Finite Group Databasebeta

← Group #13167083

Character table — Group #13167083

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size111122224444444444444444444888888888888888818181818242424242424242424242424242424242424363636363636363672727272108108108108
order122236663333466666666666612123666121212121212121212121212224444121212121212121212121212121212124444661212121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1
χ6111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-1-1-1111111-1-111-1-111-1-111-1-111
χ7111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ8111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-1111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1
χ92222222222222222222222222222222222222222222-2-2-2-20000000000000000000000-2-2-2-200000000
χ10222222222222-2222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-222-2-2000000000000000000000022-2-200000000
χ112222-1-1-1-122-1-1222-1-122-1-12-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222-1-1-1-122-1-1-1-122-1-1-1-10000-1-1-1-100000000
χ122222-1-1-1-122-1-1222-1-122-1-12-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-21111-2-21111-2-211110000-1-1-1-100000000
χ132222-1-1-1-122-1-1222-1-122-1-12-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-200−i3i3−i3i300−i3−i3i3i300−i3−i3i3i30000111100000000
χ142222-1-1-1-122-1-1222-1-122-1-12-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-200i3−i3i3−i300i3i3−i3−i300i3i3−i3−i30000111100000000
χ152222-1-1-1-122-1-1-222-1-122-1-12-1-1211-1-1-1-1-2-2-2-21111111122-2-200−i3i3i3−i300−i3−i3i3i300i3i3−i3−i30000-1-11100000000
χ162222-1-1-1-122-1-1-222-1-122-1-12-1-1211-1-1-1-1-2-2-2-21111111122-2-200i3−i3−i3i300i3i3−i3−i300−i3−i3i3i30000-1-11100000000
χ172222-1-1-1-122-1-1-222-1-122-1-12-1-1211-1-1-1-1-2-2-2-211111111-2-2222-211-1-1-2-2111122-1-1-1-1000011-1-100000000
χ182222-1-1-1-122-1-1-222-1-122-1-12-1-1211-1-1-1-1-2-2-2-211111111-2-222-22-1-11122-1-1-1-1-2-21111000011-1-100000000
χ1922-2-222-2-2222202222-2-2-2-2-2-2-2-20022-2-20000000000002-20000000000000000000000002-20000002−22−2
χ2022-2-222-2-2222202222-2-2-2-2-2-2-2-20022-2-20000000000002-20000000000000000000000002-2000000−22−22
χ2122-2-222-2-2222202222-2-2-2-2-2-2-2-20022-2-2000000000000-22000000000000000000000000-220000002−2−22
χ2222-2-222-2-2222202222-2-2-2-2-2-2-2-20022-2-2000000000000-22000000000000000000000000-22000000−222−2
χ232-22-22-2-2222220-2-2-2-22-2-2-2222-2002-2-22000000000000002-2000000000000000000002i−2i002-2002i−2i0000
χ242-22-22-2-2222220-2-2-2-22-2-2-2222-2002-2-22000000000000002-200000000000000000000−2i2i002-200−2i2i0000
χ252-22-22-2-2222220-2-2-2-22-2-2-2222-2002-2-2200000000000000-220000000000000000002i−2i0000-222i−2i000000
χ262-22-22-2-2222220-2-2-2-22-2-2-2222-2002-2-2200000000000000-22000000000000000000−2i2i0000-22−2i2i000000
χ27444444441-21141-211-2111111-244-2-2-2-2-2-2111111-2-2-2-20000222222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ28444444441-21141-211-2111111-244-2-2-2-2-2-2111111-2-2-2-20000-2-2-2-2-2-21111111111110000000000000000
χ29444444441-211-41-211-2111111-2-4-4-2-2-2-222-1-1-1-1-1-1222200002-2-2-222111111-1-1-1-1-1-10000000000000000
χ30444444441-211-41-211-2111111-2-4-4-2-2-2-222-1-1-1-1-1-122220000-2222-2-2-1-1-1-1-1-11111110000000000000000
χ3144444444-21-2-24-21-2-21-2-2-2-2-2-2144111111-2-2-2-2-2-21111000000000000000000000022220000-1-1-1-10000
χ3244444444-21-2-24-21-2-21-2-2-2-2-2-2144111111-2-2-2-2-2-211110000000000000000000000-2-2-2-2000011110000
χ3344444444-21-2-2-4-21-2-21-2-2-2-2-2-21-4-41111-1-1222222-1-1-1-1000000000000000000000022-2-20000-1-1110000
χ3444444444-21-2-2-4-21-2-21-2-2-2-2-2-21-4-41111-1-1222222-1-1-1-10000000000000000000000-2-222000011-1-10000
χ354444-2-2-2-21-2−1−3i32−1+3i3241-2−1−3i32−1+3i32-21−1−3i32−1+3i321−1−3i32−1+3i32-2-2-21111-2-211−1−3i32−1−3i32−1+3i32−1+3i321111000022−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i320000000000000000
χ364444-2-2-2-21-2−1−3i32−1+3i3241-2−1−3i32−1+3i32-21−1−3i32−1+3i321−1−3i32−1+3i32-2-2-21111-2-211−1−3i32−1−3i32−1+3i32−1+3i3211110000-2-21+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i320000000000000000
χ374444-2-2-2-21-2−1−3i32−1+3i32-41-2−1−3i32−1+3i32-21−1−3i32−1+3i321−1−3i32−1+3i32-222111122-1-11+3i321+3i321−3i321−3i32-1-1-1-100002-21+i31−i3−1−i3−1+i311−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i320000000000000000
χ384444-2-2-2-21-2−1−3i32−1+3i32-41-2−1−3i32−1+3i32-21−1−3i32−1+3i321−1−3i32−1+3i32-222111122-1-11+3i321+3i321−3i321−3i32-1-1-1-10000-22−1−i3−1+i31+i31−i3-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i320000000000000000
χ394444-2-2-2-21-2−1+3i32−1−3i3241-2−1+3i32−1−3i32-21−1+3i32−1−3i321−1+3i32−1−3i32-2-2-21111-2-211−1+3i32−1+3i32−1−3i32−1−3i321111000022−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i320000000000000000
χ404444-2-2-2-21-2−1+3i32−1−3i3241-2−1+3i32−1−3i32-21−1+3i32−1−3i321−1+3i32−1−3i32-2-2-21111-2-211−1+3i32−1+3i32−1−3i32−1−3i3211110000-2-21−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i320000000000000000
χ414444-2-2-2-21-2−1+3i32−1−3i32-41-2−1+3i32−1−3i32-21−1+3i32−1−3i321−1+3i32−1−3i32-222111122-1-11−3i321−3i321+3i321+3i32-1-1-1-100002-21−i31+i3−1+i3−1−i311−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i320000000000000000
χ424444-2-2-2-21-2−1+3i32−1−3i32-41-2−1+3i32−1−3i32-21−1+3i32−1−3i321−1+3i32−1−3i32-222111122-1-11−3i321−3i321+3i321+3i32-1-1-1-10000-22−1+i3−1−i31−i31+i3-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i320000000000000000
χ4344-4-4-2-22244-2-2044-2-2-4-422-422-400-2-2220000000000004-4000000000000000000000000-220000000000
χ4444-4-4-2-22244-2-2044-2-2-4-422-422-400-2-222000000000000-440000000000000000000000002-20000000000
χ454-44-44-4-44-21-2-202-1221222-2-2-2-1001-1-113-300000033-3-300000000000000000000002i−2i2i−2i0000−ii−ii0000
χ464-44-44-4-44-21-2-202-1221222-2-2-2-1001-1-113-300000033-3-30000000000000000000000−2i2i−2i2i0000i−ii−i0000
χ474-44-44-4-44-21-2-202-1221222-2-2-2-1001-1-11-33000000-3-33300000000000000000000002i−2i−2i2i0000−iii−i0000
χ484-44-44-4-44-21-2-202-1221222-2-2-2-1001-1-11-33000000-3-3330000000000000000000000−2i2i2i−2i0000i−i−ii0000
χ494-44-4-222-244-2-20-4-4224-4224-2-2-400-222-2000000000000004-4000000000000000000000000-2200000000
χ504-44-4-222-244-2-20-4-4224-4224-2-2-400-222-200000000000000-440000000000000000000000002-200000000
χ514-4-444-44-41-2110-12-1-12111-1-1-1-200-22-22003i−3i3i−3i3i−3i00000000000000−i3i3−i3i3−i3i33−33−33−30000000000000000
χ524-4-444-44-41-2110-12-1-12111-1-1-1-200-22-22003i−3i3i−3i3i−3i00000000000000i3−i3i3−i3i3−i3−33−33−330000000000000000
χ534-4-444-44-41-2110-12-1-12111-1-1-1-200-22-2200−3i3i−3i3i−3i3i00000000000000−i3i3−i3i3−i3i3−33−33−330000000000000000
χ544-4-444-44-41-2110-12-1-12111-1-1-1-200-22-2200−3i3i−3i3i−3i3i00000000000000i3−i3i3−i3i3−i33−33−33−30000000000000000
χ554-4-444-44-444440-4-4-4-4-4444-4-4-44004-44-400000000000000000000000000000000000000000000000000
χ564-4-44-22-221-2−1−3i32−1+3i320-121+3i321−3i3221−1−3i32−1+3i32-11+3i321−3i32-223−231-11-1003i−3iζ14+2ζ22−ζ14−2ζ222ζ14+ζ22−2ζ14−ζ223−33−30000000000−i3i3−3+i323−i323+i32−3−i323−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ220000000000000000
χ574-4-44-22-221-2−1−3i32−1+3i320-121+3i321−3i3221−1−3i32−1+3i32-11+3i321−3i32-223−231-11-1003i−3iζ14+2ζ22−ζ14−2ζ222ζ14+ζ22−2ζ14−ζ223−33−30000000000i3−i33−i32−3+i32−3−i323+i32−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ220000000000000000
χ584-4-44-22-221-2−1−3i32−1+3i320-121+3i321−3i3221−1−3i32−1+3i32-11+3i321−3i32-2−23231-11-100−3i3i−ζ14−2ζ22ζ14+2ζ22−2ζ14−ζ222ζ14+ζ22−33−330000000000−i3i3−3+i323−i323+i32−3−i32−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ220000000000000000
χ594-4-44-22-221-2−1−3i32−1+3i320-121+3i321−3i3221−1−3i32−1+3i32-11+3i321−3i32-2−23231-11-100−3i3i−ζ14−2ζ22ζ14+2ζ22−2ζ14−ζ222ζ14+ζ22−33−330000000000i3−i33−i32−3+i32−3−i323+i323−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ220000000000000000
χ604-4-44-22-221-2−1+3i32−1−3i320-121−3i321+3i3221−1+3i32−1−3i32-11−3i321+3i32-223−231-11-100−3i3i−2ζ14−ζ222ζ14+ζ22−ζ14−2ζ22ζ14+2ζ223−33−30000000000−i3i33+i32−3−i32−3+i323−i32−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ220000000000000000
χ614-4-44-22-221-2−1+3i32−1−3i320-121−3i321+3i3221−1+3i32−1−3i32-11−3i321+3i32-223−231-11-100−3i3i−2ζ14−ζ222ζ14+ζ22−ζ14−2ζ22ζ14+2ζ223−33−30000000000i3−i3−3−i323+i323−i32−3+i323−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ220000000000000000
χ624-4-44-22-221-2−1+3i32−1−3i320-121−3i321+3i3221−1+3i32−1−3i32-11−3i321+3i32-2−23231-11-1003i−3i2ζ14+ζ22−2ζ14−ζ22ζ14+2ζ22−ζ14−2ζ22−33−330000000000−i3i33+i32−3−i32−3+i323−i323−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ220000000000000000
χ634-4-44-22-221-2−1+3i32−1−3i320-121−3i321+3i3221−1+3i32−1−3i32-11−3i321+3i32-2−23231-11-1003i−3i2ζ14+ζ22−2ζ14−ζ22ζ14+2ζ22−ζ14−2ζ22−33−330000000000i3−i3−3−i323+i323−i32−3+i32−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ220000000000000000
χ644-4-44-22-2244-2-20-4-422-44-2-2-422423−23-22-22000023−23−2323−2323−232300000000000000000000000000000000000000
χ654-4-44-22-2244-2-20-4-422-44-2-2-4224−2323-22-220000−232323−2323−2323−2300000000000000000000000000000000000000
χ668888-4-4-4-4-42228-42222-422-4222-4-4-1-1-1-122-4-42222-1-1-1-100000000000000000000000000000000000000
χ678888-4-4-4-4-4222-8-42222-422-422244-1-1-1-1-2-244-2-2-2-2111100000000000000000000000000000000000000
χ6888-8-888-8-82-42202-4224-2-2-2-2-2-2400-4-44400000000000000000000000000000000000000000000000000
χ6988-8-888-8-8-42-4-40-42-4-4-2444444-20022-2-200000000000000000000000000000000000000000000000000
χ7088-8-8-4-4442-4−1−3i3−1+3i302-4−1−3i3−1+3i34-21+3i31−3i3-21+3i31−3i340022-2-200000000000000000000000000000000000000000000000000
χ7188-8-8-4-4442-4−1+3i3−1−3i302-4−1+3i3−1−3i34-21−3i31+3i3-21−3i31+3i340022-2-200000000000000000000000000000000000000000000000000
χ7288-8-8-4-444-42220-4222-24-2-24-2-2-200-1-1110000000033−33−333300000000000000000000000000000000000000
χ7388-8-8-4-444-42220-4222-24-2-24-2-2-200-1-11100000000−333333−3300000000000000000000000000000000000000
χ748-88-88-8-882-4220-24-2-2-4-2-2-2222400-444-400000000000000000000000000000000000000000000000000
χ758-88-8-444-42-4−1−3i3−1+3i30-241+3i31−3i3-4-21+3i31−3i32−1−3i3−1+3i34002-2-2200000000000000000000000000000000000000000000000000
χ768-88-8-444-42-4−1+3i3−1−3i30-241−3i31+3i3-4-21−3i31+3i32−1+3i3−1−3i34002-2-2200000000000000000000000000000000000000000000000000
χ778-88-8-444-4-422204-2-2-224-2-2-422-200-111-16-6000000-3-33300000000000000000000000000000000000000
χ788-88-8-444-4-422204-2-2-224-2-2-422-200-111-1-6600000033-3-300000000000000000000000000000000000000
χ798-8-888-88-8-42-4-404-244-2-4-4-44442002-22-200000000000000000000000000000000000000000000000000
χ808-8-88-44-44-422204-2-2-2-2-4224-2-2243−43-11-110000−232323−23−33−3300000000000000000000000000000000000000
χ818-8-88-44-44-422204-2-2-2-2-4224-2-22−4343-11-11000023−23−23233−33−300000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.