Finite Group Databasebeta

← Group #13169344

Character table — Group #13169344

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order1222333666666666333466666666612124444366612121212121212121212121244441212121212121212121212121212121244121212121212121212121212121212121212121244444121212121212121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-11-1-1-1111111-1-11111111111111-11-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-1111-1-1-1-111111111-1-1-1-1-1-1-1-111-1111111111-1-1-1-1-11-11-111-1-1-1-11-1-1-1
χ4111111111111111111111111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-11111-1-1-1-1-1-11-11-1-111-1-1-1111
χ51111111111111111111111111111111-1-1111111111111111111-1111111111-1-111-1-1-1-111-1-1-1-1-1-1-11111111-1-1-1-11111-1-11-11-1-111-1-1-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-11-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-11111-11-11-111-1-1-1-11-111
χ71111111111111111111111111111111-1-1-1-11111111111111111-11-1111-1-1-1-1-1-111-1-1-1-1-1-1111111-11-111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-111
χ81111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-111-1-111-1-111111111-11-1-111-1-111-1-111-1-1-11-1-11-1-111-1-11-11-1
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1111111-1-111111111-1-1-11-1-11111-1-111-1-1-1-111-111-1-1-1-1-11-11
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-111-111-1-111-1-1-1-111111-1-1-1-1-1-11111-11
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111-1-111111111-1-11-1
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-11-1-111111111-1-1-11
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-1-1-111-1-11111-1-1-1-1-1-11-1-11-1-111-1-11111-1-1111-1-1-1-1-1-111111-1
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-111-1-1-1-1-1-111-1-1111111111-111-1-1-1-111-1-111-1-111-111-1-1-1-1-111-1
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-111-1-111-1-111-1-11111111-111-1-111-1-111-1-111-11-1-11-1-111-1-11-1-11
χ17222222-12222-1-1-1222-1-1222-1-1-1-1-1-12222200-1-1-1-1-12-1-1-1-122-1-1-1-12202220000-1-1-1-1222200000000-1-102-1-1-1-1-1-1-1-1000002020-1-10000-1000
χ18222222-12222-1-1-1222-1-1222-1-1-1-1-1-12222200-1-1-1-1-12-1-1-1-122-1-1-1-12-20-2-2-20000-1-111222200000000-110-21111-1-1-1-100000-20-201100001000
χ19222222-12222-1-1-1222-1-1222-1-1-1-1-1-1222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-1-220222000011-1-1-2-2-2-2000000001-102-1-1-1-1111100000-20-201100001000
χ20222222-12222-1-1-1222-1-1222-1-1-1-1-1-1222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-1-2-20-2-2-200001111-2-2-2-200000000110-211111111000002020-1-10000-1000
χ21222222-12222-1-1-1222-1-1-222-1-1-1-1-1-12-2-22200-1-1-1-11-21111-2-21111-220-2220000-1-11122-2-2000000001-10-2-1-111-1-1110000020-20110000-1000
χ22222222-12222-1-1-1222-1-1-222-1-1-1-1-1-12-2-22200-1-1-1-11-21111-2-21111-2-202-2-20000-1-1-1-122-2-200000000110211-1-1-1-11100000-2020-1-100001000
χ23222222-12222-1-1-1222-1-1-222-1-1-1-1-1-12-2-2-2-200-1-1-1-11-21111-2-21111220-22200001111-2-22200000000-1-10-2-1-11111-1-100000-2020-1-100001000
χ24222222-12222-1-1-1222-1-1-222-1-1-1-1-1-12-2-2-2-200-1-1-1-11-21111-2-211112-202-2-2000011-1-1-2-22200000000-110211-1-111-1-10000020-20110000-1000
χ2522222-122-12-1222-12-12-12-1-12-1-122-1-1-1-12222-1-1-1-122-1-122-1-1-1-1-1-1202000-1-1-1-12200-1-1-1-12222-1-1-1-120200000-1-1-1-1-1-1-1-1200000000-1-10000
χ2622222-122-12-1222-12-12-12-1-12-1-122-1-1-1-122-2-2-1-1-1-122-1-122-1-1-1-1-1-120-200011112200-1-1-1-1-2-2-2-2111120-200000-1-1-1-11111-200000000110000
χ2722222-122-12-1222-12-12-12-1-12-1-122-1-1-1-1-2-222-1-1-1-122-1-122-1-1-1-1-1-1-202000-1-1-1-1-2-200111122-2-21111-202000001111-1-1-1-1-200000000110000
χ2822222-122-12-1222-12-12-12-1-12-1-122-1-1-1-1-2-2-2-2-1-1-1-122-1-122-1-1-1-1-1-1-20-20001111-2-2001111-2-222-1-1-1-1-20-20000011111111200000000-1-10000
χ2922222-122-12-1222-12-12-1-2-1-12-1-122-1-1112222-1-1-1-1-2-211-2-2111111-20-2000-1-1112200-1-1112222-1-1-1-1-20-200000-1-111-1-111-200000000110000
χ3022222-122-12-1222-12-12-1-2-1-12-1-122-1-11122-2-2-1-1-1-1-2-211-2-2111111-20200011-1-12200-1-111-2-2-2-21111-20200000-1-11111-1-1200000000-1-10000
χ3122222-122-12-1222-12-12-1-2-1-12-1-122-1-111-2-222-1-1-1-1-2-211-2-211111120-2000-1-111-2-20011-1-122-2-2111120-20000011-1-1-1-111200000000-1-10000
χ3222222-122-12-1222-12-12-1-2-1-12-1-122-1-111-2-2-2-2-1-1-1-1-2-211-2-211111120200011-1-1-2-20011-1-1-2-222-1-1-1-12020000011-1-111-1-1-200000000110000
χ332222-122-12-122222-1-1-122-1-1-122-1-12-1220022-1-1-1-12-122-1-1-1-1-1-1-1-10222-1-1222200220000-1-100000002-1-1-1-1-1-10000-1-1-1-10020200-1-1000-100
χ342222-122-12-122222-1-1-122-1-1-122-1-12-1220022-1-1-1-12-122-1-1-1-1-1-1-1-10-22-211222200-2-20000-1-10000000-2-1111110000-1-1-1-100-20-20011000100
χ352222-122-12-122222-1-1-122-1-1-122-1-12-12200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-102-22-1-1-2-2-2-20022000011000000021-1-1-1-1-10000111100-20-20011000100
χ362222-122-12-122222-1-1-122-1-1-122-1-12-12200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-10-2-2-211-2-2-2-200-2-20000110000000-2111111000011110020200-1-1000-100
χ372222-122-12-122222-1-1-12-2-1-1-122-1-12-1-2-20022-1-1-1-1-21-2-21111111102-2-2-1-122-2-200-2-20000-1-10000000211-1-1110000-1-11100-20200-1-1000100
χ382222-122-12-122222-1-1-12-2-1-1-122-1-12-1-2-20022-1-1-1-1-21-2-2111111110-2-221122-2-200220000-1-10000000-21-111-1-10000-1-1110020-20011000-100
χ392222-122-12-122222-1-1-12-2-1-1-122-1-12-1-2-200-2-2-1-1-1-1-21-2-211111111022-2-1-1-2-22200-2-200001100000002-11-1-111000011-1-10020-20011000-100
χ402222-122-12-122222-1-1-12-2-1-1-122-1-12-1-2-200-2-2-1-1-1-1-21-2-2111111110-22211-2-22200220000110000000-2-1-111-1-1000011-1-100-20200-1-1000100
χ412-22-2222-22-2-2-2-22-222220-2-2-2-22-22-22002i−2i2-22-2-220000000000000000002-2002i−2i002i−2i002-22i−2i2i2i−2i−2i000000002i−2i002-200000000000000000
χ422-22-2222-22-2-2-2-22-222220-2-2-2-22-22-22002i−2i-222-2-22000000000000000000-22002i−2i002i−2i00-22−2i2i−2i−2i2i2i000000002i−2i00-2200000000000000000
χ432-22-2222-22-2-2-2-22-222220-2-2-2-22-22-2200−2i2i2-22-2-220000000000000000002-200−2i2i00−2i2i002-2−2i2i−2i−2i2i2i00000000−2i2i002-200000000000000000
χ442-22-2222-22-2-2-2-22-222220-2-2-2-22-22-2200−2i2i-222-2-22000000000000000000-2200−2i2i00−2i2i00-222i−2i2i2i−2i−2i00000000−2i2i00-2200000000000000000
χ452-22-22-12-2-1-21-2-2212-12-1011-21-1-221-1−i3i32i−2i2-2-111-100−i3i300−i3i3−i3−i3i3i3000000-11−i3i32i−2i00−ii3−32-22i−2i−i−iii00000000−ii3−3-11−i3i30000000003−30000
χ462-22-22-12-2-1-21-2-2212-12-1011-21-1-221-1−i3i32i−2i-22-111-100−i3i300−i3i3−i3−i3i3i30000001-1i3−i32i−2i00−ii3−3-22−2i2iii−i−i00000000−ii3−31-1i3−i3000000000−330000
χ472-22-22-12-2-1-21-2-2212-12-1011-21-1-221-1−i3i3−2i2i2-2-111-100−i3i300−i3i3−i3−i3i3i3000000-11−i3i3−2i2i00i−i−332-2−2i2iii−i−i00000000i−i−33-11−i3i3000000000−330000
χ482-22-22-12-2-1-21-2-2212-12-1011-21-1-221-1−i3i3−2i2i-22-111-100−i3i300−i3i3−i3−i3i3i30000001-1i3−i3−2i2i00i−i−33-222i−2i−i−iii00000000i−i−331-1i3−i30000000003−30000
χ492-22-22-12-2-1-21-2-2212-12-1011-21-1-221-1i3−i32i−2i2-2-111-100i3−i300i3−i3i3i3−i3−i3000000-11i3−i32i−2i00−ii−332-22i−2i−i−iii00000000−ii−33-11i3−i3000000000−330000
χ502-22-22-12-2-1-21-2-2212-12-1011-21-1-221-1i3−i32i−2i-22-111-100i3−i300i3−i3i3i3−i3−i30000001-1−i3i32i−2i00−ii−33-22−2i2iii−i−i00000000−ii−331-1−i3i30000000003−30000
χ512-22-22-12-2-1-21-2-2212-12-1011-21-1-221-1i3−i3−2i2i2-2-111-100i3−i300i3−i3i3i3−i3−i3000000-11i3−i3−2i2i00i−i3−32-2−2i2iii−i−i00000000i−i3−3-11i3−i30000000003−30000
χ522-22-22-12-2-1-21-2-2212-12-1011-21-1-221-1i3−i3−2i2i-22-111-100i3−i300i3−i3i3i3−i3−i30000001-1−i3i3−2i2i00i−i3−3-222i−2i−i−iii00000000i−i3−31-1−i3i3000000000−330000
χ5344444-2-24-24-2-2-2-2-24-2-214-2-2-211-2-21-2-2-244001111-2411-2-2-2-211114000000000-2-200-2-2-2-200000000-2000000011110000000000000000000
χ5444444-2-24-24-2-2-2-2-24-2-214-2-2-211-2-21-2-2-2-4-4001111-2411-2-2-2-21111-4000000000220022220000000020000000-1-1-1-10000000000000000000
χ5544444-2-24-24-2-2-2-2-24-2-21-4-2-2-211-2-21-222440011112-4-1-12222-1-1-1-1-4000000000-2-200-2-222000000002000000011-1-10000000000000000000
χ5644444-2-24-24-2-2-2-2-24-2-21-4-2-2-211-2-21-222-4-40011112-4-1-12222-1-1-1-14000000000220022-2-200000000-20000000-1-1110000000000000000000
χ574444-24-2-24-24-2-2-24-2-21-24-2-21-2-211-2-24400001111-2-2-2-211-2-211110404-2-2000000-2-20000000000000-20-2111100000000000000000000000
χ584444-24-2-24-24-2-2-24-2-21-24-2-21-2-211-2-24400001111-2-2-2-211-2-211110-40-422000000220000000000000202-1-1-1-100000000000000000000000
χ594444-24-2-24-24-2-2-24-2-21-2-4-2-21-2-211-2-2-4-4000011112222-1-122-1-1-1-1040-4-2-2000000220000000000000-20211-1-100000000000000000000000
χ604444-24-2-24-24-2-2-24-2-21-2-4-2-21-2-211-2-2-4-4000011112222-1-122-1-1-1-10-40422000000-2-2000000000000020-2-1-11100000000000000000000000
χ614444-2-24-2-2-2-2444-2-21-2-2411-2-2-2-2-2-21-2-2004411114-2-2-2-2-2111111004000-2-2-2-200000000-2-200000000-20000000001111000000000000000
χ624444-2-24-2-2-2-2444-2-21-2-2411-2-2-2-2-2-21-2-200-4-411114-2-2-2-2-211111100-400022220000000022000000002000000000-1-1-1-1000000000000000
χ634444-2-24-2-2-2-2444-2-21-2-2-411-2-2-2-2-2-212200441111-422222-1-1-1-1-1-100-4000-2-22200000000-2-200000000200000000011-1-1000000000000000
χ644444-2-24-2-2-2-2444-2-21-2-2-411-2-2-2-2-2-212200-4-41111-422222-1-1-1-1-1-100400022-2-2000000002200000000-2000000000-1-111000000000000000
χ6544-4-44444-4-4-44-4-44-444404-4-4-4-44-44-400000044-4-4000000000000000000000000000000000000000000000000000000000000000000000
χ6644-4-444-24-4-4-4-2224-44-2-204-4222-22-2-4000000-2-22200000000000000000000000023−2300000000000000000023−2300000000000000000000000
χ6744-4-444-24-4-4-4-2224-44-2-204-4222-22-2-4000000-2-222000000000000000000000000−2323000000000000000000−232300000000000000000000000
χ6844-4-44-2442-424-4-4-2-4-24-20-22-4224-4-22000000-2-222000000000000000000000000000000000023−2323−230000000000000000000000000000000
χ6944-4-44-2442-424-4-4-2-4-24-20-22-4224-4-22000000-2-2220000000000000000000000000000000000−2323−23230000000000000000000000000000000
χ7044-4-4-244-2-42-44-4-442-2-240-222-4-4-2242000000-2-2220000000000000000−2i32i3000000000000000000000000−2i32i30000000000000000000000000
χ7144-4-4-244-2-42-44-4-442-2-240-222-4-4-2242000000-2-22200000000000000002i3−2i30000000000000000000000002i3−2i30000000000000000000000000
χ7244-4-4-24-2-2-42-4-22242-21-20-22-1221-1-2200000011-1-100003i−3i003i−3i3i−3i0000−2i32i300000023−230000000000000000i3−i3−3300000000000000000000000
χ7344-4-4-24-2-2-42-4-22242-21-20-22-1221-1-2200000011-1-100003i−3i003i−3i3i−3i00002i3−2i3000000−23230000000000000000−i3i33−300000000000000000000000
χ7444-4-4-24-2-2-42-4-22242-21-20-22-1221-1-2200000011-1-10000−3i3i00−3i3i−3i3i0000−2i32i3000000−23230000000000000000i3−i33−300000000000000000000000
χ7544-4-4-24-2-2-42-4-22242-21-20-22-1221-1-2200000011-1-10000−3i3i00−3i3i−3i3i00002i3−2i300000023−230000000000000000−i3i3−3300000000000000000000000
χ764-44-444-2-44-4-422-2-444-2-20-4-422-22-224004i−4i00-222-20000000000000000000000−2i2i004i−4i000000000000000000−2i2i000000000000000000000
χ774-44-444-2-44-4-422-2-444-2-20-4-422-22-22400−4i4i00-222-200000000000000000000002i−2i00−4i4i0000000000000000002i−2i000000000000000000000
χ784-44-44-2-2-4-2-4222-224-2-210222-112-2-1-2−2i32i34i−4i001-1-1100i3−i300−2i32i3i3i3−i3−i30000000000−2i2i00−2i2i23−230000000000000000i−i−330000000000000000000
χ794-44-44-2-2-4-2-4222-224-2-210222-112-2-1-2−2i32i3−4i4i001-1-1100i3−i300−2i32i3i3i3−i3−i300000000002i−2i002i−2i−23230000000000000000−ii3−30000000000000000000
χ804-44-44-2-2-4-2-4222-224-2-210222-112-2-1-22i3−2i34i−4i001-1-1100−i3i3002i3−2i3−i3−i3i3i30000000000−2i2i00−2i2i−23230000000000000000i−i3−30000000000000000000
χ814-44-44-2-2-4-2-4222-224-2-210222-112-2-1-22i3−2i3−4i4i001-1-1100−i3i3002i3−2i3−i3−i3i3i300000000002i−2i002i−2i23−230000000000000000−ii−330000000000000000000
χ824-44-4-244242-4-4-44-4-2-2-240222-442-2-4-200004-4-222-20000000000000000004-40000000000-22000000000000000000-2200000000000000000
χ834-44-4-244242-4-4-44-4-2-2-240222-442-2-4-20000-44-222-2000000000000000000-4400000000002-20000000000000000002-200000000000000000
χ844-44-4-2-242-222-4-442-21-2-20-1-122-22-221−2i32i3004-41-1-1100−2i32i300i3−i3i3i3−i3−i3000000-22−2i32i300000000-220000000000000000001-1i3−i3000000000000000
χ854-44-4-2-242-222-4-442-21-2-20-1-122-22-221−2i32i300-441-1-1100−2i32i300i3−i3i3i3−i3−i30000002-22i3−2i3000000002-2000000000000000000-11−i3i3000000000000000
χ864-44-4-2-242-222-4-442-21-2-20-1-122-22-2212i3−2i3004-41-1-11002i3−2i300−i3i3−i3−i3i3i3000000-222i3−2i300000000-220000000000000000001-1−i3i3000000000000000
χ874-44-4-2-242-222-4-442-21-2-20-1-122-22-2212i3−2i300-441-1-11002i3−2i300−i3i3−i3−i3i3i30000002-2−2i32i3000000002-2000000000000000000-11i3−i3000000000000000
χ884-4-44444-4-444-44-4-4-44440-4444-4-4-4-4-40000004-44-4000000000000000000000000000000000000000000000000000000000000000000000
χ894-4-4444-2-4-4442-22-4-44-2-20-44-2-22222-4000000-22-2200000000000000000000000000000000000000000000000000000000000−2i32i300000000
χ904-4-4444-2-4-4442-22-4-44-2-20-44-2-22222-4000000-22-22000000000000000000000000000000000000000000000000000000000002i3−2i300000000
χ914-4-444-24-424-2-44-42-4-24-202-24-22-4-422000000-22-220000000000000000000000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ924-4-444-24-424-2-44-42-4-24-202-24-22-4-422000000-22-2200000000000000000000000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ934-4-44-2442-4-24-44-4-42-2-2402-2-24-422-42000000-22-220000000000000000000000000000000000000000000000000000000000000−2i32i3000000
χ944-4-44-2442-4-24-44-4-42-2-2402-2-24-422-42000000-22-2200000000000000000000000000000000000000000000000000000000000002i3−2i3000000
χ958888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-40000-1-1-1-1-4-4222222-1-1-1-1000000000000000000000000000000000000000000000000000000000
χ968888-4-4-4-4-4-4-4-4-4-4-4-4222-8222222222440000-1-1-1-144-2-2-2-2-2-21111000000000000000000000000000000000000000000000000000000000
χ9788-8-88-4-484-84-444-4-8-4-420-444-2-2-442400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-48-44448-8-8-442-4-402-2444-44-4-200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-4-4444-444-4422202-2-2-2-22-22-2000000-1-11100006i−6i00−3i3i−3i3i000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-4-4444-444-4422202-2-2-2-22-22-2000000-1-1110000−6i6i003i−3i3i−3i000000000000000000000000000000000000000000000000000000000
χ1018-88-8-48-4484-844-4-8-4-42-4044-24-4-224-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4-44-44444-44-42220-2-2-2-22-22-22−4i34i30000-111-1002i3−2i3002i3−2i3−i3−i3i3i3000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-44-44444-44-42220-2-2-2-22-22-224i3−4i30000-111-100−2i32i300−2i32i3i3i3−i3−i3000000000000000000000000000000000000000000000000000000000
χ1048-8-888-4-4-848-44-444-8-4-4204-4-42-244-240000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1058-8-88-48-44-8-484-44-84-42-404-42-44-2-2440000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-4844-4-4-88-8442-4-40-22-4-44444-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-444-4-44-44442220-2222-2-2-2-2-2000000-11-110000000033−33−3333000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-444-4-44-44442220-2222-2-2-2-2-2000000-11-1100000000−333333−33000000000000000000000000000000000000000000000000000000000

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