Finite Group Databasebeta

← Group #13171652

Character table — Group #13171652

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size1122222223344444444444466666666688888888888121212121212121212121212121212121212121616161618181818242424242424242424242424243636363636363636363648727272108108
order12333466644333466612121212122241212121212123612121212121212121222466666666812121212122424121212122466666666661212242424244881212122424126122428
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-111111111-111111-1-11111111111111111-1-1-1-1-1-11-1-1-1111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-11111-1-1111111111111-11-11111-1-1-11-111-1-1111111-1-1-1-1-11111-1-1-1111111-1-11-1-1-1-11111-1-1-1-1
χ4111111111111111111111111-1-11111-1-1111111111111-1-1-11111-1-1-1-1-111-1-1-1-11111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-11111
χ511111111111111-11111-1-11111111111111-1-111-1-1-1-11-1-11111-1-11-1-1-111111-1-1-11-1-11111-1-11-1-11-1-111-1-1-11-11-1-11-1-1-1-1111-11-1
χ611111111111111-11111-1-11111111111111-1-111-1-1-1-11-1-1-1111-1-11-1-111111111-11-1-11111-1-11-1-11-1-1-1-1111-1-1-1111-1-111-1-1-11-11
χ711111111111111-11111-1-1111-1-11111-1-111-1-111-1-1-1-11-111-111-1-1-111-1-111-1-1-1-1-11-1-1-1-1-1-11-11-1-1-11111-1-1-111-1-11-111-1-111-11-11
χ811111111111111-11111-1-1111-1-11111-1-111-1-111-1-1-1-11-11-1-111-1-1-1111-111-1-111-11-1-1-1-1-1-11-11-1-1-111-1-1111-1111-1-11111-1-11-11-1
χ9111111111-1-1111111111111-111-1-1-1-11111111111111-1111-1-1-1-111111-1-111111111-1-1-1-11-1-1-1-111111111-1-11-11-1-1-1-1-11-111-1-1
χ10111111111-1-1111111111111-111-1-1-1-11111111111111-11-11-1-1-1-1111-11-1-111-1-11111-1-1-1-11-1-1-1-1111-1-1-1-1-11-1-11-1-1-1-111-11-1-111
χ11111111111-1-1111111111111-1-1-1-1-1-1-1-1-111111111111-1-11-1-1-1-1-1-1-1-11-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111-11-1-1-1111-1-11-1-1-111
χ12111111111-1-1111111111111-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1111-1-1
χ13111111111-1-1111-11111-1-111-111-1-1-1-11111-1-111-1-1-1-111-111-1-1111-1-1-11-1-111-1-1-11-1-1-1-1-1-1-11-1111-1-111-1-1-1-1111-1-111111-11-1-11
χ14111111111-1-1111-11111-1-111-111-1-1-1-11111-1-111-1-1-1-111-1-11-1-1111-1-111-1-11111-11-1-1-1-1-1-1-11-1111-1-1-1-111111-1-11-111-1-1-11-111-1
χ15111111111-1-1111-11111-1-111-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-111-111-1-1-1-1-1-1-1-1-11-1-1111111-111-11111-1-1-1-1-1-1111-1-1111-1-111-1
χ16111111111-1-1111-11111-1-111-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111-1-1-1-111-1111-1-1-1-1-111-11-1-1111111-111-111-1-11111-11-1-11-1-1-1-1-111-1-11
χ1722222-2222222220222-200-2-2-22-22222-2-22200-2-20000-20002-2-2002000-222-2-2000-200-22-2-200-200200000000000020000000000
χ1822222-2222222220222-200-2-2-2-222222222200-2-20000-2000-2-2-200-200022222000-2002-22200-200-2000000000000-20000000000
χ1922222-2222-2-22220222-200-2-222-2-2-2-2-2-2-22200-2-20000-2000222002000-2-2-2-2-2000-2002-222002002000000000000-20000000000
χ2022222-2222-2-22220222-200-2-22-22-2-2-2-2222200-2-20000-2000-22200-20002-2-222000-200-22-2-200200-200000000000020000000000
χ212222-1222-1222-1-12-1-12-1-1-12222222-1-1-1-1-1-122-1-1-1-1-1-1222022-1-1-1-1-1-102-1-1-1-1002-1-1-122-1-122-1-1-1-1-1-10000002000-1-1-100000000
χ222222-1222-1222-1-12-1-12-1-1-1222-2-222-1-111-1-122-1-1-1-1-1-122-20-22-1-1-11110-2-1-111002-1-1-1-2-211-22-1-1-1111000000-200011100000000
χ232222-1222-1222-1-1-2-1-12-1112222222-1-1-1-1-1-1-2-2-1-111112-2-2022-111-11102-1-1-1-100-2-11122-1-1-2-2-111-111000000-2000-11100000000
χ242222-1222-1222-1-1-2-1-12-111222-2-222-1-111-1-1-2-2-1-111112-220-22-1111-1-10-2-1-11100-2-111-2-2112-2-1111-1-100000020001-1-100000000
χ252222-1222-1-2-22-1-12-1-12-1-1-122-222-2-211-1-1-1-122-1-1-1-1-1-12-2202-2111-1-1-10211-1-1002-1-1-1-2-2112-2111-1-1-1000000-200011100000000
χ262222-1222-1-2-22-1-12-1-12-1-1-122-2-2-2-2-21111-1-122-1-1-1-1-1-12-2-20-2-21111110-21111002-1-1-122-1-1-2-21111110000002000-1-1-100000000
χ272222-1222-1-2-22-1-1-2-1-12-11122-222-2-211-1-1-1-1-2-2-1-1111122-202-21-1-1-1110211-1-100-2-111-2-211-221-1-1-11100000020001-1-100000000
χ282222-1222-1-2-22-1-1-2-1-12-11122-2-2-2-2-21111-1-1-2-2-1-111112220-2-21-1-11-1-10-2111100-2-11122-1-1221-1-11-1-1000000-2000-11100000000
χ292222-1-222-1222-1-10-1-121−i3i3-2-2-22-222-1-111-1-10011−i3−i3i3i3-20002-21−i3i3-1−i3i30-2-1-1110001−i3i3-2211001−i3i3-1−i3i30000000000-1−i3i300000000
χ302222-1-222-1222-1-10-1-121−i3i3-2-2-2-2222-1-1-1-1-1-10011−i3−i3i3i3-2000-2-21−i3i31i3−i302-1-1-1-10001−i3i32-2-1-1001−i3i31i3−i300000000001i3−i300000000
χ312222-1-222-1222-1-10-1-121i3−i3-2-2-22-222-1-111-1-10011i3i3−i3−i3-20002-21i3−i3-1i3−i30-2-1-1110001i3−i3-2211001i3−i3-1i3−i30000000000-1i3−i300000000
χ322222-1-222-1222-1-10-1-121i3−i3-2-2-2-2222-1-1-1-1-1-10011i3i3−i3−i3-2000-2-21i3−i31−i3i302-1-1-1-10001i3−i32-2-1-1001i3−i31−i3i300000000001−i3i300000000
χ332222-1-222-1-2-22-1-10-1-121−i3i3-2-222-2-2-21111-1-10011−i3−i3i3i3-200022-1i3−i3-1−i3i30-211110001−i3i32-2-1-100-1i3−i3-1−i3i300000000001i3−i300000000
χ342222-1-222-1-2-22-1-10-1-121−i3i3-2-22-22-2-211-1-1-1-10011−i3−i3i3i3-2000-22-1i3−i31i3−i30211-1-10001−i3i3-221100-1i3−i31i3−i30000000000-1−i3i300000000
χ352222-1-222-1-2-22-1-10-1-121i3−i3-2-222-2-2-21111-1-10011i3i3−i3−i3-200022-1−i3i3-1i3−i30-211110001i3−i32-2-1-100-1−i3i3-1i3−i300000000001−i3i300000000
χ362222-1-222-1-2-22-1-10-1-121i3−i3-2-22-22-2-211-1-1-1-10011i3i3−i3−i3-2000-22-1−i3i31−i3i30211-1-10001i3−i3-221100-1−i3i31−i3i30000000000-1i3−i300000000
χ37222-122-12222-12-122-1-1222-12200-1-12200-1-1-122-12-12-1-12020-122200020-1-100-1-1-1-1-1-100000-1-1-1-1000-122-1-120020000-1-1-1-10000
χ38222-122-12222-12-122-1-1222-12200-1-12200-1-1-122-12-12-1-120-20-1222000-20-1-10011-1-1-1-100000-1-1-1-10001-2-211-200-2000011110000
χ39222-122-12222-12-1-22-1-12-2-2-12200-1-12200-1-11-22-1-21-21-1-2020-12-2-2000-20-1-100111-111000001-111000-12-211200-2000011-1-10000
χ40222-122-12222-12-1-22-1-12-2-2-12200-1-12200-1-11-22-1-21-21-1-20-20-12-2-200020-1-100-1-11-111000001-1110001-22-1-1-20020000-1-1110000
χ41222-122-122-2-2-12-122-1-1222-12-20011-2-200-1-1-122-12-12-1-1-20201-2-2-2000201100-1-1-1-1-1-1000001111000-122-1-1-200-2000011-110000
χ42222-122-122-2-2-12-122-1-1222-12-20011-2-200-1-1-122-12-12-1-1-20-201-2-2-2000-20110011-1-1-1-10000011110001-2-21120020000-1-11-10000
χ43222-122-122-2-2-12-1-22-1-12-2-2-12-20011-2-200-1-11-22-1-21-21-120201-222000-201100111-11100000-11-1-1000-12-211-20020000-1-1-110000
χ44222-122-122-2-2-12-1-22-1-12-2-2-12-20011-2-200-1-11-22-1-21-21-120-201-222000201100-1-11-11100000-11-1-10001-22-1-1200-20000111-10000
χ4522-12222-1200-1-122-12-12222-1022000022-1-12-1-12-12-12-1022-100002222-100-1-122-1-1-1-10000-10000-1-1-12-1-1-1-10020200000-10-1-100
χ4622-12222-1200-1-122-12-12222-1022000022-1-12-1-12-12-12-102-2-10000222-2-100-1-1-2-2-1-1-1-10000-10000-1-1-1-2111100-20-200000101100
χ4722-12222-1200-1-122-12-12222-10-2-20000-2-2-1-12-1-12-12-12-10-2210000-2-2-221001122-1-1-1-10000100001112-1-1-1-100-20-200000-101100
χ4822-12222-1200-1-122-12-12222-10-2-20000-2-2-1-12-1-12-12-12-10-2-210000-2-2-2-210011-2-2-1-1-1-1000010000111-21111002020000010-1-100
χ4922-12222-1200-1-12-2-12-12-2-22-1022000022-1-1-21-121-21-2-10-22-100002-2-2-2-100-1-1-2-21-111000010000-1112-11110020-200000-10-1100
χ5022-12222-1200-1-12-2-12-12-2-22-1022000022-1-1-21-121-21-2-10-2-2-100002-2-22-100-1-1221-111000010000-111-21-1-1-100-20200000101-100
χ5122-12222-1200-1-12-2-12-12-2-22-10-2-20000-2-2-1-1-21-121-21-2-102210000-222-210011-2-21-1110000-100001-1-12-111100-20200000-101-100
χ5222-12222-1200-1-12-2-12-12-2-22-10-2-20000-2-2-1-1-21-121-21-2-102-210000-222210011221-1110000-100001-1-1-21-1-1-10020-20000010-1100
χ53444-24-4-24444-24-204-2-2-4002-4-400-2-24400-2-200-420000200002-40000000-2-200000200000000200000000000000000000000000
χ54444-24-4-244-4-4-24-204-2-2-4002-440022-4-400-2-200-42000020000-2400000002200000200000000-200000000000000000000000000
χ55444-2-24-24-244-2-214-21-2-2-2-2-24400-2-2-2-20011-24-21-21-21-24000-2-2-2-200000110000-211100000-2111000000000000000000000000
χ56444-2-24-24-244-2-21-4-21-2-222-24400-2-2-2-200112-4-212-12-1-2-4000-2-2220000011000021-1-10000021-1-1000000000000000000000000
χ57444-2-24-24-2-4-4-2-214-21-2-2-2-2-24-40022220011-24-21-21-21-2-4000222200000-1-10000-2111000002-1-1-1000000000000000000000000
χ58444-2-24-24-2-4-4-2-21-4-21-2-222-24-400222200112-4-212-12-1-2400022-2-200000-1-1000021-1-100000-2-111000000000000000000000000
χ59444-2-2-4-24-244-2-210-21-22−2i32i32-4-400-2-2-2-20011002-1−2i3i32i3−i32000022−2i32i3000001100000-1i3−i3000000-1i3−i3000000000000000000000000
χ60444-2-2-4-24-244-2-210-21-222i3−2i32-4-400-2-2-2-20011002-12i3−i3−2i3i320000222i3−2i3000001100000-1−i3i3000000-1−i3i3000000000000000000000000
χ61444-2-2-4-24-2-4-4-2-210-21-22−2i32i32-440022220011002-1−2i3i32i3−i320000-2-22i3−2i300000-1-100000-1i3−i30000001−i3i3000000000000000000000000
χ62444-2-2-4-24-2-4-4-2-210-21-222i3−2i32-440022220011002-12i3−i3−2i3i320000-2-2−2i32i300000-1-100000-1−i3i30000001i3−i3000000000000000000000000
χ6344-244-44-2400-2-240-24-2-400-4204-40000-4-4-2-2002-400002000-20000400020022000200000000000-200000000000000000000000
χ6444-244-44-2400-2-240-24-2-400-420-44000044-2-2002-40000200020000-4000-200-2-2000200000000000200000000000000000000000
χ6544-24-244-2-200-21-241-2-2-2-2-24-20440000-2-2114-21-21-21-2-2040-20000-2-2-20-2001100-21110000-20000111000000000000000000000
χ6644-24-244-2-200-21-241-2-2-2-2-24-20-4-4000022114-21-21-21-2-20-40200002220200-1-100-2111000020000-1-1-1000000000000000000000
χ6744-24-244-2-200-21-2-41-2-2-2224-20440000-2-211-421-2-12-12-20-40-20000-2220-200110021-1-10000200001-1-1000000000000000000000
χ6844-24-244-2-200-21-2-41-2-2-2224-20-4-400002211-421-2-12-12-2040200002-2-20200-1-10021-1-10000-20000-111000000000000000000000
χ6944-24-2-44-2-200-21-201-2-22−2i32i3-4204-40000221100-12i3−2i3−i32i32000-20000-2−2i32i30200-1-1000-1i3−i30000000001i3−i3000000000000000000000
χ7044-24-2-44-2-200-21-201-2-22−2i32i3-420-440000-2-21100-12i3−2i3−i32i320002000022i3−2i30-20011000-1i3−i3000000000-1−i3i3000000000000000000000
χ7144-24-2-44-2-200-21-201-2-222i3−2i3-4204-40000221100-12−i32i3i3−2i32000-20000-22i3−2i30200-1-1000-1−i3i30000000001−i3i3000000000000000000000
χ7244-24-2-44-2-200-21-201-2-222i3−2i3-420-440000-2-21100-12−i32i3i3−2i32000200002−2i32i30-20011000-1−i3i3000000000-1i3−i3000000000000000000000
χ7344-2-244-2-24001-2-24-2-21444-2-200000000011-2-2-2-2-2-2-2-2100400000000400000-2-21111000000000000-2-2-2110000000000100000
χ7444-2-244-2-24001-2-24-2-21444-2-200000000011-2-2-2-2-2-2-2-2100-400000000-400000221111000000000000222-1-10000000000-100000
χ7544-2-244-2-24001-2-2-4-2-214-4-4-2-20000000001122-2-22222100400000000-40000022-11-1-1000000000000-2-22-1-10000000000100000
χ7644-2-244-2-24001-2-2-4-2-214-4-4-2-20000000001122-2-22222100-400000000400000-2-2-11-1-100000000000022-2110000000000-100000
χ774-44440-4-4-44i−4i4440-4-4-4000000004i−4i4i−4i004-400000000000000000000004i−4i00000000000000000000000000000000000000000
χ784-44440-4-4-4−4i4i4440-4-4-400000000−4i4i−4i4i004-40000000000000000000000−4i4i00000000000000000000000000000000000000000
χ794-444-20-4-424i−4i4-2-2022-4000000004i−4i−2i2i23−23-220000000000000000000000−2i2i23−2300000000−2i32i300000000000000000000000000000
χ804-444-20-4-424i−4i4-2-2022-4000000004i−4i−2i2i−2323-220000000000000000000000−2i2i−2323000000002i3−2i300000000000000000000000000000
χ814-444-20-4-42−4i4i4-2-2022-400000000−4i4i2i−2i23−23-2200000000000000000000002i−2i23−23000000002i3−2i300000000000000000000000000000
χ824-444-20-4-42−4i4i4-2-2022-400000000−4i4i2i−2i−2323-2200000000000000000000002i−2i−232300000000−2i32i300000000000000000000000000000
χ834-44-2402-4-44i−4i-24-20-42200000000−2i2i4i−4i00-220000000000000000000000−2i2i00i6−i60000000000000000000i6−i6000000006−6000000
χ844-44-2402-4-44i−4i-24-20-42200000000−2i2i4i−4i00-220000000000000000000000−2i2i00−i6i60000000000000000000−i6i600000000−66000000
χ854-44-2402-4-4−4i4i-24-20-422000000002i−2i−4i4i00-2200000000000000000000002i−2i00i6−i60000000000000000000i6−i600000000−66000000
χ864-44-2402-4-4−4i4i-24-20-422000000002i−2i−4i4i00-2200000000000000000000002i−2i00−i6i60000000000000000000−i6i6000000006−6000000
χ8788-4-48-8-4-48002-4-40-4-42-800440000000002200440000-200000000000000000000-200000000000000000000000000000000000
χ8888-4-4-48-4-4-4002228222-4-4-4-4-4000000000-1-1-4-4222222200000000000000000002-1-1-1000000000000000000000000000000000
χ8988-4-4-48-4-4-400222-8222-444-4-4000000000-1-14422-2-2-2-220000000000000000000-2-111000000000000000000000000000000000
χ9088-4-4-4-8-4-4-40022202224−4i34i344000000000-1-100-2-22i32i3−2i3−2i3-2000000000000000000001−i3i3000000000000000000000000000000000
χ9188-4-4-4-8-4-4-400222022244i3−4i344000000000-1-100-2-2−2i3−2i32i32i3-2000000000000000000001i3−i3000000000000000000000000000000000
χ928-88-4-404-848i−8i-4-4204-2400000000−4i4i−4i4i002-200000000000000000000002i−2i00000000000000000000000000000000000000000
χ938-88-4-404-84−8i8i-4-4204-24000000004i−4i4i−4i002-20000000000000000000000−2i2i00000000000000000000000000000000000000000
χ948-8-4880-84-800-4-4804-8400000000000000-4400000000000000000000000000000000000000000000000000000000000000000
χ958-8-48-40-84400-42-40-24400000000000043−432-2000000000000000000000000−2323000000000000000000000000000000000000000
χ968-8-48-40-84400-42-40-244000000000000−43432-200000000000000000000000023−23000000000000000000000000000000000000000
χ978-8-4-48044-8002-4-4044-2000000000000002-2000000000000000000000000002i6−2i60000000000000000000−i6i60000000000000000
χ988-8-4-48044-8002-4-4044-2000000000000002-200000000000000000000000000−2i62i60000000000000000000i6−i60000000000000000
χ9916-16-8-8-80888004440-4-4-400000000000000-2200000000000000000000000000000000000000000000000000000000000000000

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