Finite Group Databasebeta

← Group #13171590

Character table — Group #13171590

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size11222222244444444444466666666668888888888812121212121212121212121212121212121212121216161616181824242424242424242424242436363636363636363636363636487272108108
order1233346662333666661212122244881212121236666666121212444666612121212121212121212242424246661224661212121212121212242422468812121224242424126628
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111-1-111111111111111111-111111111111111-1-1-1-11111111111-1-11111-1-1-1-111-1-1111-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-11-11111-1-1111111111111-111-11-1111-1-1-111-1-111111111-1-11-11-11111-1-1111-1-1-11-1-1-1-111-1-111-1-1-1
χ41111111111111111111111-11-1-1-111-1-1111111111111-1-11-11-1111-1-1-111-1-1-1-1-1-11111-1-11-11-1-1-111-1-1-1-1-11-1-1-11-1-1-1-1-111-1-1111
χ5111111111111111111111-11-1111-1-11111111111111-111-11-11-1-1-1111-1-11111111111-1-1-11-1111-1-11111-11-1-1-11-1-1-1-1-1111-11-1-1
χ6111111111111111111111-11-11-1-1-1-11111111111111-11-1-11-11-1-1-1111-1-111-1-1-1-11111-1-1-11-11-1-1-1-111-1-11-1-1-11-1-1-1-111-1-1-11-111
χ7111111111111111111111-1-1-1-111-1-1-1-111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111-1-111-1-1111-1-1-1-11-1-111
χ8111111111111111111111-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-111-1-1
χ9111111111-1111-1-111111111111111111-1-1-1-1-1-11111-1-1-111111-1-11-1-111111111-1-1-111111-1-1-1-1-1-1-1-111-1-1-11111-1-11111-1-1-1-11
χ10111111111-1111-1-11111111111-1-111111-1-1-1-1-1-11111-1-1111111-1-11-1-11111-1-1-1-1-1-1-111111-1-111-1-1-1-1-1-111-11-1-11-1-1-1-1-1-11111-1
χ11111111111-1111-1-11111111-11-11111-1-11-1-1-1-1-1-11111-11-11-11-11-1-1-11111-1-11111-1-1-11-1-11-1-11-1-1-1-11111-111-11-1-11111-1-1-1-111-1
χ12111111111-1111-1-11111111-11-1-1-111-1-11-1-1-1-1-1-11111-1111-11-11-1-1-11111-1-1-1-1-1-1-1-1-11-1-11-1-1111-1-111-1-11-11-1-11-111-1-11111-1-11
χ13111111111-1111-1-1111111-11-1111-1-1111-1-1-1-1-1-111111-1-1-11-11-1111-1-1-1-1111111-1-1-11-1-1-111-1-1-111-1-1111-11-1-11-111-1-111-11-11-1
χ14111111111-1111-1-1111111-11-11-1-1-1-1111-1-1-1-1-1-111111-11-11-11-1111-1-1-1-111-1-1-1-1-1-1-11-1-1-111-11111-1-1-1-1-111-11-1-11111-1-11-11-11
χ15111111111-1111-1-1111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1111111-1-1-1-1-1-111-111-1-1-1-11111-1-1-1111-1-111-1-111111111-11-1-11-1-1-1-1-1-1-111-11
χ16111111111-1111-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111111-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-1-1111-1-111111111-1-1-1-1-11111-1-111111-1-11-1
χ1722222-2222022200222-2-2-222-2-200-2-2-2-220000002-2-2-20002222-200-200-2-2-2-20000000-2-22220000000000000-200200000000000
χ1822222-2222022200222-2-2-22-2-2200-2-22220000002-2-2-20002-22-2-200200-2-2220000000-22-22-20000000000000200-200000000000
χ1922222-2222022200222-2-2-2-222-20022-2-220000002-2-2-2000-22-22200-20022-2-20000000-22-2-220000000000000200-200000000000
χ2022222-2222022200222-2-2-2-2-22200222220000002-2-2-2000-2-2-2-220020022220000000-2-22-2-20000000000000-200200000000000
χ212222-122-122-12-122-12-122-102022200-1-1-12-122-1-1-12-1-1022020-100022200-1-122-1-1-1-1-1-1000-10-12-100-1-1-1-102000200000-1-1-10-100
χ222222-122-122-12-122-12-122-10202-2-200-1-1-12-122-1-1-12-1-102-2020-100022200-1-1-2-211-1-1-1-1000-10-1-2100-1-1110-2000-2000001110100
χ232222-122-122-12-122-12-122-10-20-2220011-12-122-1-1-12-1-10-220-201000-2-2-2001122-1-1-1-1-1-10001012-10011-1-10-2000-20000011-10100
χ242222-122-122-12-122-12-122-10-20-2-2-20011-12-122-1-1-12-1-10-2-20-201000-2-2-20011-2-211-1-1-1-1000101-2100111102000200000-1-110-100
χ252222-122-12-2-12-1-2-2-12-122-102022200-1-1-1-21-2-211-12-1-10-2-2020-10002-2-200-1-122-1-1111-1000-101-210011-1-10-2000200000-1-110100
χ262222-122-12-2-12-1-2-2-12-122-10202-2-200-1-1-1-21-2-211-12-1-10-22020-10002-2-200-1-1-2-211111-1000-1012-100111102000-20000011-10-100
χ272222-122-12-2-12-1-2-2-12-122-10-20-2220011-1-21-2-211-12-1-102-20-201000-222001122-1-1111-100010-1-2100-1-1-1-102000-2000001110-100
χ282222-122-12-2-12-1-2-2-12-122-10-20-2-2-20011-1-21-2-211-12-1-10220-201000-2220011-2-211111-100010-12-100-1-1110-2000200000-1-1-10100
χ29222-122-1222-1-1222-1-122-12202022-1-100-1-12-1-122-1-12-120220-10222000-1-100-1-122-1-1-1-100-10-10-12-1-100-1-1200020000-1-100-1-1000
χ30222-122-1222-1-1222-1-122-122020-2-2-1-100-1-12-1-122-1-12-120-220-10222000-1-10011-2-2-1-1-1-100-10-101-2-1-10011-2000-20000110011000
χ31222-122-1222-1-1222-1-122-12-20-20221100-1-12-1-122-1-12-1-202-2010-2-2-20001100-1-122-1-1-1-1001010-121100-1-1-2000-200001100-11000
χ32222-122-1222-1-1222-1-122-12-20-20-2-21100-1-12-1-122-1-12-1-20-2-2010-2-2-2000110011-2-2-1-1-1-10010101-2110011200020000-1-1001-1000
χ33222-122-122-2-1-12-2-2-1-122-12202022-1-100-11-211-2-2-1-12-1-20-220-102-2-2000-1-100-1-122111-100-10101-21100-1-1-200020000-1-10011000
χ34222-122-122-2-1-12-2-2-1-122-122020-2-2-1-100-11-211-2-2-1-12-1-20220-102-2-2000-1-10011-2-2111-100-1010-121100112000-200001100-1-1000
χ35222-122-122-2-1-12-2-2-1-122-12-20-20221100-11-211-2-2-1-12-120-2-2010-2220001100-1-122111-10010-101-2-1-100-1-12000-2000011001-1000
χ36222-122-122-2-1-12-2-2-1-122-12-20-20-2-21100-11-211-2-2-1-12-1202-2010-222000110011-2-2111-10010-10-12-1-10011-200020000-1-100-11000
χ3722-122222-122-1-1-1-12-1-1-1222222002222-122-1-1-1-1-1-1-12220-1-122-1-1-1-1-1-1-1-1-1-100002-1-1-122-1-12200-1-1-1-100002-100-1-1-1000000000
χ3822-122222-122-1-1-1-12-1-1-1222-22-20022-2-2-122-1-1-1-1-1-1-122-20-112-2-1-1-1111-1-11100002-1-1-1-2-2-112-200-1-1110000-2100111000000000
χ3922-122222-122-1-1-1-12-1-1-122-22-2200-2-222-122-1-1-1-1-1-1-12-2201-1-22111-1-1-111-1-100002-1-1-1-2-21-1-220011-1-10000-2100111000000000
χ4022-122222-122-1-1-1-12-1-1-122-2-2-2-200-2-2-2-2-122-1-1-1-1-1-1-12-2-2011-2-2111111111100002-1-1-12211-2-200111100002-100-1-1-1000000000
χ4122-122222-1-22-1-1112-1-1-1222222002222-1-2-21111-1-1-12-2-20-1-122-111-111-1-1-1-10000-211-122-1-1-2-20011110000-2-100-111000000000
χ4222-122222-1-22-1-1112-1-1-1222-22-20022-2-2-1-2-21111-1-1-12-220-112-2-1111-1-1-1-1110000-211-1-2-2-11-220011-1-1000021001-1-1000000000
χ4322-122222-1-22-1-1112-1-1-122-22-2200-2-222-1-2-21111-1-1-122-201-1-221-1-1-11111-1-10000-211-1-2-21-12-200-1-111000021001-1-1000000000
χ4422-122222-1-22-1-1112-1-1-122-2-2-2-200-2-2-2-2-1-2-21111-1-1-1222011-2-21-1-11-1-111110000-211-122112200-1-1-1-10000-2-100-111000000000
χ4522-122-222-102-1-1−i3i32-1-11-2-222-2-200-2-2-2-2-100−i3i3−i3i3-111-2000-1-1221−i3i31−i3i3111100000−i3i31-22-1-10000−i3i3−i3i300000100-1−i3i3000000000
χ4622-122-222-102-1-1−i3i32-1-11-2-22-2-2200-2-222-100−i3i3−i3i3-111-2000-112-21−i3i3-1i3−i311-1-100000−i3i312-2-110000−i3i3i3−i300000-1001i3−i3000000000
χ4722-122-222-102-1-1−i3i32-1-11-2-2-222-20022-2-2-100−i3i3−i3i3-111-20001-1-22-1i3−i31−i3i3-1-11100000−i3i312-21-10000i3−i3−i3i300000-1001i3−i3000000000
χ4822-122-222-102-1-1−i3i32-1-11-2-2-2-222002222-100−i3i3−i3i3-111-200011-2-2-1i3−i3-1i3−i3-1-1-1-100000−i3i31-22110000i3−i3i3−i300000100-1−i3i3000000000
χ4922-122-222-102-1-1i3−i32-1-11-2-222-2-200-2-2-2-2-100i3−i3i3−i3-111-2000-1-1221i3−i31i3−i3111100000i3−i31-22-1-10000i3−i3i3−i300000100-1i3−i3000000000
χ5022-122-222-102-1-1i3−i32-1-11-2-22-2-2200-2-222-100i3−i3i3−i3-111-2000-112-21i3−i3-1−i3i311-1-100000i3−i312-2-110000i3−i3−i3i300000-1001−i3i3000000000
χ5122-122-222-102-1-1i3−i32-1-11-2-2-222-20022-2-2-100i3−i3i3−i3-111-20001-1-22-1−i3i31i3−i3-1-11100000i3−i312-21-10000−i3i3i3−i300000-1001−i3i3000000000
χ5222-122-222-102-1-1i3−i32-1-11-2-2-2-222002222-100i3−i3i3−i3-111-200011-2-2-1−i3i3-1−i3i3-1-1-1-100000i3−i31-22110000−i3i3−i3i300000100-1i3−i3000000000
χ534444-2-44-240-24-200-24-2-4-42040-4000022-2000000-2-422000040-2000-400002200000002000-20000000000000000000000000000
χ544444-2-44-240-24-200-24-2-4-420-4040000-2-2-2000000-2-4220000-40200040000-2-20000000200020000000000000000000000000000
χ55444-24-4-2440-2-2400-2-24-42-440-40002200-2000000-22-4200040-20-40000022000000000200-200000000000000000000000000000
χ56444-24-4-2440-2-2400-2-24-42-4-404000-2-200-2000000-22-42000-4020400000-2-2000000000200200000000000000000000000000000
χ57444-2-24-2-2441-2-2441-2-24-2-200004400001-2-2-2-2-2-21-2-2100400000000000000-2-2-2-21111000000-2-2000011000000000000010000
χ58444-2-24-2-2441-2-2441-2-24-2-20000-4-400001-2-2-2-2-2-21-2-2100-40000000000000022221111000000220000-1-10000000000000-10000
χ59444-2-24-2-24-41-2-2-4-41-2-24-2-2000044000012222221-2-2100-400000000000000-2-2-2-2-1-1-11000000220000110000000000000-10000
χ60444-2-24-2-24-41-2-2-4-41-2-24-2-20000-4-4000012222221-2-21004000000000000002222-1-1-11000000-2-20000-1-1000000000000010000
χ6144-24-244-2-24-2-21-2-2-2-21-24-204040000-2-214-2-2-2111-21-20400-20-2000-2-2-200110000-211100010-200001100000000000000000000
χ6244-24-244-2-24-2-21-2-2-2-21-24-20-40-400002214-2-2-2111-21-20-40020200022200-1-10000-2111000-1020000-1-100000000000000000000
χ6344-24-244-2-2-4-2-2122-2-21-24-204040000-2-21-4222-1-11-21-20-400-20-2000-222001100002-1-110001020000-1-100000000000000000000
χ6444-24-244-2-2-4-2-2122-2-21-24-20-40-40000221-4222-1-11-21-204002020002-2-200-1-100002-1-11000-10-200001100000000000000000000
χ6544-24-2-44-2-20-2-21−2i32i3-2-212-42040-4000022100−2i32i3i3−i312-120000-20-20002−2i32i300-1-100000i3−i3-10001000000i3−i300000000000000000000
χ6644-24-2-44-2-20-2-21−2i32i3-2-212-420-4040000-2-2100−2i32i3i3−i312-120000202000-22i3−2i3001100000i3−i3-1000-1000000−i3i300000000000000000000
χ6744-24-2-44-2-20-2-212i3−2i3-2-212-42040-40000221002i3−2i3−i3i312-120000-20-200022i3−2i300-1-100000−i3i3-10001000000−i3i300000000000000000000
χ6844-24-2-44-2-20-2-212i3−2i3-2-212-420-4040000-2-21002i3−2i3−i3i312-120000202000-2−2i32i3001100000−i3i3-1000-1000000i3−i300000000000000000000
χ6944-2-244-24-24-21-2-2-2-21-2-2-24404000-2-2001-2411-2-211-2-2400-20-20-2-2-200011000000-21110010-2000110000000000000000000000
χ7044-2-244-24-24-21-2-2-2-21-2-2-24-40-400022001-2411-2-211-2-2-4002020222000-1-1000000-211100-102000-1-10000000000000000000000
χ7144-2-244-24-2-4-21-222-21-2-2-24404000-2-20012-4-1-12211-2-2-400-20-20-222000110000002-1-1100102000-1-10000000000000000000000
χ7244-2-244-24-2-4-21-222-21-2-2-24-40-4000220012-4-1-12211-2-240020202-2-2000-1-10000002-1-1100-10-2000110000000000000000000000
χ7344-2-24-4-24-20-21-2−2i32i3-21-222-440-40002200100i3−i3−2i32i31-122000-20-202−2i32i3000-1-10000000i3−i3-100100000i3−i30000000000000000000000
χ7444-2-24-4-24-20-21-2−2i32i3-21-222-4-404000-2-200100i3−i3−2i32i31-1220002020-22i3−2i3000110000000i3−i3-100-100000−i3i30000000000000000000000
χ7544-2-24-4-24-20-21-22i3−2i3-21-222-440-40002200100−i3i32i3−2i31-122000-20-2022i3−2i3000-1-10000000−i3i3-100100000−i3i30000000000000000000000
χ7644-2-24-4-24-20-21-22i3−2i3-21-222-4-404000-2-200100−i3i32i3−2i31-1220002020-2−2i32i3000110000000−i3i3-100-100000i3−i30000000000000000000000
χ774-44440-4-4-4044400-4-4-40000000−2i22i200004000000-400000000000000000000−2i22i2−2i22i20000000000000000−2i22i2000000000000000000
χ784-44440-4-4-4044400-4-4-400000002i2−2i200004000000-4000000000000000000002i2−2i22i2−2i200000000000000002i2−2i2000000000000000000
χ794-444-20-42-40-24-2002-420000000−2i22i20023−23-2000000200000000000000000023−23−2i22i2i2−i20000000000000000i2−i200000000000i6−i600000
χ804-444-20-42-40-24-2002-420000000−2i22i200−2323-20000002000000000000000000−2323−2i22i2i2−i20000000000000000i2−i200000000000−i6i600000
χ814-444-20-42-40-24-2002-4200000002i2−2i20023−23-2000000200000000000000000023−232i2−2i2−i2i20000000000000000−i2i200000000000−i6i600000
χ824-444-20-42-40-24-2002-4200000002i2−2i200−2323-20000002000000000000000000−23232i2−2i2−i2i20000000000000000−i2i200000000000i6−i600000
χ834-44-2402-4-40-2-240022-40000000−2i22i223−2300-20000002000000000000000023−2300i2−i2−2i22i20000000000000000i2−i2000000000i6−i60000000
χ844-44-2402-4-40-2-240022-40000000−2i22i2−232300-200000020000000000000000−232300i2−i2−2i22i20000000000000000i2−i2000000000−i6i60000000
χ854-44-2402-4-40-2-240022-400000002i2−2i223−2300-20000002000000000000000023−2300−i2i22i2−2i20000000000000000−i2i2000000000−i6i60000000
χ864-44-2402-4-40-2-240022-400000002i2−2i2−232300-200000020000000000000000−232300−i2i22i2−2i20000000000000000−i2i2000000000i6−i60000000
χ87888-4-4-8-4-4802-4-4002-4-4-84400000000002000000244-2000000000000000000000000-200000000000000000000000000000000
χ8888-4-4-48-4-4-48222-4-4222-4-4-40000000000-1-4-42222-12220000000000000000000002-1-1-100000000000000000000000000000000
χ8988-4-4-48-4-4-4-822244222-4-4-40000000000-144-2-2-2-2-1222000000000000000000000-211-100000000000000000000000000000000
χ9088-4-4-4-8-4-4-40222−4i34i32224440000000000-1002i3−2i32i3−2i3-1-2-2-20000000000000000000000−i3i3100000000000000000000000000000000
χ9188-4-4-4-8-4-4-402224i3−4i32224440000000000-100−2i32i3−2i32i3-1-2-2-20000000000000000000000i3−i3100000000000000000000000000000000
χ928-88-4-4044-802-4-400-2440000000−4i24i200002000000-2000000000000000000002i2−2i22i2−2i20000000000000000−i2i2000000000000000000
χ938-88-4-4044-802-4-400-24400000004i2−4i200002000000-200000000000000000000−2i22i2−2i22i20000000000000000i2−i2000000000000000000
χ948-8-4880-8-8408-4-400-8440000000000000-40000004000000000000000000000000000000000000000000000000000000000000
χ958-8-48-40-8440-4-420044-20000000000043−432000000-2000000000000000000−23230000000000000000000000000000000000000000
χ968-8-48-40-8440-4-420044-200000000000−43432000000-200000000000000000023−230000000000000000000000000000000000000000
χ978-8-4-4804-840-42-4004-2400000000043−43002000000-20000000000000000−2323000000000000000000000000000000000000000000
χ988-8-4-4804-840-42-4004-24000000000−4343002000000-2000000000000000023−23000000000000000000000000000000000000000000
χ9916-16-8-8-80888044400-4-4-40000000000000-20000002000000000000000000000000000000000000000000000000000000000000

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