Finite Group Databasebeta

← Group #13155935

Character table — Group #13155935

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11222222222224444444444444444444488888888888888121212121212121212121212242424242424242424242424242424242424242424363636363636363636363636727272216
order12233344666663336666666661212121212121212366661212121212121212122224666666121246666666661212121212121212121212244466121212121212824248
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1111111111-1-11-1-111-1-1-1-111-1-111-1-1-1-111-1-1-1-1
χ31111111111111111111111111111111111111111111111111-1-11111-1-1-1-11-111-1-1111111-111-1-11111-1-111-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111111111111111111-1-111-1-1-1-1111111-1-111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1
χ611111111111111111111111111111111111111111111111-1-111-1-1-1-11111-11-1-111-1-1-1-1-1-11-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-11
χ711111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-111-111-1-1111111-1-111-1-1-1-111-1-1-11
χ811111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1
χ9222222-2-222222222222222222-2-2-2-2-2-2-2-222222-2-2-2-2-2-2-2-2-22-20022-2-20000002-20022-2-2000000000000000000000000000
χ10222222-2-222222222222222222-2-2-2-2-2-2-2-222222-2-2-2-2-2-2-2-2-2-2200-2-222000000-2200-2-222000000000000000000000000000
χ1122222-1222222-12-1-12-122-1-1-1-12222-1-1-1-12-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-10222-1-1-1-1-1-100200-1-100002200-1-10000-1-10000
χ1222222-1222222-12-1-12-122-1-1-1-12222-1-1-1-12-1-1-1-1-1-1-1-122-1-1-1-122-2-2-1-1-1-111110-22211-1-1-1-100-200110000-2-200110000110000
χ1322222-1222222-12-1-12-122-1-1-1-12222-1-1-1-12-1-1-1-1-1-1-1-122-1-1-1-1-2-2221111-1-1-1-102-2-2-1-1111100200-1-10000-2-200110000110000
χ1422222-1222222-12-1-12-122-1-1-1-12222-1-1-1-12-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2111111110-2-2-211111100-2001100002200-1-10000-1-10000
χ1522222-1-2-22222-12-1-12-122-1-1-1-12-2-2-21111-2-1-1-1-1-1111-2-211112-200-1-111−i3i3−i3i3002-2−i3i3-1-11100000−i3i300000000−i3i30000−i3i30000
χ1622222-1-2-22222-12-1-12-122-1-1-1-12-2-2-21111-2-1-1-1-1-1111-2-211112-200-1-111i3−i3i3−i3002-2i3−i3-1-11100000i3−i300000000i3−i30000i3−i30000
χ1722222-1-2-22222-12-1-12-122-1-1-1-12-2-2-21111-2-1-1-1-1-1111-2-21111-220011-1-1−i3i3−i3i300-22−i3i311-1-100000−i3i300000000i3−i30000i3−i30000
χ1822222-1-2-22222-12-1-12-122-1-1-1-12-2-2-21111-2-1-1-1-1-1111-2-21111-220011-1-1i3−i3i3−i300-22i3−i311-1-100000i3−i300000000−i3i30000−i3i30000
χ192222-1222-1-1-122-12-122-1-1-1-1-12-1-1-1222222-12-1-1-1-1-12-1-1-1-1-1-122002222000020-1-100-1-1-1-1-1-102200-1-1-1-1002200-1-1-1-1000000
χ202222-1222-1-1-122-12-122-1-1-1-1-12-1-1-1222222-12-1-1-1-1-12-1-1-1-1-1-1220022220000-20-1-100-1-1-1-1110-2-200111100-2-2001111000000
χ212222-1222-1-1-122-12-122-1-1-1-1-12-1-1-1222222-12-1-1-1-1-12-1-1-1-1-1-1-2-200-2-2-2-200002011001111-1-102200-1-1-1-100-2-2001111000000
χ222222-1222-1-1-122-12-122-1-1-1-1-12-1-1-1222222-12-1-1-1-1-12-1-1-1-1-1-1-2-200-2-2-2-20000-2011001111110-2-2001111002200-1-1-1-1000000
χ232222-12-2-2-1-1-122-12-122-1-1-1-1-12-111-2-2-2-2-2-2-12-1-1-111-21111112-20022-2-2000000-1100-1-111−i3i300000−i3−i3i3i3000000−i3−i3i3i3000000
χ242222-12-2-2-1-1-122-12-122-1-1-1-1-12-111-2-2-2-2-2-2-12-1-1-111-21111112-20022-2-2000000-1100-1-111i3−i300000i3i3−i3−i3000000i3i3−i3−i3000000
χ252222-12-2-2-1-1-122-12-122-1-1-1-1-12-111-2-2-2-2-2-2-12-1-1-111-2111111-2200-2-2220000001-10011-1-1−i3i300000−i3−i3i3i3000000i3i3−i3−i3000000
χ262222-12-2-2-1-1-122-12-122-1-1-1-1-12-111-2-2-2-2-2-2-12-1-1-111-2111111-2200-2-2220000001-10011-1-1i3−i300000i3i3−i3−i3000000−i3−i3i3i3000000
χ27222-12222222-12-1-12-12-1-1222-1-122-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-10022000022222-100-1-1000022-1-1-1-1-1-1-1-1-10000000000002-1-10
χ28222-12222222-12-1-12-12-1-1222-1-122-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1002200002222-2-100-1-10000-2-2-111-1-11111000000000000-2110
χ29222-12222222-12-1-12-12-1-1222-1-122-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-100-2-20000-2-2-2-22100110000221-1-111-1-1-1-1000000000000-2110
χ30222-12222222-12-1-12-12-1-1222-1-122-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-100-2-20000-2-2-2-2-2100110000-2-21111111110000000000002-1-10
χ3122-22222-22-2-222222-2-2-2-2-2-22222-2-22-2-2-222-2-2-222-222-222-2-2002-2000022-2-2020022000000-200-2-200000000000000000000
χ3222-22222-22-2-222222-2-2-2-2-2-22222-2-22-2-2-222-2-2-222-222-222-2-200-220000-2-2220-200-2-20000002002200000000000000000000
χ3322-2222-222-2-222222-2-2-2-2-2-2222-222-2222-22-2-2-22-22-2-22-2-2220000000000000000000000000000000002-200220000-2-20000
χ3422-2222-222-2-222222-2-2-2-2-2-2222-222-2222-22-2-2-22-22-2-22-2-222000000000000000000000000000000000-2200-2-20000220000
χ3522-222-12-22-2-22-12-1-1-21-2-211-1-122-2-2-11112-1111-1-11-12-2-1-111002-2−i3i3−i3i3-1-1110200-1-1−i3i3−i3i300-2001100000000−i3i30000i3−i30000
χ3622-222-12-22-2-22-12-1-1-21-2-211-1-122-2-2-11112-1111-1-11-12-2-1-111002-2i3−i3i3−i3-1-1110200-1-1i3−i3i3−i300-2001100000000i3−i30000−i3i30000
χ3722-222-12-22-2-22-12-1-1-21-2-211-1-122-2-2-11112-1111-1-11-12-2-1-11100-22−i3i3−i3i311-1-10-20011−i3i3−i3i300200-1-100000000i3−i30000−i3i30000
χ3822-222-12-22-2-22-12-1-1-21-2-211-1-122-2-2-11112-1111-1-11-12-2-1-11100-22i3−i3i3−i311-1-10-20011i3−i3i3−i300200-1-100000000−i3i30000i3−i30000
χ3922-222-1-222-2-22-12-1-1-21-2-211-1-12-2221-1-1-1-2-1111-11-11-2211-1-10000−i3i3i3−i3−i3i3i3−i30000−i3i3−i3i3i3−i300000i3−i300002-200-1-10000110000
χ4022-222-1-222-2-22-12-1-1-21-2-211-1-12-2221-1-1-1-2-1111-11-11-2211-1-10000−i3i3i3−i3i3−i3−i3i30000i3−i3−i3i3i3−i300000−i3i30000-2200110000-1-10000
χ4122-222-1-222-2-22-12-1-1-21-2-211-1-12-2221-1-1-1-2-1111-11-11-2211-1-10000i3−i3−i3i3−i3i3i3−i30000−i3i3i3−i3−i3i300000i3−i30000-2200110000-1-10000
χ4222-222-1-222-2-22-12-1-1-21-2-211-1-12-2221-1-1-1-2-1111-11-11-2211-1-10000i3−i3−i3i3i3−i3−i3i30000i3−i3i3−i3−i3i300000−i3i300002-200-1-10000110000
χ4322-2-1222-22-2-2-12-1-121-211-2-22-1-12-212-211-1-1111-12-2-1-11-1-111002-2000022-2-20-100-1-10000001−i3i311−i3i3−i3i30000000000000−i3i30
χ4422-2-1222-22-2-2-12-1-121-211-2-22-1-12-212-211-1-1111-12-2-1-11-1-111002-2000022-2-20-100-1-10000001i3−i311i3−i3i3−i30000000000000i3−i30
χ4522-2-1222-22-2-2-12-1-121-211-2-22-1-12-212-211-1-1111-12-2-1-11-1-11100-220000-2-222010011000000-1−i3i3-1-1−i3i3−i3i30000000000000i3−i30
χ4622-2-1222-22-2-2-12-1-121-211-2-22-1-12-212-211-1-1111-12-2-1-11-1-11100-220000-2-222010011000000-1i3−i3-1-1i3−i3i3−i30000000000000−i3i30
χ474444-2-244-2-2-24-2-2-214-2-2-2111-2-2-2-24-2-2-2-241-211111-2-2-211114400-2-2-2-2000000-2-2001111000000000000000000000000000
χ484444-2-244-2-2-24-2-2-214-2-2-2111-2-2-2-24-2-2-2-241-211111-2-2-21111-4-40022220000002200-1-1-1-1000000000000000000000000000
χ494444-2-2-4-4-2-2-24-2-2-214-2-2-2111-2-222-42222-41-2111-1-1222-1-1-1-14-400-2-222000000-220011-1-1000000000000000000000000000
χ504444-2-2-4-4-2-2-24-2-2-214-2-2-2111-2-222-42222-41-2111-1-1222-1-1-1-1-440022-2-20000002-200-1-111000000000000000000000000000
χ51444-244-4-4444-24-2-24-24-2-2444-2-2-4-42-4-4222-2-2-2-2-2-4-422222220000000000000000000000000000000000000000000000000
χ52444-24-244444-2-2-21-2-2-2-2-2-2-2-21-244-2-2-211-211111-2-21-2-2111100440000-2-2-2-20-20011000000-2001100000000000000000000
χ53444-24-244444-2-2-21-2-2-2-2-2-2-2-21-244-2-2-211-211111-2-21-2-2111100-4-4000022220200-1-1000000200-1-100000000000000000000
χ54444-24-2-4-4444-2-2-21-2-2-2-2-2-2-2-21-2-4-4222-1-121111122-122-1-1-1-100000000−2i32i3−2i32i30000i3−i3000000000i3−i300000000000000000000
χ55444-24-2-4-4444-2-2-21-2-2-2-2-2-2-2-21-2-4-4222-1-121111122-122-1-1-1-1000000002i3−2i32i3−2i30000−i3i3000000000−i3i300000000000000000000
χ56444-2-2444-2-2-2-241-2-2-2411-2-2-2-21-2-2-244-2-2-21-2111-2-2-21111110000000000004000000000-2-20-2-20011110000000000000000
χ57444-2-2444-2-2-2-241-2-2-2411-2-2-2-21-2-2-244-2-2-21-2111-2-2-2111111000000000000-40000000002202200-1-1-1-10000000000000000
χ58444-2-24-4-4-2-2-2-241-2-2-2411-2-2-2-21222-4-42221-2111222-1-1-1-1-1-10000000000000000000000−2i32i300000i3i3−i3−i30000000000000000
χ59444-2-24-4-4-2-2-2-241-2-2-2411-2-2-2-21222-4-42221-2111222-1-1-1-1-1-100000000000000000000002i3−2i300000−i3−i3i3i30000000000000000
χ6044-44-244-4-22244-24-2-4-42222-24-2-22-44-4-4-44-2-422-2-224-22-2-2220000000000000000000000000000000000000000000000000
χ6144-44-24-44-22244-24-2-4-42222-24-22-24-4444-4-2-422-22-2-42-222-2-20000000000000000000000000000000000000000000000000
χ6244-44-2-24-4-2224-2-2-21-4222-1-11-2-2-22-4-2222412-1-111-1-2-2211-1-10000−2i32i3−2i32i30000000000i3−i3i3−i3000000000000000000000000000
χ6344-44-2-24-4-2224-2-2-21-4222-1-11-2-2-22-4-2222412-1-111-1-2-2211-1-100002i3−2i32i3−2i30000000000−i3i3−i3i3000000000000000000000000000
χ6444-44-2-2-44-2224-2-2-21-4222-1-11-2-22-242-2-2-2-412-1-11-1122-2-1-1110000−2i32i32i3−2i30000000000i3−i3−i3i3000000000000000000000000000
χ6544-44-2-2-44-2224-2-2-21-4222-1-11-2-22-242-2-2-2-412-1-11-1122-2-1-11100002i3−2i3−2i32i30000000000−i3i3i3−i3000000000000000000000000000
χ6644-4-244-444-4-4-24-2-242-422-4-44-2-2-44-2-44-2-22-2222-2-4422-222-2-20000000000000000000000000000000000000000000000000
χ6744-4-24-24-44-4-4-2-2-21-2222222-21-24-42-22-1-1-21-1-1-11-221-2211-1-1004-40000-2-2220-20011000000200-1-100000000000000000000
χ6844-4-24-24-44-4-4-2-2-21-2222222-21-24-42-22-1-1-21-1-1-11-221-2211-1-100-44000022-2-20200-1-1000000-2001100000000000000000000
χ6944-4-24-2-444-4-4-2-2-21-2222222-21-2-44-22-21121-1-1-112-2-12-2-1-11100000000−2i32i32i3−2i30000i3−i3000000000−i3i300000000000000000000
χ7044-4-24-2-444-4-4-2-2-21-2222222-21-2-44-22-21121-1-1-112-2-12-2-1-111000000002i3−2i3−2i32i30000−i3i3000000000i3−i300000000000000000000
χ7144-4-2-244-4-222-241-2-22-4-1-122-2-21-2224-422-212-1-11-22-21-111-1-10000000000000000000000000−2i32i300i3−i3i3−i30000000000000000
χ7244-4-2-244-4-222-241-2-22-4-1-122-2-21-2224-422-212-1-11-22-21-111-1-100000000000000000000000002i3−2i300−i3i3−i3i30000000000000000
χ7344-4-2-24-44-222-241-2-22-4-1-122-2-212-2-2-44-2-2212-1-112-22-11-1-111000000000000000000000000000003-3-330000000000000000
χ7444-4-2-24-44-222-241-2-22-4-1-122-2-212-2-2-44-2-2212-1-112-22-11-1-11100000000000000000000000000000-333-30000000000000000
χ754-4044400-400-4-4444000000-4-4-4000000004000-4000000000000000000000000000000000000000000002i−2i002i−2i2i−2i000000
χ764-4044400-400-4-4444000000-4-4-4000000004000-400000000000000000000000000000000000000000000−2i2i00−2i2i−2i2i000000
χ774-404-24002−2i32i3-4-4-24-200−2i32i3−2i32i32-4200000000-20−2i32i32000000000000000000000000000000000000000000002i−2i002ζ7−2ζ72ζ11−2ζ11000000
χ784-404-24002−2i32i3-4-4-24-200−2i32i3−2i32i32-4200000000-20−2i32i3200000000000000000000000000000000000000000000−2i2i00−2ζ72ζ7−2ζ112ζ11000000
χ794-404-240022i3−2i3-4-4-24-2002i3−2i32i3−2i32-4200000000-202i3−2i32000000000000000000000000000000000000000000002i−2i002ζ11−2ζ112ζ7−2ζ7000000
χ804-404-240022i3−2i3-4-4-24-2002i3−2i32i3−2i32-4200000000-202i3−2i3200000000000000000000000000000000000000000000−2i2i00−2ζ112ζ11−2ζ72ζ7000000
χ81888-4-4-488-4-4-4-4-4222-4-42222222-4-4-4-4-422-4-12-1-1-122222-1-1-1-10000000000000000000000000000000000000000000000000
χ82888-4-4-4-8-8-4-4-4-4-4222-4-4222222244444-2-24-12-1-1-1-2-2-2-2-211110000000000000000000000000000000000000000000000000
χ8388-8-4-4-48-8-444-4-422244-2-2-2-2222-444-44-2-2-4-1-211-12-222-2-1-1110000000000000000000000000000000000000000000000000
χ8488-8-4-4-4-88-444-4-422244-2-2-2-22224-4-44-4224-1-211-1-22-2-2211-1-10000000000000000000000000000000000000000000000000
χ858-8088-400-800-848-4-400000044-800000000-400040000000000000000000000000000000000000000000000000000000000
χ868-808-4-4004−4i34i3-84-4-4200−4i34i32i3−2i3-24400000000202i3−2i3-20000000000000000000000000000000000000000000000000000000000
χ878-808-4-40044i3−4i3-84-4-42004i3−4i3−2i32i3-2440000000020−2i32i3-20000000000000000000000000000000000000000000000000000000000
χ888-80-48800-8004-8-4-48000000-84400000000-400040000000000000000000000000000000000000000000000000000000000
χ898-80-48-400-80044-42-40000004-24000006i−6i02000-200000006i−6i0000000000000000000000000000000000000000000000000
χ908-80-48-400-80044-42-40000004-2400000−6i6i02000-20000000−6i6i0000000000000000000000000000000000000000000000000
χ918-80-4-48004−4i34i34-82-4-4002i3−2i3−4i34i344-200000000202i3−2i3-20000000000000000000000000000000000000000000000000000000000
χ928-80-4-480044i3−4i34-82-4-400−2i32i34i3−4i344-20000000020−2i32i3-20000000000000000000000000000000000000000000000000000000000
χ938-80-4-4-4004−4i34i344222002i3−2i32i3−2i3-2-2-2000006i−6i0-10−i3i310000033−33−3i3i0000000000000000000000000000000000000000000000000
χ948-80-4-4-4004−4i34i344222002i3−2i32i3−2i3-2-2-200000−6i6i0-10−i3i3100000−33333i−3i0000000000000000000000000000000000000000000000000
χ958-80-4-4-40044i3−4i34422200−2i32i3−2i32i3-2-2-2000006i−6i0-10i3−i3100000−3333−3i3i0000000000000000000000000000000000000000000000000
χ968-80-4-4-40044i3−4i34422200−2i32i3−2i32i3-2-2-200000−6i6i0-10i3−i310000033−333i−3i0000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.