Finite Group Databasebeta

← Group #13169454

Character table — Group #13169454

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order122233366666666633346666666661212121212121212444412121212366612121212121212121244441212121212121212121212121212121212121212121244121212121212121212121212244441212121212126121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-111-111-1-1111111111111111111111-1-1-1-1-1-1-11111-1-1-11-1-1-11111-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-11111111111111111111-111111-1-111-1-1-1-11111111111-1-1-11111111-1-1-1-1-11-1-11-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111111-1-111111111111111111-11-1-111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-11-1-111
χ51111111111111111111111111111111111111-1-111-1-1-1-111111111111111-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-11-1-111-1-1-1-11-1-1-1-1
χ61111111111111111111111111111111111111-1-111-1-1-1-11111111111111-1-11-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-11111-11-1-11-1-1-1-1-1-1-11111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111111-1-1-1-1-1-1-11-1-1-11111-1-1-111
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
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-111-11-1111-1-111-1-11-1-1-11-1-111-1-111-11-1
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-111-1-1111111-1-1-1-111-1-11-1-1-11111-1-1-111-1-11111-1-1-1-11-11
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1111-1-1-1-111-1-111111-1-111-11-1-11
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-11-11-1-1-111-1-11111-11-1-1-1-1-1111-111-1
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-11-1111-1-111-1-111-11-1-1-1-1-1111-11-11
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-111111111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-11111-1-1-1-111111-1-111-11-11-1
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-111-1-1-1-111-1-111-1-1-1-1-1-111111111-1111-1-1-1-111-111-1-11111-1-1-1-111-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111-1-111-1-111-1-1-1-1-1-11111111-11-1-1-111-1-1111-1-1-11-1-111-1-111-1-11
χ17222222-122-1-12-12222-1-12-1-12-122-1-1-12222222200220000-1-1-1-1-1-1-1-1-1-1-1-1-1202200-1-1-1-1002222000000000000-1-122-1-1-1-1-1-1-1-120200-1-10000-10000
χ18222222-122-1-12-12222-1-12-1-12-122-1-1-12222222200220000-1-1-1-1-1-1-1-1-1-1-1-1-1-202-20011-1-1002222000000000000-11-2-21111-1-1-1-1-20-20011000010000
χ19222222-122-1-12-12222-1-12-1-12-122-1-1-12222222200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-120-2200-1-11100-2-2-2-20000000000001-122-1-1-1-11111-20-20011000010000
χ20222222-122-1-12-12222-1-12-1-12-122-1-1-12222222200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-1-20-2-200111100-2-2-2-200000000000011-2-21111111120200-1-10000-10000
χ21222222-122-1-12-12222-1-1-2-1-12-122-1-1-1-2-2-2-2-2-2-2-200220000-1-1-1-111111111120-2-20011-1-10022-2-20000000000001-1-22-1-111-1-11120-200110000-10000
χ22222222-122-1-12-12222-1-1-2-1-12-122-1-1-1-2-2-2-2-2-2-2-200220000-1-1-1-1111111111-20-2200-1-1-1-10022-2-2000000000000112-211-1-1-1-111-20200-1-1000010000
χ23222222-122-1-12-12222-1-1-2-1-12-122-1-1-1-2-2-2-2-2-2-2-200-2-20000-1-1-1-1111111111202-200111100-2-222000000000000-1-1-22-1-11111-1-1-20200-1-1000010000
χ24222222-122-1-12-12222-1-1-2-1-12-122-1-1-1-2-2-2-2-2-2-2-200-2-20000-1-1-1-1111111111-202200-1-11100-2-222000000000000-112-211-1-111-1-120-200110000-10000
χ2522222-122-12222-1-12-12-122-1-12-1-1-1-12-1-122-1-1-1-122002222-1-1-1-1222-1-1-1-1-1-12202-1-12200220000-1-1-1-1-1-1-1-1-1-10002-1-1-1-1-1-10000020020000000-1-100
χ2622222-122-12222-1-12-12-122-1-12-1-1-1-12-1-122-1-1-1-122002222-1-1-1-1222-1-1-1-1-1-1-220-2-1-1-2-200220000-1-1-1-1-1-1-1-1-1-1000-211111100000-200-200000001100
χ2722222-122-12222-1-12-12-122-1-12-1-1-1-12-1-122-1-1-1-1-2-200-2-2-2-2-1-1-1-1222-1-1-1-1-1-12-202112200-2-2000011111111110002-1-1-1-1-1-100000-200-200000001100
χ2822222-122-12222-1-12-12-122-1-12-1-1-1-12-1-122-1-1-1-1-2-200-2-2-2-2-1-1-1-1222-1-1-1-1-1-1-2-20-211-2-200-2-200001111111111000-21111110000020020000000-1-100
χ2922222-122-12222-1-12-12-1-22-1-12-1-1-1-1211-2-2111122002222-1-1-1-1-2-2-21111112-20-211-2-200-2-20000-1-1-1-1-1-1111100021-1-1-11100000-20020000000-1100
χ3022222-122-12222-1-12-12-1-22-1-12-1-1-1-1211-2-2111122002222-1-1-1-1-2-2-2111111-2-202112200-2-20000-1-1-1-1-1-11111000-2-1111-1-100000200-200000001-100
χ3122222-122-12222-1-12-12-1-22-1-12-1-1-1-1211-2-21111-2-200-2-2-2-2-1-1-1-1-2-2-2111111220-2-1-1-2-200220000111111-1-1-1-100021-1-1-11100000200-200000001-100
χ3222222-122-12222-1-12-12-1-22-1-12-1-1-1-1211-2-21111-2-200-2-2-2-2-1-1-1-1-2-2-2111111-2202-1-12200220000111111-1-1-1-1000-2-1111-1-100000-20020000000-1100
χ332222-122-1222-1222-1-1-122-12-1-1-1-122-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-12-1-122-1-1-1-10220220022-1-1-1-1-1-122-1-1-1-1-1-1-1-12220000000-1-1-1-10002000-1-1-1-100000
χ342222-122-1222-1222-1-1-122-12-1-1-1-122-122-1-1-1-1-1-122-2-2-1-1-1-1-1-1-1-12-1-122-1-1-1-102-202200-2-2-1-1111122-1-1-1-1-1-1-1-1-2-2-200000001111000-2000111100000
χ352222-122-1222-1222-1-1-122-12-1-1-1-122-122-1-1-1-1-1-1-2-2221111-1-1-1-12-1-122-1-1-1-10-220-2-2002211-1-1-1-1-2-211111111-2-220000000-1-1-1-1000-2000111100000
χ362222-122-1222-1222-1-1-122-12-1-1-1-122-122-1-1-1-1-1-1-2-2-2-21111-1-1-1-12-1-122-1-1-1-10-2-20-2-200-2-2111111-2-21111111122-2000000011110002000-1-1-1-100000
χ372222-122-1222-1222-1-1-12-2-12-1-1-1-122-1-2-21111112222-1-1-1-1-1-1-1-1-211-2-211110-2-20-2-2002211-1-11122-1-1-1-1111122-20000000-1-111000-2000-1-11100000
χ382222-122-1222-1222-1-1-12-2-12-1-1-1-122-1-2-211111122-2-2-1-1-1-1-1-1-1-1-211-2-211110-220-2-200-2-21111-1-122-1-1-1-11111-2-22000000011-1-1000200011-1-100000
χ392222-122-1222-1222-1-1-12-2-12-1-1-1-122-1-2-2111111-2-2221111-1-1-1-1-211-2-2111102-20220022-1-1-1-111-2-21111-1-1-1-1-2-2-20000000-1-111000200011-1-100000
χ402222-122-1222-1222-1-1-12-2-12-1-1-1-122-1-2-2111111-2-2-2-21111-1-1-1-1-211-2-2111102202200-2-2-1-111-1-1-2-21111-1-1-1-1222000000011-1-1000-2000-1-11100000
χ412-2-22222-2-22-2-2-22-222220-2-222-2-2-22-2000000002i−2i2i−2i2i2i−2i−2i2-2-22000000000000000002i−2i002i−2i002i−2i2i2i−2i−2i00002-2000000002i−2i0000000002-20000000
χ422-2-22222-2-22-2-2-22-222220-2-222-2-2-22-2000000002i−2i−2i2i2i2i−2i−2i2-2-2200000000000000000−2i2i00−2i2i002i−2i2i2i−2i−2i0000-2200000000−2i2i000000000-220000000
χ432-2-22222-2-22-2-2-22-222220-2-222-2-2-22-200000000−2i2i2i−2i−2i−2i2i2i2-2-22000000000000000002i−2i002i−2i00−2i2i−2i−2i2i2i0000-22000000002i−2i000000000-220000000
χ442-2-22222-2-22-2-2-22-222220-2-222-2-2-22-200000000−2i2i−2i2i−2i−2i2i2i2-2-2200000000000000000−2i2i00−2i2i00−2i2i−2i−2i2i2i00002-200000000−2i2i0000000002-20000000
χ452-2-22-1221-22-21-22-2-1-1-1201-2-1-111-22100−i3i3−i3−i3i3i32i−2i2i−2i−i−iii-111-10−i3i300−i3−i3i3i3000000002i−2i3−3−ii3−32i−2i−i−iii33−3−32-200000000−ii3−30000000-11−i3i300000
χ462-2-22-1221-22-21-22-2-1-1-1201-2-1-111-22100−i3i3−i3−i3i3i32i−2i−2i2i−i−iii-111-10−i3i300−i3−i3i3i300000000−2i2i3−3i−i−332i−2i−i−iii33−3−3-2200000000i−i−3300000001-1i3−i300000
χ472-2-22-1221-22-21-22-2-1-1-1201-2-1-111-22100−i3i3−i3−i3i3i3−2i2i2i−2iii−i−i-111-10−i3i300−i3−i3i3i3000000002i−2i−33−ii3−3−2i2iii−i−i−3−333-2200000000−ii3−300000001-1i3−i300000
χ482-2-22-1221-22-21-22-2-1-1-1201-2-1-111-22100−i3i3−i3−i3i3i3−2i2i−2i2iii−i−i-111-10−i3i300−i3−i3i3i300000000−2i2i−33i−i−33−2i2iii−i−i−3−3332-200000000i−i−330000000-11−i3i300000
χ492-2-22-1221-22-21-22-2-1-1-1201-2-1-111-22100i3−i3i3i3−i3−i32i−2i2i−2i−i−iii-111-10i3−i300i3i3−i3−i3000000002i−2i−33−ii−332i−2i−i−iii−3−3332-200000000−ii−330000000-11i3−i300000
χ502-2-22-1221-22-21-22-2-1-1-1201-2-1-111-22100i3−i3i3i3−i3−i32i−2i−2i2i−i−iii-111-10i3−i300i3i3−i3−i300000000−2i2i−33i−i3−32i−2i−i−iii−3−333-2200000000i−i3−300000001-1−i3i300000
χ512-2-22-1221-22-21-22-2-1-1-1201-2-1-111-22100i3−i3i3i3−i3−i3−2i2i2i−2iii−i−i-111-10i3−i300i3i3−i3−i3000000002i−2i3−3−ii−33−2i2iii−i−i33−3−3-2200000000−ii−3300000001-1−i3i300000
χ522-2-22-1221-22-21-22-2-1-1-1201-2-1-111-22100i3−i3i3i3−i3−i3−2i2i−2i2iii−i−i-111-10i3−i300i3i3−i3−i300000000−2i2i3−3i−i3−3−2i2iii−i−i33−3−32-200000000i−i3−30000000-11i3−i300000
χ5344444-2-24-2-2-24-2-2-24-2-214-21-2-2-2-211-2-2-244-2-2-2-2000000001111-2-2-2111111400400-2-2000000000000000000000-2-2-2111100000000000000000000
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χ604444-24-2-24-2-2-2-244-2-21-2-41-2-21-2-2-2-21-4-422222200-4-4000011112-1-122-1-1-1-100400000220022-2-2000000000000-20000000-1-1110000000000000000
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χ7644-4-4-2-24-22-4-4242-221-2-20-22-121-1-22223−2300−33−330000−2i32i3−2i32i311-1-100023−23−33−33000000000000000000i3−i3i3−i33i−3i3i−3i000000000000000000000000000000
χ7744-4-4-2-24-22-4-4242-221-2-20-22-121-1-22223−2300−33−3300002i3−2i32i3−2i311-1-100023−23−33−33000000000000000000−i3i3−i3i3−3i3i−3i3i000000000000000000000000000000
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χ7944-4-4-2-24-22-4-4242-221-2-20-22-121-1-222−2323003−33−300002i3−2i32i3−2i311-1-1000−23233−33−3000000000000000000−i3i3−i3i33i−3i3i−3i000000000000000000000000000000
χ804-44-4444-44-444-4-4-4-44440-44-4-4-44-4-4400000000000000004-44-400000000000000000000000000000000000000000000000000000000000000000
χ814-44-444-2-442-242-4-4-44-2-202-2-42-4422-20000000000000000-22-2200000000000000000000000000000000000000000000000000000023−23000000000
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χ844-44-44-24-4-2-444-422-4-24-20-4-22-42-22240000000000000000-22-2200000000000002i3−2i300000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ854-44-4-24424-44-2-4-4-42-2-24024222-2-4-4-200000000000023−23−2323-22-2200000000000000000000000000023−23−23230000000000000000000000000000000000
χ864-44-4-24424-44-2-4-4-42-2-24024222-2-4-4-2000000000000−232323−23-22-22000000000000000000000000000−232323−230000000000000000000000000000000000
χ874-44-4-2-242-2-44-2-42221-2-202-2-12-1122-200003i−3i−3i3i000023−23−23231-11-1000003i−3i−3i3i00002i3−2i3000000000000−333−3−i3i3i3−i3000000000000000000000000000000
χ884-44-4-2-242-2-44-2-42221-2-202-2-12-1122-200003i−3i−3i3i0000−232323−231-11-1000003i−3i−3i3i0000−2i32i30000000000003−3−33i3−i3−i3i3000000000000000000000000000000
χ894-44-4-2-242-2-44-2-42221-2-202-2-12-1122-20000−3i3i3i−3i000023−23−23231-11-100000−3i3i3i−3i0000−2i32i3000000000000−333−3i3−i3−i3i3000000000000000000000000000000
χ904-44-4-2-242-2-44-2-42221-2-202-2-12-1122-20000−3i3i3i−3i0000−232323−231-11-100000−3i3i3i−3i00002i3−2i30000000000003−3−33−i3i3i3−i3000000000000000000000000000000
χ914-4-4444-2-4-4-22-424-444-2-20224-2-4-42-2200000000004i−4i0000-222-200000000000000000−2i2i004i−4i0000000000000000000000−2i2i000000000000000000
χ924-4-4444-2-4-4-22-424-444-2-20224-2-4-42-220000000000−4i4i0000-222-2000000000000000002i−2i00−4i4i00000000000000000000002i−2i000000000000000000
χ934-4-444-24-424-4-4-4-224-24-20-42-24222-2-4000000004i−4i004i4i−4i−4i-222-20000000000000000000000000−2i2i−2i−2i2i2i0000000000000000000000000000000000
χ944-4-444-24-424-4-4-4-224-24-20-42-24222-2-400000000−4i4i00−4i−4i4i4i-222-200000000000000000000000002i−2i2i2i−2i−2i0000000000000000000000000000000000
χ954-4-44-24-22-4-22224-4-2-21-20-12-21222-2-100−2i32i3−2i3−2i32i32i3004i−4i00001-1-110i3−i300i3i3−i3−i300000000−2i2i00−2i2i23−2300000000000000000000i−i−330000000000000000
χ964-4-44-24-22-4-22224-4-2-21-20-12-21222-2-100−2i32i3−2i3−2i32i32i300−4i4i00001-1-110i3−i300i3i3−i3−i3000000002i−2i002i−2i−232300000000000000000000−ii3−30000000000000000
χ974-4-44-24-22-4-22224-4-2-21-20-12-21222-2-1002i3−2i32i32i3−2i3−2i3004i−4i00001-1-110−i3i300−i3−i3i3i300000000−2i2i00−2i2i−232300000000000000000000i−i3−30000000000000000
χ984-4-44-24-22-4-22224-4-2-21-20-12-21222-2-1002i3−2i32i32i3−2i3−2i300−4i4i00001-1-110−i3i300−i3−i3i3i3000000002i−2i002i−2i23−2300000000000000000000−ii−330000000000000000
χ994-4-44-2-24224-42-4-22-21-2-20221-2-1-12-2200−2i32i3i3i3−i3−i34i−4i00−2i−2i2i2i1-1-110−2i32i300i3i3−i3−i3000000000023−230000−2i2iii−i−i−3−333000000000000000000000000000000
χ1004-4-44-2-24224-42-4-22-21-2-20221-2-1-12-2200−2i32i3i3i3−i3−i3−4i4i002i2i−2i−2i1-1-110−2i32i300i3i3−i3−i30000000000−232300002i−2i−i−iii33−3−3000000000000000000000000000000
χ1014-4-44-2-24224-42-4-22-21-2-20221-2-1-12-22002i3−2i3−i3−i3i3i34i−4i00−2i−2i2i2i1-1-1102i3−2i300−i3−i3i3i30000000000−23230000−2i2iii−i−i33−3−3000000000000000000000000000000
χ1024-4-44-2-24224-42-4-22-21-2-20221-2-1-12-22002i3−2i3−i3−i3i3i3−4i4i002i2i−2i−2i1-1-1102i3−2i300−i3−i3i3i3000000000023−2300002i−2i−i−iii−3−333000000000000000000000000000000
χ1038888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4-4-4222200000000-1-1-1-1-42222-1-1-1-100000000000000000000000000000000000000000000000000000000
χ1048888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224444-2-2-2-200000000-1-1-1-14-2-2-2-2111100000000000000000000000000000000000000000000000000000000
χ10588-8-8-48-4-4-8444-4-884-42-40244-2-44-44-2000000000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-4-44444-44-4422202-2-2-22-22-2-243−4300−2323−232300000000-1-111000−23233−33−300000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-4-44444-44-4422202-2-2-22-22-2-2−43430023−2323−2300000000-1-11100023−23−33−3300000000000000000000000000000000000000000000000000000000
χ1088-88-88-4-4-8-44-48444-8-4-42042444-4-2-2-400000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-48-4484-4-44-8-84-42-40-2-44-24-444200000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-44-44-4-444442220-22-2-2-22-2-2200006i−6i−6i6i00000000-11-1100000−3i3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1118-88-8-4-4-44-44-4-444442220-22-2-2-22-2-220000−6i6i6i−6i00000000-11-11000003i−3i−3i3i00000000000000000000000000000000000000000000000000000000
χ1128-8-888-4-4-84-44-84-448-4-4204-2-4-444-22400000000000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-444-4444-44-42220-2-222-2-2-22-200−4i34i32i32i3−2i3−2i300000000-111-102i3−2i300−i3−i3i3i300000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-444-4444-44-42220-2-222-2-2-22-2004i3−4i3−2i3−2i32i32i300000000-111-10−2i32i300i3i3−i3−i300000000000000000000000000000000000000000000000000000000

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