Finite Group Databasebeta

← Group #13156993

Character table — Group #13156993

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11222222222224444444444444444444488888888888888121212121212121212121212242424242424242424242424242424242424242424363636363636363636363636727272216
order12222333666663336666666666666666636666666666666224466661212121246666661212121212121212121212121212244466121212121212412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-11111111-1-111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-11-111-1-111-1-111-111-1-1111-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1
χ4111111111111111111111111111111111111111111111111-11-111-1-111-1-1-11-111-1-11-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-11
χ511111111111111111111111111111111111111111111111-11-11-1-111-1-1111-11-1-111-1111-1-111111111-1-111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111111111111-11-11-1-111-1-111-1-11-1-111-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-111-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-11
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
χ92222222-1222-122-1-1222-1-1-12-1-1-1-1222-1-12-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1022-1-1-1-12002-1-1-1-10000002200-1-1-1-100000000
χ102222222-1222-122-1-1222-1-1-12-1-1-1-1222-1-12-122-1-1-1-1-1-1-1-1-1-1-12-22-2-1-111-1-11102-2-1-111200-2-1-111000000-2-200111100000000
χ112222222-1222-122-1-1222-1-1-12-1-1-1-1222-1-12-122-1-1-1-1-1-1-1-1-1-1-1-22-2211-1-111-1-10-2211-1-1-200211-1-1000000-2-200111100000000
χ122222222-1222-122-1-1222-1-1-12-1-1-1-1222-1-12-122-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110-2-21111-200-211110000002200-1-1-1-100000000
χ13222222-1222-122-12-122-1222-122-1-1-1-1-12-1-1-1-1-122-1-1-1-1-1-1-1-1-12020220022002-10-1-100-1220-1-100-1-1-1-1-1-10000000000002-1-10
χ14222222-1222-122-12-122-1222-122-1-1-1-1-12-1-1-1-1-122-1-1-1-1-1-1-1-1-1202022002200-2-10-1-100-1-2-20-1-100111111000000000000-2110
χ15222222-1222-122-12-122-1222-122-1-1-1-1-12-1-1-1-1-122-1-1-1-1-1-1-1-1-1-20-20-2-200-2-200210110012201100-1-1-1-1-1-1000000000000-2110
χ16222222-1222-122-12-122-1222-122-1-1-1-1-12-1-1-1-1-122-1-1-1-1-1-1-1-1-1-20-20-2-200-2-200-21011001-2-2011001111110000000000002-1-10
χ1722222-122-1-122-1-1-12-1-12222-1-1-1222-1-1-122-1-1-1-1-122-1-1-1-1-1-1-102020022002220-100-1-10-1-1-100-1-122-1-1-1-100220000-1-1-1-10000
χ1822222-122-1-122-1-1-12-1-12222-1-1-1222-1-1-122-1-1-1-1-122-1-1-1-1-1-1-1020200220022-20-100-1-1011-100-1-1-2-2111100-2-2000011110000
χ1922222-122-1-122-1-1-12-1-12222-1-1-1222-1-1-122-1-1-1-1-122-1-1-1-1-1-1-10-20-200-2-200-2-220100110-1-11001122-1-1-1-100-2-2000011110000
χ2022222-122-1-122-1-1-12-1-12222-1-1-1222-1-1-122-1-1-1-1-122-1-1-1-1-1-1-10-20-200-2-200-2-2-201001101110011-2-2111100220000-1-1-1-10000
χ21222-2-222222222222-2-2-22-2-2222-2-222222-22-2-2-2-22-2222-2-2-2-2020-2002200-2-20020022000-200-2-20000000000000000000000
χ22222-2-222222222222-2-2-22-2-2222-2-222222-22-2-2-2-22-2222-2-2-2-20-20200-2-2002200-200-2-2000200220000000000000000000000
χ23222-2-222-1222-122-1-1-2-2-2-1112-1-111222-1-1-2-1-2-211-11-1-1-11111020-2−i3i3-1-1−i3i311002−i3i3-1-1000-2−i3i3110000000000−i3i3−i3i300000000
χ24222-2-222-1222-122-1-1-2-2-2-1112-1-111222-1-1-2-1-2-211-11-1-1-11111020-2i3−i3-1-1i3−i311002i3−i3-1-1000-2i3−i3110000000000i3−i3i3−i300000000
χ25222-2-222-1222-122-1-1-2-2-2-1112-1-111222-1-1-2-1-2-211-11-1-1-111110-202−i3i311−i3i3-1-100-2−i3i3110002−i3i3-1-10000000000i3−i3i3−i300000000
χ26222-2-222-1222-122-1-1-2-2-2-1112-1-111222-1-1-2-1-2-211-11-1-1-111110-202i3−i311i3−i3-1-100-2i3−i3110002i3−i3-1-10000000000−i3i3−i3i300000000
χ27222-2-2-122-1-122-1-1-1211-22-2-2-1-1-1-2-22-1-1-12-2-111112-2-1-1-11111020-2002200-2-200-100-1-10−i3i31001100−i3−i3i3i300000000−i3−i3i3i30000
χ28222-2-2-122-1-122-1-1-1211-22-2-2-1-1-1-2-22-1-1-12-2-111112-2-1-1-11111020-2002200-2-200-100-1-10i3−i31001100i3i3−i3−i300000000i3i3−i3−i30000
χ29222-2-2-122-1-122-1-1-1211-22-2-2-1-1-1-2-22-1-1-12-2-111112-2-1-1-111110-20200-2-2002200100110−i3i3-100-1-100−i3−i3i3i300000000i3i3−i3−i30000
χ30222-2-2-122-1-122-1-1-1211-22-2-2-1-1-1-2-22-1-1-12-2-111112-2-1-1-111110-20200-2-2002200100110i3−i3-100-1-100i3i3−i3−i300000000−i3−i3i3i30000
χ3122-22-2222-2-22222222-2-2-22-22-2-2-2-2-2-2-222222-22-2-222-2-222-2-20000000000000000000000000000000002-20022-2-200000000
χ3222-22-2222-2-22222222-2-2-22-22-2-2-2-2-2-2-222222-22-2-222-2-222-2-2000000000000000000000000000000000-2200-2-22200000000
χ3322-22-222-1-2-22-122-1-12-2-21-1121111-2-2-2-1-12-12-2-111-1-111-1-1110000−i3i3−i3i3i3−i3−i3i3000−i3i3−i3i30000i3−i3−i3i30000002-200-1-11100000000
χ3422-22-222-1-2-22-122-1-12-2-21-1121111-2-2-2-1-12-12-2-111-1-111-1-1110000−i3i3i3−i3i3−i3i3−i3000−i3i3i3−i30000i3−i3i3−i3000000-220011-1-100000000
χ3522-22-222-1-2-22-122-1-12-2-21-1121111-2-2-2-1-12-12-2-111-1-111-1-1110000i3−i3−i3i3−i3i3−i3i3000i3−i3−i3i30000−i3i3−i3i3000000-220011-1-100000000
χ3622-22-222-1-2-22-122-1-12-2-21-1121111-2-2-2-1-12-12-2-111-1-111-1-1110000i3−i3i3−i3−i3i3i3−i3000i3−i3i3−i30000−i3i3i3−i30000002-200-1-11100000000
χ3722-2-22222-2-2222222-222-2-222-2-222-2-2-222-22-22-22-2-22-2-2-2-22220-202200-2-2000202200-2000-2-2000000000000000000000000
χ3822-2-22222-2-2222222-222-2-222-2-222-2-2-222-22-22-22-2-22-2-2-2-222-2020-2-20022000-20-2-200200022000000000000000000000000
χ3922-2-2222-1-2-22-122-1-1-22211-1211-1-1-2-2-2-1-1-2-1-221-111-11111-1-120-20-1-1−i3i311i3−i3020-1-1−i3i3-200011i3−i30000000000−i3i3i3−i300000000
χ4022-2-2222-1-2-22-122-1-1-22211-1211-1-1-2-2-2-1-1-2-1-221-111-11111-1-120-20-1-1i3−i311−i3i3020-1-1i3−i3-200011−i3i30000000000i3−i3−i3i300000000
χ4122-2-2222-1-2-22-122-1-1-22211-1211-1-1-2-2-2-1-1-2-1-221-111-11111-1-1-202011−i3i3-1-1i3−i30-2011−i3i32000-1-1i3−i30000000000i3−i3−i3i300000000
χ4222-2-2222-1-2-22-122-1-1-22211-1211-1-1-2-2-2-1-1-2-1-221-111-11111-1-1-202011i3−i3-1-1−i3i30-2011i3−i32000-1-1−i3i30000000000−i3i3i3−i300000000
χ4322-2-222-12-2-2-122-12-1-22-1-2-22-1-2-2-1-11112-11-11-1-2211-11111-1-120-202200-2-2000-10-1-100100011003−33−33−300000000000003−30
χ4422-2-222-12-2-2-122-12-1-22-1-2-22-1-2-2-1-11112-11-11-1-2211-11111-1-120-202200-2-2000-10-1-10010001100−33−33−330000000000000−330
χ4522-2-222-12-2-2-122-12-1-22-1-2-22-1-2-2-1-11112-11-11-1-2211-11111-1-1-2020-2-20022000101100-1000-1-1003−33−33−30000000000000−330
χ4622-2-222-12-2-2-122-12-1-22-1-2-22-1-2-2-1-11112-11-11-1-2211-11111-1-1-2020-2-20022000101100-1000-1-100−33−33−3300000000000003−30
χ47444444-2-244-2-24-2-2144-2-2-2-2-2-2-211-2-2-2-21-21-2-2-2-21111111114040-2-200-2-2000-201100-200011000000000000000000000000
χ48444444-2-244-2-24-2-2144-2-2-2-2-2-2-211-2-2-2-21-21-2-2-2-2111111111-40-4022002200020-1-1002000-1-1000000000000000000000000
χ4944444-24-2-2-24-2-2-21-2-2-24-2-2-2-211-2-24-2-21-241-2-211-2-21111111040400-2-200-2-200-20011000-200110000000000000000000000
χ5044444-24-2-2-24-2-2-21-2-2-24-2-2-2-211-2-24-2-21-241-2-211-2-211111110-40-40022002200200-1-1000200-1-10000000000000000000000
χ5144444-2-24-2-2-24-21-2-2-2-2-24441-2-2-2-2-211-2-2-2111-2-2-2-2111111100000000000040000000-2-200000-2-211110000000000000000
χ5244444-2-24-2-2-24-21-2-2-2-2-24441-2-2-2-2-211-2-2-2111-2-2-2-21111111000000000000-40000000220000022-1-1-1-10000000000000000
χ53444-4-44-2444-244-24-2-4-424-4-4-24422-2-2-24-22-222-4-4-22-2-2-222220000000000000000000000000000000000000000000000000
χ54444-4-44-2-244-2-24-2-21-4-42-222-2-2-2-1-1-2-2-2-212122221-1111-1-1-1-10000−2i32i300−2i32i300000i3−i3000000i3−i3000000000000000000000000
χ55444-4-44-2-244-2-24-2-21-4-42-222-2-2-2-1-1-2-2-2-212122221-1111-1-1-1-100002i3−2i3002i3−2i300000−i3i3000000−i3i3000000000000000000000000
χ56444-4-4-24-2-2-24-2-2-21-222-4-222-211224-2-21-2-4122-1-1-22111-1-1-1-1040-400-2-2002200-20011000200-1-10000000000000000000000
χ57444-4-4-24-2-2-24-2-2-21-222-4-222-211224-2-21-2-4122-1-1-22111-1-1-1-10-404002200-2-200200-1-1000-200110000000000000000000000
χ58444-4-4-2-24-2-2-24-21-2-22224-4-41-2-222-211-2-221-1-122-22111-1-1-1-100000000000000000000−2i32i30000000i3i3−i3−i30000000000000000
χ59444-4-4-2-24-2-2-24-21-2-22224-4-41-2-222-211-2-221-1-122-22111-1-1-1-1000000000000000000002i3−2i30000000−i3−i3i3i30000000000000000
χ6044-44-44-24-4-4-244-24-24-42-44-4-2-4-4222224-2-2-2-224-42-2-222-2-2220000000000000000000000000000000000000000000000000
χ6144-44-44-2-2-4-4-2-24-2-214-422-22-222-1-1222-21-21-22-22-111-1-111-1-10000−2i32i3002i3−2i300000i3−i3000000−i3i3000000000000000000000000
χ6244-44-44-2-2-4-4-2-24-2-214-422-22-222-1-1222-21-21-22-22-111-1-111-1-100002i3−2i300−2i32i300000−i3i3000000i3−i3000000000000000000000000
χ6344-44-4-2442244-2-2-24-22-4-44-4-222-4-4-422-244-2-22-22-44-222-2-2220000000000000000000000000000000000000000000000000
χ6444-44-4-24-2224-2-2-21-2-22-42-22-2-1-122-4221-241-221-12-21-1-111-1-1000000−2i32i300−2i32i300000i3−i3000000i3−i30000000000000000000000
χ6544-44-4-24-2224-2-2-21-2-22-42-22-2-1-122-4221-241-221-12-21-1-111-1-10000002i3−2i3002i3−2i300000−i3i3000000−i3i30000000000000000000000
χ6644-44-4-2-2422-24-21-2-2-222-44-4122222-1-1-2-2-211-1-222-21-1-111-1-1000000000000000000000000000003i−3i−3i3i0000000000000000
χ6744-44-4-2-2422-24-21-2-2-222-44-4122222-1-1-2-2-211-1-222-21-1-111-1-100000000000000000000000000000−3i3i3i−3i0000000000000000
χ6844-4-444-2-2-4-4-2-24-2-21-44-222-2-22211222-21212-22-2-1-11-1-1-1-11140-40-2-20022000-2011002000-1-1000000000000000000000000
χ6944-4-444-2-2-4-4-2-24-2-21-44-222-2-22211222-21212-22-2-1-11-1-1-1-111-40402200-2-200020-1-100-200011000000000000000000000000
χ7044-4-44-2442244-2-2-242-24-4-44-22244-422-24-4-22-22-2-4-4-22222-2-20000000000000000000000000000000000000000000000000
χ7144-4-44-24-2224-2-2-21-22-2422-2-2-1-1-2-2-4221-2-412-2-11221-1-1-1-111000000−2i32i3002i3−2i300000i3−i3000000−i3i30000000000000000000000
χ7244-4-44-24-2224-2-2-21-22-2422-2-2-1-1-2-2-4221-2-412-2-11221-1-1-1-1110000002i3−2i300−2i32i300000−i3i3000000i3−i30000000000000000000000
χ7344-4-44-2-2422-24-21-2-22-2-2-4-44122-2-22-1-1-2-221-112-2221-1-1-1-11100000000000000000000000000023−23−33−330000000000000000
χ7444-4-44-2-2422-24-21-2-22-2-2-4-44122-2-22-1-1-2-221-112-2221-1-1-1-111000000000000000000000000000−23233−33−30000000000000000
χ754-400044400-4-4-4444000000-40000000-4-404000000-4000000000000000000000000000000000000000002i−2i00002i−2i2i−2i0000
χ764-400044400-4-4-4444000000-40000000-4-404000000-400000000000000000000000000000000000000000−2i2i0000−2i2i−2i2i0000
χ774-4000-244−2i32i3-4-42-2-240000002−2i32i3000−2i32i32-40-20000002−2i32i30000000000000000000000000000000000000002i−2i00002ζ11−2ζ112ζ7−2ζ70000
χ784-4000-244−2i32i3-4-42-2-240000002−2i32i3000−2i32i32-40-20000002−2i32i3000000000000000000000000000000000000000−2i2i0000−2ζ112ζ11−2ζ72ζ70000
χ794-4000-2442i3−2i3-4-42-2-2400000022i3−2i30002i3−2i32-40-200000022i3−2i30000000000000000000000000000000000000002i−2i00002ζ7−2ζ72ζ11−2ζ110000
χ804-4000-2442i3−2i3-4-42-2-2400000022i3−2i30002i3−2i32-40-200000022i3−2i3000000000000000000000000000000000000000−2i2i0000−2ζ72ζ7−2ζ112ζ110000
χ8188888-4-4-4-4-4-4-4-4222-4-4-4-4-4-422222-42222-4-1222222-1-1-1-1-1-1-10000000000000000000000000000000000000000000000000
χ82888-8-8-4-4-4-4-4-4-4-4222444-444222-2-2-422224-1-2-2-2-22-2-1-1-111110000000000000000000000000000000000000000000000000
χ8388-88-8-4-4-444-4-4-4222-4444-442-2-2-2-24-2-222-4-12-22-2-22-111-1-1110000000000000000000000000000000000000000000000000
χ8488-8-88-4-4-444-4-4-42224-4-444-42-2-2224-2-2224-1-22-22-2-2-11111-1-10000000000000000000000000000000000000000000000000
χ858-800088-400-84-88-4-4000000-80000000440-400000040000000000000000000000000000000000000000000000000000000
χ868-80008-48004-8-8-48-400000040000000-840-400000040000000000000000000000000000000000000000000000000000000
χ878-80008-4-40044-8-4-420000004006-60004-202000000-200006-60000000000000000000000000000000000000000000000000
χ888-80008-4-40044-8-4-42000000400-660004-202000000-20000-660000000000000000000000000000000000000000000000000
χ898-8000-48-4−4i34i3-844-42-400000042i3−2i3000−4i34i3-2402000000-22i3−2i300000000000000000000000000000000000000000000000000000
χ908-8000-48-44i3−4i3-844-42-40000004−2i32i30004i3−4i3-2402000000-2−2i32i300000000000000000000000000000000000000000000000000000
χ918-8000-4-48−4i34i34-842-4-4000000-2−4i34i30002i3−2i34402000000-22i3−2i300000000000000000000000000000000000000000000000000000
χ928-8000-4-484i3−4i34-842-4-4000000-24i3−4i3000−2i32i34402000000-2−2i32i300000000000000000000000000000000000000000000000000000
χ938-8000-4-4-4−4i34i3444222000000-22i3−2i36-602i3−2i3-2-20-10000001−i3i3−3i33i3-330000000000000000000000000000000000000000000000000
χ948-8000-4-4-4−4i34i3444222000000-22i3−2i3-6602i3−2i3-2-20-10000001−i3i33i3−3i33-30000000000000000000000000000000000000000000000000
χ958-8000-4-4-44i3−4i3444222000000-2−2i32i36-60−2i32i3-2-20-10000001i3−i33i3−3i3-330000000000000000000000000000000000000000000000000
χ968-8000-4-4-44i3−4i3444222000000-2−2i32i3-660−2i32i3-2-20-10000001i3−i3−3i33i33-30000000000000000000000000000000000000000000000000

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