Finite Group Databasebeta

← Group #13155936

Character table — Group #13155936

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11222222222224444444444444444444488888888888888121212121212121212121212242424242424242424242424242424242424242424363636363636363636363636727272216
order12233344666121233366666612121212121212121212123666666121212121212122244666612121212666666812121212121224242424242424242244666612121212412128
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-11-111-1-111-1-11-111-1-111-111-1-111111111-1-111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-11-111-1-111-1-11-111-1-1-11-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111111111111111111-11-11-1-111-1-111-11-1-1111-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1
χ611111111111111111111111111111111111111111111111-11-11-1-111-1-111-11-1-111-1-11-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-11
χ711111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-11
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
χ9222222-2-2222-2-2222222222-2-2-2-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-20000000000000000000000000000000002-20022-2-200000000
χ10222222-2-2222-2-2222222222-2-2-2-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2000000000000000000000000000000000-2200-2-22200000000
χ1122222-1222-12222-1-12-12-1-122-1-12-1-1-1-1222-12-1-1-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1022-1-1-1-1000000002200-1-1-1-100000000
χ1222222-1222-12222-1-12-12-1-122-1-12-1-1-1-1222-12-1-1-1-1-12-1-1-1-1-1-12-22-2-1-111-1-1112-2-1-11102-2-1-11100000000-2-200111100000000
χ1322222-1222-12222-1-12-12-1-122-1-12-1-1-1-1222-12-1-1-1-1-12-1-1-1-1-1-1-22-2211-1-111-1-1-2211-1-10-2211-1-100000000-2-200111100000000
χ1422222-1222-12222-1-12-12-1-122-1-12-1-1-1-1222-12-1-1-1-1-12-1-1-1-1-1-1-2-2-2-211111111-2-211110-2-21111000000002200-1-1-1-100000000
χ1522222-1-2-22-12-2-22-1-12-12-1-12-211-21111-2-2-2-12-1-1-1-1-1-21111110000−i3i3−i3i3−i3i3−i3i300−i3i3−i3i3000−i3i3−i3i3000000002-200-1-11100000000
χ1622222-1-2-22-12-2-22-1-12-12-1-12-211-21111-2-2-2-12-1-1-1-1-1-21111110000−i3i3i3−i3−i3i3i3−i300−i3i3i3−i3000−i3i3i3−i300000000-220011-1-100000000
χ1722222-1-2-22-12-2-22-1-12-12-1-12-211-21111-2-2-2-12-1-1-1-1-1-21111110000i3−i3−i3i3i3−i3−i3i300i3−i3−i3i3000i3−i3−i3i300000000-220011-1-100000000
χ1822222-1-2-22-12-2-22-1-12-12-1-12-211-21111-2-2-2-12-1-1-1-1-1-21111110000i3−i3i3−i3i3−i3i3−i300i3−i3i3−i3000i3−i3i3−i3000000002-200-1-11100000000
χ192222-122222-122-12-1-12-12-12222-122-1-1-1-1-1-1-12-1-1-1-1-12-1-1-1-1-10202002200220-100-1-120-100-1-122-1-1-1-1-1-10000000000002-1-10
χ202222-122222-122-12-1-12-12-12222-122-1-1-1-1-1-1-12-1-1-1-1-12-1-1-1-1-10202002200220-100-1-1-20-100-1-1-2-2111111000000000000-2110
χ212222-122222-122-12-1-12-12-12222-122-1-1-1-1-1-1-12-1-1-1-1-12-1-1-1-1-10-20-200-2-200-2-2010011201001122-1-1-1-1-1-1000000000000-2110
χ222222-122222-122-12-1-12-12-12222-122-1-1-1-1-1-1-12-1-1-1-1-12-1-1-1-1-10-20-200-2-200-2-2010011-2010011-2-21111110000000000002-1-10
χ23222-12222-122-1-1-1-1222-1-12-1-1222-1-1222-1-1-1-1-12-1-1-1-1-12-1-1-1-1202022002200-10-1-1002-10-1-100-1-122-1-1-1-100220000-1-1-1-10000
χ24222-12222-122-1-1-1-1222-1-12-1-1222-1-1222-1-1-1-1-12-1-1-1-1-12-1-1-1-1202022002200-10-1-100-2-10-1-10011-2-2111100-2-2000011110000
χ25222-12222-122-1-1-1-1222-1-12-1-1222-1-1222-1-1-1-1-12-1-1-1-1-12-1-1-1-1-20-20-2-200-2-2001011002101100-1-122-1-1-1-100-2-2000011110000
χ26222-12222-122-1-1-1-1222-1-12-1-1222-1-1222-1-1-1-1-12-1-1-1-1-12-1-1-1-1-20-20-2-200-2-200101100-210110011-2-2111100220000-1-1-1-10000
χ2722-22222-222222222-2-2222-2-22-2-222-2-22222-2-2-2-2-22-2-2222-2-2020-2002200-2-202002200-200-2-2000000000000000000000000
χ2822-22222-222222222-2-2222-2-22-2-222-2-22222-2-2-2-2-22-2-2222-2-20-20200-2-200220-200-2-20020022000000000000000000000000
χ2922-2222-22222-2-2222-2-2222-22-222-2-222-2-2-22-2-2-2-2-2222-2-2-22220-202200-2-2002022000-20-2-200000000000000000000000000
χ3022-2222-22222-2-2222-2-2222-22-222-2-222-2-2-22-2-2-2-2-2222-2-2-222-2020-2-2002200-20-2-2000202200000000000000000000000000
χ3122-222-12-22-12222-1-1-212-1-1-2-2-11-2-1-111222-1-21111-1-21-1-1-111020-2−i3i3-1-1i3−i31102−i3i3-1-100-2i3−i311000000000000−i3i3−i3i300000000
χ3222-222-12-22-12222-1-1-212-1-1-2-2-11-2-1-111222-1-21111-1-21-1-1-111020-2i3−i3-1-1−i3i31102i3−i3-1-100-2−i3i311000000000000i3−i3i3−i300000000
χ3322-222-12-22-12222-1-1-212-1-1-2-2-11-2-1-111222-1-21111-1-21-1-1-1110-202−i3i311i3−i3-1-10-2−i3i311002i3−i3-1-1000000000000i3−i3i3−i300000000
χ3422-222-12-22-12222-1-1-212-1-1-2-2-11-2-1-111222-1-21111-1-21-1-1-1110-202i3−i311−i3i3-1-10-2i3−i311002−i3i3-1-1000000000000−i3i3−i3i300000000
χ3522-222-1-222-12-2-22-1-1-212-1-1-221-1211-1-1-2-2-2-1-21111-12-1111-1-120-20-1-1−i3i311i3−i320-1-1−i3i30-2011i3−i3000000000000−i3i3i3−i300000000
χ3622-222-1-222-12-2-22-1-1-212-1-1-221-1211-1-1-2-2-2-1-21111-12-1111-1-120-20-1-1i3−i311−i3i320-1-1i3−i30-2011−i3i3000000000000i3−i3−i3i300000000
χ3722-222-1-222-12-2-22-1-1-212-1-1-221-1211-1-1-2-2-2-1-21111-12-1111-1-1-202011−i3i3-1-1i3−i3-2011−i3i3020-1-1i3−i3000000000000i3−i3−i3i300000000
χ3822-222-1-222-12-2-22-1-1-212-1-1-221-1211-1-1-2-2-2-1-21111-12-1111-1-1-202011i3−i3-1-1−i3i3-2011i3−i3020-1-1−i3i3000000000000−i3i3i3−i300000000
χ3922-22-122-222-122-12-11-2-12-1-2-22-212211-1-1-1-11-2111-11-2-1-1-111020-2002200-2-20-100-1-1001001100−i3i3−i3−i3i3i30000000000000−i3i30
χ4022-22-122-222-122-12-11-2-12-1-2-22-212211-1-1-1-11-2111-11-2-1-1-111020-2002200-2-20-100-1-1001001100i3−i3i3i3−i3−i30000000000000i3−i30
χ4122-22-122-222-122-12-11-2-12-1-2-22-212211-1-1-1-11-2111-11-2-1-1-1110-20200-2-2002201001100-100-1-100−i3i3−i3−i3i3i30000000000000i3−i30
χ4222-22-122-222-122-12-11-2-12-1-2-22-212211-1-1-1-11-2111-11-2-1-1-1110-20200-2-2002201001100-100-1-100i3−i3i3i3−i3−i30000000000000−i3i30
χ4322-2-122-22-12211-1-12-2-2-1-121-1-2221122-211-111-211-1-1-1-211-1-120-202200-2-200-10-1-10001011003−3003−33−30000000033−3−30000
χ4422-2-122-22-12211-1-12-2-2-1-121-1-2221122-211-111-211-1-1-1-211-1-120-202200-2-200-10-1-1000101100−3300−33−3300000000−3−3330000
χ4522-2-122-22-12211-1-12-2-2-1-121-1-2221122-211-111-211-1-1-1-211-1-1-2020-2-20022001011000-10-1-1003−3003−33−300000000−3−3330000
χ4622-2-122-22-12211-1-12-2-2-1-121-1-2221122-211-111-211-1-1-1-211-1-1-2020-2-20022001011000-10-1-100−3300−33−330000000033−3−30000
χ474444-24-4-444-2-4-4-24-2-24-24-24-4-4-42-4-422222-2-24-2-2-2-22-4222220000000000000000000000000000000000000000000000000
χ484444-2-2444-2-244-2-21-2-2-2-2144-2-2-2-2-211-2-2-21-2-21111-2-211111040400-2-200-2-20-2001100-20011000000000000000000000000
χ494444-2-2444-2-244-2-21-2-2-2-2144-2-2-2-2-211-2-2-21-2-21111-2-2111110-40-4002200220200-1-100200-1-1000000000000000000000000
χ504444-2-2-4-44-2-2-4-4-2-21-2-2-2-214-422222-1-12221-2-2111122-1-1-1-1-1000000−2i32i300−2i32i30000i3−i300000i3−i3000000000000000000000000
χ514444-2-2-4-44-2-2-4-4-2-21-2-2-2-214-422222-1-12221-2-2111122-1-1-1-1-10000002i3−2i3002i3−2i30000−i3i300000−i3i3000000000000000000000000
χ52444-244-4-4-24422-2-2444-2-24-22-4-4-422-4-4-422-2-2-24-2-2-222-422220000000000000000000000000000000000000000000000000
χ53444-24-244-2-24-2-2-21-24-2-21-2-2-2-2-2411-2-24-2-21-21-2111-21-211114040-2-200-2-200-2011000-201100000000000000000000000000
χ54444-24-244-2-24-2-2-21-24-2-21-2-2-2-2-2411-2-24-2-21-21-2111-21-21111-40-402200220020-1-100020-1-100000000000000000000000000
χ55444-24-2-4-4-2-2422-21-24-2-21-2-2222-4-1-122-4221-21-21112-12-1-1-1-10000−2i32i300−2i32i30000i3−i300000i3−i300000000000000000000000000
χ56444-24-2-4-4-2-2422-21-24-2-21-2-2222-4-1-122-4221-21-21112-12-1-1-1-100002i3−2i3002i3−2i30000−i3i300000−i3i300000000000000000000000000
χ57444-2-2444-24-2-2-21-2-2-241-2-2-2-244-2-2-2-2-2-21111-2-21111-2-211110000000000000000004000000-2-2-2-211110000000000000000
χ58444-2-2444-24-2-2-21-2-2-241-2-2-2-244-2-2-2-2-2-21111-2-21111-2-21111000000000000000000-40000002222-1-1-1-10000000000000000
χ59444-2-24-4-4-24-2221-2-2-241-2-2-22-4-4222222-1-111-2-2111-122-1-1-1-1000000000000000000000000000003i−3i−3i3i0000000000000000
χ60444-2-24-4-4-24-2221-2-2-241-2-2-22-4-4222222-1-111-2-2111-122-1-1-1-100000000000000000000000000000−3i3i3i−3i0000000000000000
χ6144-44-24-4444-2-4-4-24-22-4-24-2-44-44-2-4-4-2-2222-22-4222-2-24222-2-20000000000000000000000000000000000000000000000000
χ6244-44-2-24-44-2-244-2-2122-2-21-4-4-222-2-2-1-1-2-2-2122-1-1-1122111-1-1040-400-2-200220-2001100200-1-1000000000000000000000000
χ6344-44-2-24-44-2-244-2-2122-2-21-4-4-222-2-2-1-1-2-2-2122-1-1-1122111-1-10-404002200-2-20200-1-100-20011000000000000000000000000
χ6444-44-2-2-444-2-2-4-4-2-2122-2-21-442-2-22211222122-1-1-11-2-2-1-1-111000000−2i32i3002i3−2i30000i3−i300000−i3i3000000000000000000000000
χ6544-44-2-2-444-2-2-4-4-2-2122-2-21-442-2-22211222122-1-1-11-2-2-1-1-1110000002i3−2i300−2i32i30000−i3i300000i3−i3000000000000000000000000
χ6644-4-2444-4-244-2-2-2-24-4-4-2-24224-4-4-2-2-4-44-2-2-222-422-2224-2-2220000000000000000000000000000000000000000000000000
χ6744-4-24-24-4-2-24-2-2-21-2-42-21-222-22-411224-2-212-12-1-112-1-211-1-10000−2i32i3002i3−2i30000i3−i300000−i3i300000000000000000000000000
χ6844-4-24-24-4-2-24-2-2-21-2-42-21-222-22-411224-2-212-12-1-112-1-211-1-100002i3−2i300−2i32i30000−i3i300000i3−i300000000000000000000000000
χ6944-4-24-2-44-2-2422-21-2-42-21-22-22-24-1-1-2-2-42212-12-1-11-212-1-11140-40-2-2002200-201100020-1-100000000000000000000000000
χ7044-4-24-2-44-2-2422-21-2-42-21-22-22-24-1-1-2-2-42212-12-1-11-212-1-111-40402200-2-20020-1-1000-201100000000000000000000000000
χ7144-4-2-244-4-24-2-2-21-2-22-41-2-2224-42-2-222-2111-122-1-11-12-211-1-1000000000000000000000000000−2i32i3i3i3−i3−i30000000000000000
χ7244-4-2-244-4-24-2-2-21-2-22-41-2-2224-42-2-222-2111-122-1-11-12-211-1-10000000000000000000000000002i3−2i3−i3−i3i3i30000000000000000
χ7344-4-2-24-44-24-2221-2-22-41-2-22-2-44-222-2-22-1-11-122-1-111-22-1-111000000000000000000000000023−2300−33−330000000000000000
χ7444-4-2-24-44-24-2221-2-22-41-2-22-2-44-222-2-22-1-11-122-1-111-22-1-1110000000000000000000000000−2323003−33−30000000000000000
χ754-4044400-4-4-40044400-4-4-4000000000000400000-40000000000000000000000000000000000000000002i−2i00002i−2i2i−2i0000
χ764-4044400-4-4-40044400-4-4-4000000000000400000-4000000000000000000000000000000000000000000−2i2i0000−2i2i−2i2i0000
χ774-40-244002-4-423−23-2-240022-40000023−2300023−23-200000200023−2300000000000000000000000000000000000002i−2i0000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ110000
χ784-40-244002-4-423−23-2-240022-40000023−2300023−23-200000200023−230000000000000000000000000000000000000−2i2i0000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ110000
χ794-40-244002-4-4−2323-2-240022-400000−2323000−2323-2000002000−232300000000000000000000000000000000000002i−2i0000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ110000
χ804-40-244002-4-4−2323-2-240022-400000−2323000−2323-2000002000−23230000000000000000000000000000000000000−2i2i0000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ110000
χ81888-4-4-488-4-4-4-4-4222-4-4222-4-4-4-4-42222-422-1222-1-1-1222-1-1-1-10000000000000000000000000000000000000000000000000
χ82888-4-4-4-8-8-4-4-444222-4-4222-44444-2-2-2-24-2-2-1222-1-1-1-2-2-211110000000000000000000000000000000000000000000000000
χ8388-8-4-4-48-8-4-4-4-4-42224422244-44422-2-2-422-1-2-2-211-1-2-22-1-1110000000000000000000000000000000000000000000000000
χ8488-8-4-4-4-88-4-4-444222442224-44-4-4-2-2224-2-2-1-2-2-211-122-211-1-10000000000000000000000000000000000000000000000000
χ858-8088-400-84-8008-4-400-844000000000000-400000400000000000000000000000000000000000000000000000000000000
χ868-808-4800-8-8400-48-4004-84000000000000-400000400000000000000000000000000000000000000000000000000000000
χ878-808-4-400-84400-4-420044-200000006i−6i000200000-2000006i−6i0000000000000000000000000000000000000000000000000
χ888-808-4-400-84400-4-420044-20000000−6i6i000200000-200000−6i6i0000000000000000000000000000000000000000000000000
χ898-80-48-40044-843−43-42-4004-2400000−232300043−43200000-2000−2323000000000000000000000000000000000000000000000000000
χ908-80-48-40044-8−4343-42-4004-240000023−23000−4343200000-200023−23000000000000000000000000000000000000000000000000000
χ918-80-4-48004-8443−432-4-400-2440000043−43000−2323200000-2000−2323000000000000000000000000000000000000000000000000000
χ928-80-4-48004-84−43432-4-400-24400000−434300023−23200000-200023−23000000000000000000000000000000000000000000000000000
χ938-80-4-4-40044443−4322200-2-2-200000−23236i−6i0−2323-1000−3i33i310003−3−3i3i0000000000000000000000000000000000000000000000000
χ948-80-4-4-40044443−4322200-2-2-200000−2323−6i6i0−2323-10003i3−3i310003−33i−3i0000000000000000000000000000000000000000000000000
χ958-80-4-4-400444−434322200-2-2-20000023−236i−6i023−23-10003i3−3i31000−33−3i3i0000000000000000000000000000000000000000000000000
χ968-80-4-4-400444−434322200-2-2-20000023−23−6i6i023−23-1000−3i33i31000−333i−3i0000000000000000000000000000000000000000000000000

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