-2-2-2-24-41-2-2222211-2-1-1-1-1-2-2-2-2-21-4-40022221-42222111-1-1-1-10400000022-2-2-2-20000-1-1-1-11111000000000000000000000000000000
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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−i30000−2i32i300000000000000000000000i3−i300000003-30000000000000000
χ7344-4-4-24-22-4-22-22-4420-2-21−2i32i300222−2i32i3−2i32i3-1-1-221-2000000001000i3−i3-11-1i3−i3i3−i300002i3−2i300000000000000000000000−i3i30000000-330000000000000000
χ7444-4-4-24-22-4-22-22-4420-2-212i3−2i3002222i3−2i32i3−2i3-1-1-221-2000000001000−i3i3-11-1−i3i3−i3i30000−2i32i300000000000000000000000i3−i30000000-330000000000000000
χ7544-4-4-24-22-4-22-22-4420-2-212i3−2i3002222i3−2i32i3−2i3-1-1-221-2000000001000−i3i3-11-1−i3i3−i3i300002i3−2i300000000000000000000000−i3i300000003-30000000000000000
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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χ1004-4-44-2-24-4-2-422-222401-2-20000-1123-3-332-22-22-10000−232323−23100000-1-113-3-330000000000−23230000003−3−333−3−33000000000000000000000000000000
χ1014-4-44-2-24-4-2-422-222401-2-20000-112-333-32-22-22-1000023−23−2323100000-1-11-333-30000000000−2323000000−333−33−3−33000000000000000000000000000000
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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
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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).