Finite Group Databasebeta

← Group #13172033

Character table — Group #13172033

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order1222333666666666233366666666666224436666666666666664444666612121212121212121212121244121212126612121212121212121212121212122444412121212121261244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-11111111111-1-1-1-111111111111-1-11111111-1-1-1-1-1-1-11-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111-1-11111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-111-1-1-1-111111-1-1-1111-1-1-1-11-1-1-1
χ4111111111111111111111111111111111-1-11111111111111111-11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1111
χ51111111111111111111111111111111-1-11111111111111111111-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1111-1-111111111-111-1-1-1-111-1-1-11-1-1
χ61111111111111111111111111111111-1-11111111111111111111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-11-1-1-1111-1-1-1-11-111
χ71111111111111111111111111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-111-1-1-1-1-1-1-11111-1-1-11-1-1-1-1-111-1-111
χ81111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ91111111111111111-1111-1-111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-11-11111-1-1-1-11111-1-11111111111-11-1-1-1-111-1-111-1-111-1-1-1-1-111-1-11-1-11
χ101111111111111111-1111-1-111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111111-1-1-1-111-1-1111111111111-1-11-1-1-111-1-1-1-111-1-11-1111-1-1-1-1-111-1
χ111111111111111111-1111-1-111111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-11-11111-1-111-1-111-1-1-1-1-1-1-1-1-1-111-11-11-1-1-1-11111-1-11-111-1-1-1-1-111111-1
χ121111111111111111-1111-1-111111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-1-111111-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111-11-111111111-1-1-11
χ131111111111111111-1111-1-1111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-11-111111111-1-11-1
χ141111111111111111-1111-1-1111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-1-11-11-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11-11-11111-1-1-1-1111-111-1-1-1-1-11111-11
χ151111111111111111-1111-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-1-11111-1-111-1-1-1-1111111-1-111-1111-1-11111-1-1-1-11-1111-1-1-1-1-11-11
χ161111111111111111-1111-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-111-11-1-1-1-11111-1-1-1-111-1-1111111-1-11-11111-1-111-1-11111-1-1-1-1-111-1-11-11-1
χ17222222-1-1222-122-1222-1-1222-1-1-122-1-1-12200-12-122-1-1-1-1-1-1-1-1-1-1-1022222-1-122000022-1-100000000-1-1-1-120-1-10000-1-1-1-120002-1-10000-1000
χ18222222-1-1222-122-1222-1-1222-1-1-122-1-1-12200-12-122-1-1-1-1-1-1-1-1-1-1-102-2-222-1-1220000-2-21100000000-1-1-11-20-1-100001111-2000-21100001000
χ19222222-1-1222-122-1222-1-1222-1-1-122-1-1-1-2-200-12-122-1-1-1-1-1-1-1-1-1-1-10-222-2-211-2-2000022-1-100000000111-120110000-1-1-1-1-2000-21100001000
χ20222222-1-1222-122-1222-1-1222-1-1-122-1-1-1-2-200-12-122-1-1-1-1-1-1-1-1-1-1-10-2-2-2-2-211-2-20000-2-211000000001111-20110000111120002-1-10000-1000
χ21222222-1-1222-122-12-22-1-1-2-22-1-1-122-1-1-12200-1-21-2-21111-1-1-111110-22-222-1-1-2-20000221100000000-1-11-1-20110000-1-1112000-2110000-1000
χ22222222-1-1222-122-12-22-1-1-2-22-1-1-122-1-1-12200-1-21-2-21111-1-1-111110-2-2222-1-1-2-20000-2-2-1-100000000-1-1112011000011-1-1-20002-1-100001000
χ23222222-1-1222-122-12-22-1-1-2-22-1-1-122-1-1-1-2-200-1-21-2-21111-1-1-11111022-2-2-21122000022110000000011-1-1-20-1-10000-1-111-20002-1-100001000
χ24222222-1-1222-122-12-22-1-1-2-22-1-1-122-1-1-1-2-200-1-21-2-21111-1-1-1111102-22-2-211220000-2-2-1-10000000011-1120-1-1000011-1-12000-2110000-1000
χ2522222-122-1-122222-12-12-1-1-1-12-1-1-1-122-12222-122-1-122-1-1-1-1-1-1-1-1-12200-1-122-1-1-1-1220000-1-122-1-1-1-1-1-12002-1-1-1-1-1-10000000200000-1-10000
χ2622222-122-1-122222-12-12-1-1-1-12-1-1-1-122-122-2-2-122-1-122-1-1-1-1-1-1-1-1-1-2200-1-122-1-111-2-2000011-2-21111-1-1200-2-1-111110000000-200000110000
χ2722222-122-1-122222-12-12-1-1-1-12-1-1-1-122-1-2-222-122-1-122-1-1-1-1-1-1-1-1-12-20011-2-211-1-1220000-1-1-2-2111111-200211-1-1-1-10000000-200000110000
χ2822222-122-1-122222-12-12-1-1-1-12-1-1-1-122-1-2-2-2-2-122-1-122-1-1-1-1-1-1-1-1-1-2-20011-2-21111-2-200001122-1-1-1-111-200-21111110000000200000-1-10000
χ2922222-122-1-122222-1-2-12-111-12-1-1-1-122-12222-1-2-211-2-211-1-1-11111-2-200-1-1221111220000-1-122-1-1-1-1-1-1-200-211-1-1110000000-200000110000
χ3022222-122-1-122222-1-2-12-111-12-1-1-1-122-122-2-2-1-2-211-2-211-1-1-111112-200-1-12211-1-1-2-2000011-2-21111-1-1-20021111-1-10000000200000-1-10000
χ3122222-122-1-122222-1-2-12-111-12-1-1-1-122-1-2-222-1-2-211-2-211-1-1-11111-220011-2-2-1-111220000-1-1-2-2111111200-2-1-1-1-1110000000200000-1-10000
χ3222222-122-1-122222-1-2-12-111-12-1-1-1-122-1-2-2-2-2-1-2-211-2-211-1-1-11111220011-2-2-1-1-1-1-2-200001122-1-1-1-1112002-1-111-1-10000000-200000110000
χ332222-122222-12-1-1222-1-1222-1-122-1-1-1-120022-1-12-1-1-1-122-1-1-1-1-1-1-1202200000022-1-1-1-122220000000002-1-100-1-1-1-1-1-1-1-10220000-1-1000-100
χ342222-122222-12-1-1222-1-1222-1-122-1-1-1-120022-1-12-1-1-1-122-1-1-1-1-1-1-120-2-200000022-1-111-2-222000000000-21-100-1-1-1-111110-2-2000011000100
χ352222-122222-12-1-1222-1-1222-1-122-1-1-1-1200-2-2-1-12-1-1-1-122-1-1-1-1-1-1-1-2022000000-2-211-1-122-2-20000000002-11001111-1-1-1-10-2-2000011000100
χ362222-122222-12-1-1222-1-1222-1-122-1-1-1-1200-2-2-1-12-1-1-1-122-1-1-1-1-1-1-1-20-2-2000000-2-21111-2-2-2-2000000000-21100111111110220000-1-1000-100
χ372222-122222-12-1-122-2-1-12-2-2-1-122-1-1-1-120022-11-21111-2-2-1-1-11111-202-2000000-2-2-1-1-1-1-2-22200000000021100-1-111-1-11102-20000-1-1000100
χ382222-122222-12-1-122-2-1-12-2-2-1-122-1-1-1-120022-11-21111-2-2-1-1-11111-20-22000000-2-2-1-1112222000000000-2-1100-1-11111-1-10-22000011000-100
χ392222-122222-12-1-122-2-1-12-2-2-1-122-1-1-1-1200-2-2-11-21111-2-2-1-1-11111202-20000002211-1-1-2-2-2-200000000021-10011-1-1-1-1110-22000011000-100
χ402222-122222-12-1-122-2-1-12-2-2-1-122-1-1-1-1200-2-2-11-21111-2-2-1-1-1111120-2200000022111122-2-2000000000-2-1-10011-1-111-1-102-20000-1-1000100
χ412-22-2222-22-2-222-2-2-20222002-2-2-2-2-22-222-22i−2i2000000002-2-2000000002-22-200002i−2i00002i−2i2i−2i2i2i−2i−2i2-20000002i−2i000000000000000000000
χ422-22-2222-22-2-222-2-2-20222002-2-2-2-2-22-222-2−2i2i2000000002-2-2000000002-22-20000−2i2i0000−2i2i−2i2i−2i−2i2i2i2-2000000−2i2i000000000000000000000
χ432-22-2222-22-2-222-2-2-20222002-2-2-2-2-22-22-222i−2i2000000002-2-200000000-22-2200002i−2i00002i−2i−2i2i−2i−2i2i2i-220000002i−2i000000000000000000000
χ442-22-2222-22-2-222-2-2-20222002-2-2-2-2-22-22-22−2i2i2000000002-2-200000000-22-220000−2i2i0000−2i2i2i−2i2i2i−2i−2i-22000000−2i2i000000000000000000000
χ452-22-22-12-2-11-222-2-210-12-1−i3i3-1-211112-2-12-22i−2i-100−i3i300−i3i3-111−i3−i3i3i30000-112-2−i3i33−32i−2i0000−ii2i−2i−i−iii-110000−i3i3−ii3−300000000000003−30000
χ462-22-22-12-2-11-222-2-210-12-1−i3i3-1-211112-2-12-2−2i2i-100−i3i300−i3i3-111−i3−i3i3i30000-112-2−i3i3−33−2i2i0000i−i−2i2iii−i−i-110000−i3i3i−i−330000000000000−330000
χ472-22-22-12-2-11-222-2-210-12-1−i3i3-1-211112-2-1-222i−2i-100−i3i300−i3i3-111−i3−i3i3i300001-1-22i3−i33−32i−2i0000−ii−2i2iii−i−i1-10000i3−i3−ii3−30000000000000−330000
χ482-22-22-12-2-11-222-2-210-12-1−i3i3-1-211112-2-1-22−2i2i-100−i3i300−i3i3-111−i3−i3i3i300001-1-22i3−i3−33−2i2i0000i−i2i−2i−i−iii1-10000i3−i3i−i−3300000000000003−30000
χ492-22-22-12-2-11-222-2-210-12-1i3−i3-1-211112-2-12-22i−2i-100i3−i300i3−i3-111i3i3−i3−i30000-112-2i3−i3−332i−2i0000−ii2i−2i−i−iii-110000i3−i3−ii−330000000000000−330000
χ502-22-22-12-2-11-222-2-210-12-1i3−i3-1-211112-2-12-2−2i2i-100i3−i300i3−i3-111i3i3−i3−i30000-112-2i3−i33−3−2i2i0000i−i−2i2iii−i−i-110000i3−i3i−i3−300000000000003−30000
χ512-22-22-12-2-11-222-2-210-12-1i3−i3-1-211112-2-1-222i−2i-100i3−i300i3−i3-111i3i3−i3−i300001-1-22−i3i3−332i−2i0000−ii−2i2iii−i−i1-10000−i3i3−ii−3300000000000003−30000
χ522-22-22-12-2-11-222-2-210-12-1i3−i3-1-211112-2-1-22−2i2i-100i3−i300i3−i3-111i3i3−i3−i300001-1-22−i3i33−3−2i2i0000i−i2i−2i−i−iii1-10000−i3i3i−i3−30000000000000−330000
χ5344444-2-2-2-2-24-244-2-24-2-21-2-2-2-211-2-2-2-21440014-2-2-2-2-21111111110400-2-2-2-2-2-2000000000000000011-20001100000000000000000000000
χ5444444-2-2-2-2-24-244-2-24-2-21-2-2-2-211-2-2-2-21-4-40014-2-2-2-2-21111111110-4002222220000000000000000-1-12000-1-100000000000000000000000
χ5544444-2-2-2-2-24-244-2-2-4-2-2122-2-211-2-2-2-2144001-422222-1-1111-1-1-1-10-400-2-2-2-2220000000000000000112000-1-100000000000000000000000
χ5644444-2-2-2-2-24-244-2-2-4-2-2122-2-211-2-2-2-21-4-4001-422222-1-1111-1-1-1-104002222-2-20000000000000000-1-1-20001100000000000000000000000
χ574444-24-2-244-2-2-2-2-244-21-244-21-2-2-2-211-200001-2-2-2-211-2-2111111100440000000000-2-2-2-200000000000-2-200000001111000000000000000
χ584444-24-2-244-2-2-2-2-244-21-244-21-2-2-2-211-200001-2-2-2-211-2-2111111100-4-40000000000222200000000000220000000-1-1-1-1000000000000000
χ594444-24-2-244-2-2-2-2-24-4-21-2-4-4-21-2-2-2-211-2000012222-1-122111-1-1-1-1004-40000000000-2-22200000000000-22000000011-1-1000000000000000
χ604444-24-2-244-2-2-2-2-24-4-21-2-4-4-21-2-2-2-211-2000012222-1-122111-1-1-1-100-44000000000022-2-2000000000002-20000000-1-111000000000000000
χ614444-2-244-2-2-24-2-24-241-2-2-2-21-2-2-211-2-2-200441-2411-2-2-2-211111114000000000-2-2-2-20000-2-200000000000-20011110000000000000000000
χ624444-2-244-2-2-24-2-24-241-2-2-2-21-2-2-211-2-2-200-4-41-2411-2-2-2-21111111-4000000000222200002200000000000200-1-1-1-10000000000000000000
χ634444-2-244-2-2-24-2-24-2-41-2-2221-2-2-211-2-2-2004412-4-1-12222111-1-1-1-1-400000000022-2-20000-2-20000000000020011-1-10000000000000000000
χ644444-2-244-2-2-24-2-24-2-41-2-2221-2-2-211-2-2-200-4-412-4-1-12222111-1-1-1-14000000000-2-22200002200000000000-200-1-1110000000000000000000
χ6544-4-44444-44-4-4-44-4-4044400-444-44-4-4-4-40000400000000-44-40000000000000000000000000000000000000000000000000000000000000
χ6644-4-444-2-2-44-42-442-404-2-200-4-2-224-42220000-2000000002-220000000000000000000023−23000000000000000000000023−23000000000000000
χ6744-4-444-2-2-44-42-442-404-2-200-4-2-224-42220000-2000000002-2200000000000000000000−23230000000000000000000000−2323000000000000000
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χ7344-4-4-24-2-2-44222-22-40-21-20021-22-22-1-120000100003-300-11-13-33-300000000000000−2323−2323000000000000000000003−33−3000000000000000
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χ764-44-444-224-4-4-24-42-404-2-2004222-4-4-22-24-400-200000000-222000000004-4-22000000000000000000-2200000000000000000000000000000
χ774-44-444-224-4-4-24-42-404-2-2004222-4-4-22-2-4400-200000000-22200000000-442-20000000000000000002-200000000000000000000000000000
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χ794-44-44-2-22-22-4-24-4220-2-21−2i32i3-22-1-122-221-4400100−2i32i300i3−i31-1-1i3i3−i3−i300002-22-22i3−2i30000000000000000-110000−i3i300000000000000000000000
χ804-44-44-2-22-22-4-24-4220-2-212i3−2i3-22-1-122-2214-4001002i3−2i300−i3i31-1-1−i3−i3i3i30000-22-222i3−2i300000000000000001-10000−i3i300000000000000000000000
χ814-44-44-2-22-22-4-24-4220-2-212i3−2i3-22-1-122-221-44001002i3−2i300−i3i31-1-1−i3−i3i3i300002-22-2−2i32i30000000000000000-110000i3−i300000000000000000000000
χ824-44-4-244-44-424-22-4-40-2-2400-22-4-422-224004i−4i-200000000-2220000000000000000−2i2i00004i−4i00000000000000−2i2i000000000000000000000
χ834-44-4-244-44-424-22-4-40-2-2400-22-4-422-22400−4i4i-200000000-22200000000000000002i−2i0000−4i4i000000000000002i−2i000000000000000000000
χ844-44-4-2-24-4-2224-22-4201-2-2−2i32i31222-1-1-22-2004i−4i100i3−i300−2i32i31-1-1i3i3−i3−i3000000000023−23−2i2i0000−2i2i00000000000000i−i−330000000000000000000
χ854-44-4-2-24-4-2224-22-4201-2-2−2i32i31222-1-1-22-200−4i4i100i3−i300−2i32i31-1-1i3i3−i3−i30000000000−23232i−2i00002i−2i00000000000000−ii3−30000000000000000000
χ864-44-4-2-24-4-2224-22-4201-2-22i3−2i31222-1-1-22-2004i−4i100−i3i3002i3−2i31-1-1−i3−i3i3i30000000000−2323−2i2i0000−2i2i00000000000000i−i3−30000000000000000000
χ874-44-4-2-24-4-2224-22-4201-2-22i3−2i31222-1-1-22-200−4i4i100−i3i3002i3−2i31-1-1−i3−i3i3i3000000000023−232i−2i00002i−2i00000000000000−ii−330000000000000000000
χ884-4-44444-4-4-44-4-4-444044400-4-4-44-44-44-40000400000000-4-440000000000000000000000000000000000000000000000000000000000000
χ894-4-4444-22-4-442-4-4-2404-2-200-422-2-442-220000-20000000022-2000000000000000000000000000000000000000000000000000−2i32i300000000
χ904-4-4444-22-4-442-4-4-2404-2-200-422-2-442-220000-20000000022-20000000000000000000000000000000000000000000000000002i3−2i300000000
χ914-4-444-24-4224-4-4-44-20-24-2002-42-22-2-4420000-20000000022-200000000000000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ924-4-444-24-4224-4-4-44-20-24-2002-42-22-2-4420000-20000000022-2000000000000000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ934-4-44-244-4-4-4-2-422440-2-240022-442-22-2-40000-20000000022-20000000000000000000000000000000000000000000000000000023−23000000
χ944-4-44-244-4-4-4-2-422440-2-240022-442-22-2-40000-20000000022-200000000000000000000000000000000000000000000000000000−2323000000
χ958888-4-4-4-4-4-4-4-4-4-4-4-48222-4-42222222220000-1-4-4222222-1-1-1-1-1-1-1000000000000000000000000000000000000000000000000000000000
χ968888-4-4-4-4-4-4-4-4-4-4-4-4-8222442222222220000-144-2-2-2-2-2-2-1-1-11111000000000000000000000000000000000000000000000000000000000
χ9788-8-88-4-4-44-4-84-88440-4-42004-42-2-4444-20000200000000-22-20000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-4884-44-84-4-8402-4-400-2-4-442-24440000200000000-22-20000000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-4-44-4444-444022200-222-22-2-2-2-20000-100006-6001-11-33-33000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-4-44-4444-444022200-222-22-2-2-2-20000-10000-66001-113-33-3000000000000000000000000000000000000000000000000000000000
χ1018-88-8-48-448-84-4-444-80-42-400-4-244442-2-400002000000002-2-20000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4-44-444-4-44440222−4i34i32-2-2-2-2-22-220000-1002i3−2i3002i3−2i3-111−i3−i3i3i3000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-44-444-4-444402224i3−4i32-2-2-2-2-22-220000-100−2i32i300−2i32i3-111i3i3−i3−i3000000000000000000000000000000000000000000000000000000000
χ1048-8-888-4-444484-8-8-4-40-4-420044-224-44-4-20000200000000-2-220000000000000000000000000000000000000000000000000000000000000
χ1058-8-88-48-44-8-8-4444-480-42-4004-24-44-4-2240000200000000-2-220000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-48-844-4-8448-402-4-400-244-4-224-440000200000000-2-220000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-4444-4444-4-4022200-2-2-22-22-22-20000-10000000011-1−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4444-4444-4-4022200-2-2-22-22-22-20000-10000000011-13i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000000

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