Finite Group Databasebeta

← Group #13168185

Character table — Group #13168185

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order1222333666666666333466666666612121212121212122244121212123666121212121212121212224466666666666612121212121212121212446666661212121212124444412121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-11-11111111111111111-1-1111111-1-111-1-11-111-1-1-11-1-1-11111-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-11111111111111-11111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111111111-1-111-1-1-1-1-111-1-11-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-11111111111111-1-11-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-111-1-11-1-1-11-1-1-1-1-1-111-111
χ51111111111111111111111111111111111111-1-1111111111111111111111-11-1-1-1-111111111-1-111111111-1-111-1-111-11-1-1111-1-1-11-1-1-1-1-1-111-1-1-1
χ61111111111111111111111111111111111111-1-111111111111111111111-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-11-1-111-11-1-1-11111-1-1-1-1-111
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
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-11-11-1-1-1-111-1-11-111-1
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-11-1-111-1-1-111-1-11111-11-1-11
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1111-1-1-1-1-111-11
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-11111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-11-1-11111-11-111-1-1111-1-11-1
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1111-111-1-111-11-111-1-1111-1-1-11
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-111-1111-1-1-1-1-1111-1
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1111-111-1-1-1-1-111-1-11111-11-11-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-111-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-1-1-11111111-11-1-1-1-111-1-11-11-11
χ17222222-1222-12-12-122-1-122-1-1-12-12-1-122-1-1-1-1-1-100222222-1-1-1-1222-1-1-1-1-1-12202000022-1-1-1-1-1-100-1-122-1-1-1-1002-100-1-10-100-1-120002000000-1-1000
χ18222222-1222-12-12-122-1-122-1-1-12-12-1-122-1-1-1-1-1-100222222-1-1-1-1222-1-1-1-1-1-12-20-2000022-1-1-1-1-1-100-1-1-2-2-1-1-1-100-210011010011-2000-200000011000
χ19222222-1222-12-12-122-1-122-1-1-12-12-1-122-1-1-1-1-1-100-2-2-2-2-2-2-1-1-1-1222-1-1-1-1-1-1-22020000-2-21111110011221111002-100-1-10-100-1-1-2000-200000011000
χ20222222-1222-12-12-122-1-122-1-1-12-12-1-122-1-1-1-1-1-100-2-2-2-2-2-2-1-1-1-1222-1-1-1-1-1-1-2-20-20000-2-21111110011-2-2111100-21001101001120002000000-1-1000
χ21222222-1222-12-12-122-1-1-22-1-1-12-12-1-1-2-211111100222222-1-1-1-1-2-2-2111111-220-20000-2-211111100-1-1-2-2-1-1-1-1002-100-1-10100112000-2000000-11000
χ22222222-1222-12-12-122-1-1-22-1-1-12-12-1-1-2-211111100222222-1-1-1-1-2-2-2111111-2-2020000-2-211111100-1-122-1-1-1-100-2100110-100-1-1-200020000001-1000
χ23222222-1222-12-12-122-1-1-22-1-1-12-12-1-1-2-211111100-2-2-2-2-2-2-1-1-1-1-2-2-2111111220-2000022-1-1-1-1-1-10011-2-21111002-100-1-1010011-200020000001-1000
χ24222222-1222-12-12-122-1-1-22-1-1-12-12-1-1-2-211111100-2-2-2-2-2-2-1-1-1-1-2-2-21111112-202000022-1-1-1-1-1-1001122111100-2100110-100-1-12000-2000000-11000
χ2522222-1222-12-12-122-12-12-12-1-1-12-12-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12-1-122-1-1-1-1202022-1-1-1-122-1-1-1-1-1-12200-1-1-1-12200-1-10020-1-10002000-1-1-1-10000000
χ2622222-1222-12-12-122-12-12-12-1-1-12-12-1-1-122-1-1-1-122-2-21111-1-1-1-12-1-122-1-1-1-1-202022-1-111-2-21111-1-1-2-2001111-2-200-1-10020-1-1000-200011110000000
χ2722222-1222-12-12-122-12-12-12-1-1-12-12-1-1-122-1-1-1-1-2-222-1-1-1-1-1-1-1-12-1-122-1-1-1-120-20-2-211-1-122-1-1-1-1112200-1-1-1-1-2-2001100-2011000-200011110000000
χ2822222-1222-12-12-122-12-12-12-1-1-12-12-1-1-122-1-1-1-1-2-2-2-21111-1-1-1-12-1-122-1-1-1-1-20-20-2-21111-2-2111111-2-200111122001100-20110002000-1-1-1-10000000
χ2922222-1222-12-12-122-12-1-2-12-1-1-12-12-111-2-211112222-1-1-1-1-1-1-1-1-211-2-21111-20-2022-1-111-2-21111112200-1-1-1-12200-1-100-2011000-200011-1-10000000
χ3022222-1222-12-12-122-12-1-2-12-1-1-12-12-111-2-2111122-2-21111-1-1-1-1-211-2-2111120-2022-1-1-1-122-1-1-1-111-2-2001111-2-200-1-100-20110002000-1-1110000000
χ3122222-1222-12-12-122-12-1-2-12-1-1-12-12-111-2-21111-2-222-1-1-1-1-1-1-1-1-211-2-21111-2020-2-21111-2-21111-1-12200-1-1-1-1-2-200110020-1-10002000-1-1110000000
χ3222222-1222-12-12-122-12-1-2-12-1-1-12-12-111-2-21111-2-2-2-21111-1-1-1-1-211-2-211112020-2-211-1-122-1-1-1-1-1-1-2-20011112200110020-1-1000-200011-1-10000000
χ332222-122-1-1222222-1-1-122-1-122-1-1-1-122222222222000000-1-1-1-1-1-1-1-1-1-1-1-1-10222-1-122000000002200-1-1000000-12-1-1-1-1-12-1-1-1-1002200000-1-100-100
χ342222-122-1-1222222-1-1-122-1-122-1-1-1-122222222222000000-1-1-1-1-1-1-1-1-1-1-1-1-10-22-2-1-122000000002200110000001-2-1-111-1-2-1-11100-2-2000001100100
χ352222-122-1-1222222-1-1-122-1-122-1-1-1-1222222222-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-102-2211-2-200000000-2-200-1-1000000-1211-1-11211-1-100-2-2000001100100
χ362222-122-1-1222222-1-1-122-1-122-1-1-1-1222222222-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-10-2-2-211-2-200000000-2-200110000001-211111-21111002200000-1-100-100
χ372222-122-1-1222222-1-1-12-2-1-122-1-1-1-12-2-2-2-2-2-2-2-222000000-1-1-1-111111111102-2-2-1-12200000000-2-20011000000-12-1-1-1-11-21111002-2000001100-100
χ382222-122-1-1222222-1-1-12-2-1-122-1-1-1-12-2-2-2-2-2-2-2-222000000-1-1-1-11111111110-2-22-1-12200000000-2-200-1-10000001-2-1-1111211-1-100-2200000-1-100100
χ392222-122-1-1222222-1-1-12-2-1-122-1-1-1-12-2-2-2-2-2-2-2-2-2-2000000-1-1-1-1111111111022-211-2-200000000220011000000-1211-1-1-1-2-1-11100-2200000-1-100100
χ402222-122-1-1222222-1-1-12-2-1-122-1-1-1-12-2-2-2-2-2-2-2-2-2-2000000-1-1-1-11111111110-22211-2-2000000002200-1-10000001-21111-12-1-1-1-1002-2000001100-100
χ412-22-2222-2-2-222-2-2-2222202-22-2-2-2-22-2000000002-22i−2i2i2i−2i−2i22-2-200000000000002-22-200000000002i−2i002i2i−2i−2i2i−2i002-20000000000000002i−2i0000000
χ422-22-2222-2-2-222-2-2-2222202-22-2-2-2-22-2000000002-2−2i2i−2i−2i2i2i22-2-200000000000002-22-20000000000−2i2i00−2i−2i2i2i−2i2i002-2000000000000000−2i2i0000000
χ432-22-2222-2-2-222-2-2-2222202-22-2-2-2-22-200000000-222i−2i2i2i−2i−2i22-2-20000000000000-22-2200000000002i−2i002i2i−2i−2i−2i2i00-22000000000000000−2i2i0000000
χ442-22-2222-2-2-222-2-2-2222202-22-2-2-2-22-200000000-22−2i2i−2i−2i2i2i22-2-20000000000000-22-220000000000−2i2i00−2i−2i2i2i2i−2i00-220000000000000002i−2i0000000
χ452-22-22-12-2-212-1-21-22-12-10-1-2-111-21213−30033−3−32-22i−2i−i−iii-1-11103−30033−3−300002-2-11−i3i300−i3−i3i3i33−32i−2i00−i−iii2i−2i00-1100003−30000000−i3i3−ii0000000
χ462-22-22-12-2-212-1-21-22-12-10-1-2-111-21213−30033−3−32-2−2i2iii−i−i-1-11103−30033−3−300002-2-11i3−i300i3i3−i3−i33−3−2i2i00ii−i−i−2i2i00-1100003−30000000i3−i3i−i0000000
χ472-22-22-12-2-212-1-21-22-12-10-1-2-111-21213−30033−3−3-222i−2i−i−iii-1-11103−30033−3−30000-221-1−i3i300−i3−i3i3i3−332i−2i00−i−iii−2i2i001-10000−330000000i3−i3i−i0000000
χ482-22-22-12-2-212-1-21-22-12-10-1-2-111-21213−30033−3−3-22−2i2iii−i−i-1-11103−30033−3−30000-221-1i3−i300i3i3−i3−i3−33−2i2i00ii−i−i2i−2i001-10000−330000000−i3i3−ii0000000
χ492-22-22-12-2-212-1-21-22-12-10-1-2-111-2121−3300−3−3332-22i−2i−i−iii-1-1110−3300−3−33300002-2-11i3−i300i3i3−i3−i3−332i−2i00−i−iii2i−2i00-110000−330000000i3−i3−ii0000000
χ502-22-22-12-2-212-1-21-22-12-10-1-2-111-2121−3300−3−3332-2−2i2iii−i−i-1-1110−3300−3−33300002-2-11−i3i300−i3−i3i3i3−33−2i2i00ii−i−i−2i2i00-110000−330000000−i3i3i−i0000000
χ512-22-22-12-2-212-1-21-22-12-10-1-2-111-2121−3300−3−333-222i−2i−i−iii-1-1110−3300−3−3330000-221-1i3−i300i3i3−i3−i33−32i−2i00−i−iii−2i2i001-100003−30000000−i3i3i−i0000000
χ522-22-22-12-2-212-1-21-22-12-10-1-2-111-2121−3300−3−333-22−2i2iii−i−i-1-1110−3300−3−3330000-221-1−i3i300−i3−i3i3i33−3−2i2i00ii−i−i2i−2i001-100003−30000000i3−i3−ii0000000
χ5344444-2-244-2-2-2-2-2-24-2-214-2-211-2-2-2-21-2-2-2-211110044-2-2-2-211114-2-2-2-2111140000000-2-2-2-2111100-2-2001111000000000000000000000000000000
χ5444444-2-244-2-2-2-2-2-24-2-214-2-211-2-2-2-21-2-2-2-2111100-4-4222211114-2-2-2-21111-400000002222-1-1-1-1002200-1-1-1-1000000000000000000000000000000
χ5544444-2-244-2-2-2-2-2-24-2-21-4-2-211-2-2-2-212222-1-1-1-10044-2-2-2-21111-42222-1-1-1-1-400000002222-1-1-1-100-2-2001111000000000000000000000000000000
χ5644444-2-244-2-2-2-2-2-24-2-21-4-2-211-2-2-2-212222-1-1-1-100-4-422221111-42222-1-1-1-140000000-2-2-2-21111002200-1-1-1-1000000000000000000000000000000
χ574444-24-2-2-24-24-24-2-2-21-24-21-2-2-21-21-244-2-2-2-2-2-2000000001111-2-2-211111104040000000000000000-2-2000000-2-200110-200110000000000000000
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χ7844-4-4-24-22-242-4-2-422-21-20212-22-1-2-1200−2323−2323−2323000000001-11-10003−33−33−30000000000000000000023−230000000000-330000−330000000000000000
χ7944-4-4-24-22-242-4-2-422-21-20212-22-1-2-1200−2323−2323−2323000000001-11-10003−33−33−300000000000000000000−232300000000003-300003−30000000000000000
χ804-44-444-2-4-4-4-242-4244-2-2042-22-42-4-2200000000004i−4i4i4i−4i−4i-2-222000000000000000000000000000−2i2i00−2i−2i2i2i000000000000000000000000000000
χ814-44-444-2-4-4-4-242-4244-2-2042-22-42-4-220000000000−4i4i−4i−4i4i4i-2-2220000000000000000000000000002i−2i002i2i−2i−2i000000000000000000000000000000
χ824-44-44-2-2-4-42-2-22224-2-210-221-1222-2-123−2300−3−333004i−4i−2i−2i2i2i11-1-1023−2300−3−33300000000−2i32i300i3i3−i3−i300−2i2i00ii−i−i000000000000000000000000000000
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χ844-44-44-2-2-4-42-2-22224-2-210-221-1222-2-1−23230033−3−3004i−4i−2i−2i2i2i11-1-10−23230033−3−3000000002i3−2i300−i3−i3i3i300−2i2i00ii−i−i000000000000000000000000000000
χ854-44-44-2-2-4-42-2-22224-2-210-221-1222-2-1−23230033−3−300−4i4i2i2i−2i−2i11-1-10−23230033−3−300000000−2i32i300i3i3−i3−i3002i−2i00−i−iii000000000000000000000000000000
χ864-44-4-24422-444-4-4-4-2-2-240-224-4222-2-4000000004-4000000-2-2220000000000000-224-40000000000000000000000-22000000000000000000000000
χ874-44-4-24422-444-4-4-4-2-2-240-224-4222-2-400000000-44000000-2-22200000000000002-2-4400000000000000000000002-2000000000000000000000000
χ884-44-4-2-242224-2-42-4-21-2-2012-22-12-1-2223−23002323−23−234-400000011-1-10−3300−3−3330000-22-220000000023−230000000000001-10000−33000000000000000000
χ894-44-4-2-242224-2-42-4-21-2-2012-22-12-1-2223−23002323−23−23-4400000011-1-10−3300−3−33300002-22-200000000−2323000000000000-1100003−3000000000000000000
χ904-44-4-2-242224-2-42-4-21-2-2012-22-12-1-22−232300−23−2323234-400000011-1-103−30033−3−30000-22-2200000000−23230000000000001-100003−3000000000000000000
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χ924-4-444444-4-4-4-4-444-44440-4-4-4-444-4-4400000000000000004-4-4400000000000000000000000000000000000000000000000000000000000000000
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χ944-4-4444-24-4-42-424-2-44-2-20-42224-2-42-20000000000000000-222-200000000000000000002i3−2i32i3−2i3−2i32i30000000000000000000000000000000000000000
χ954-4-444-244-42-42-4-24-4-24-202-422-242-4-2000000000000−2i32i32i3−2i3-222-20000000000000000000000000000000−2i32i32i3−2i3000000000000000000000000000000
χ964-4-444-244-42-42-4-24-4-24-202-422-242-4-20000000000002i3−2i3−2i32i3-222-200000000000000000000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ974-4-444-2-24-42222-2-2-4-2-21022-1-1-2-222100003-3-330000−2i32i32i3−2i31-1-11000003-3-330000000000−2i32i3i3−i3−i3i3000000i3−i3−i3i3000000000000000000000000000000
χ984-4-444-2-24-42222-2-2-4-2-21022-1-1-2-222100003-3-3300002i3−2i3−2i32i31-1-11000003-3-3300000000002i3−2i3−i3i3i3−i3000000−i3i3i3−i3000000000000000000000000000000
χ994-4-444-2-24-42222-2-2-4-2-21022-1-1-2-22210000-333-30000−2i32i32i3−2i31-1-1100000-333-300000000002i3−2i3−i3i3i3−i3000000i3−i3−i3i3000000000000000000000000000000
χ1004-4-444-2-24-42222-2-2-4-2-21022-1-1-2-22210000-333-300002i3−2i3−2i32i31-1-1100000-333-30000000000−2i32i3i3−i3−i3i3000000−i3i3i3−i3000000000000000000000000000000
χ1014-4-44-244-22-4-4-4-4442-2-24022-4-4-2-22240000000000000000-222-2000000000000000000000000000000000000000000000000000000000023−2300000
χ1024-4-44-244-22-4-4-4-4442-2-24022-4-4-2-22240000000000000000-222-20000000000000000000000000000000000000000000000000000000000−232300000
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
χ10588-8-8-4-484-4-4-8484-842-4-40-2-44-4-2424400000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-44-4-444-44442220-22-22-2-22-2-20043−43−2323−232300000000-11-11000−23233−33−300000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-44-4-444-44442220-22-22-2-22-2-200−434323−2323−2300000000-11-1100023−23−33−3300000000000000000000000000000000000000000000000000000000
χ1088-88-8-48-444-8-484-84-4-42-40-4-2-444-2424000000000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-4444-4-4444-422202-22-2-2-2-22-243−4300−23−23232300000000-1-1110−23230033−3−300000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-4444-4-4444-422202-22-2-2-2-22-2−4343002323−23−2300000000-1-111023−2300−3−33300000000000000000000000000000000000000000000000000000000
χ1118-8-88-48-4-44-84-848-44-42-404-244-424-2-400000000000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-48-444-84-8-4842-4-40-24442-4-24-400000000000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-4-444444-4-442220-2-2-2-222-2-2200006-6-6600000000-111-100000-333-300000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4-444444-4-442220-2-2-2-222-2-220000-666-600000000-111-1000003-3-3300000000000000000000000000000000000000000000000000000000

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