Finite Group Databasebeta

← Group #10590381

Character table — Group #10590381

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111222222222222222222222244444444444444444444444412121212121212121212121212121212121212121212121236363636
order12223344444466666612121212121212123666121212121212121212121212121212121212121244444444121212121212121212121212121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ6111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111
χ7111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111
χ8111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1
χ91-1-1111ii−i−i1-1-1-111-1-1iiii−i−i−i−i11-1-111-1-1ii−i−i11-1-1iiii−i−i−i−ii−ii−i1-11-1ii−i−i11-1-1ii−i−i11-1-11-1i−i
χ101-1-1111ii−i−i1-1-1-111-1-1iiii−i−i−i−i11-1-111-1-1ii−i−i11-1-1iiii−i−i−i−ii−i−ii1-1-11ii−i−i11-1-1−i−iii-1-111-11−ii
χ111-1-1111ii−i−i1-1-1-111-1-1iiii−i−i−i−i11-1-111-1-1ii−i−i11-1-1iiii−i−i−i−i−iii−i-111-1−i−iii-1-111ii−i−i11-1-1-11−ii
χ121-1-1111ii−i−i1-1-1-111-1-1iiii−i−i−i−i11-1-111-1-1ii−i−i11-1-1iiii−i−i−i−i−ii−ii-11-11−i−iii-1-111−i−iii-1-1111-1i−i
χ131-1-1111−i−iii1-1-1-111-1-1−i−i−i−iiiii11-1-111-1-1−i−iii11-1-1−i−i−i−iiiiii−ii−i-11-11ii−i−i-1-111ii−i−i-1-1111-1−ii
χ141-1-1111−i−iii1-1-1-111-1-1−i−i−i−iiiii11-1-111-1-1−i−iii11-1-1−i−i−i−iiiiii−i−ii-111-1ii−i−i-1-111−i−iii11-1-1-11i−i
χ151-1-1111−i−iii1-1-1-111-1-1−i−i−i−iiiii11-1-111-1-1−i−iii11-1-1−i−i−i−iiiii−iii−i1-1-11−i−iii11-1-1ii−i−i-1-111-11i−i
χ161-1-1111−i−iii1-1-1-111-1-1−i−i−i−iiiii11-1-111-1-1−i−iii11-1-1−i−i−i−iiiii−ii−ii1-11-1−i−iii11-1-1−i−iii11-1-11-1−ii
χ172222222-22-2-2-222222222-2-222-2-22222-2-2-2-22-22-2-2-2-2-222-2-222-2-20000000000000000000000000000
χ18222222-22-22-2-2222222-2-222-2-2222222-2-2-2-2-22-22-2-2-2-2-2-222-2-2220000000000000000000000000000
χ1922222-12222222-12-12-122-1-122-1-1-1-1-1-12-12-1-12-12-1-1-1-1-1-1-1-1-1-1-1-10022002200000000-1-1-1-1-1-1-1-10000
χ2022222-12222222-12-12-122-1-122-1-1-1-1-1-12-12-1-12-12-1-1-1-1-1-1-1-1-1-1-1-100-2-200-2-200000000111111110000
χ2122222-12-22-2-2-22-12-12-122112211-1-1-1-1-21-21-1-2-1-21111-1-111-1-1110000000000000000−i3i3−i3i3−i3i3−i3i30000
χ2222222-12-22-2-2-22-12-12-122112211-1-1-1-1-21-21-1-2-1-21111-1-111-1-1110000000000000000i3−i3i3−i3i3−i3i3−i30000
χ2322222-1-22-22-2-22-12-12-1-2-2-1-1-2-2-1-1-1-1-1-1-21-211212111111-1-111-1-10000000000000000−i3i3−i3i3i3−i3i3−i30000
χ2422222-1-22-22-2-22-12-12-1-2-2-1-1-2-2-1-1-1-1-1-1-21-211212111111-1-111-1-10000000000000000i3−i3i3−i3−i3i3−i3i30000
χ2522222-1-2-2-2-2222-12-12-1-2-211-2-211-1-1-1-12-12-11-21-2-1-1-1-111111111002200-2-200000000-1-1-1-111110000
χ2622222-1-2-2-2-2222-12-12-1-2-211-2-211-1-1-1-12-12-11-21-2-1-1-1-11111111100-2-20022000000001111-1-1-1-10000
χ272222-12222222-12-12-12-1-122-1-122-1-1-1-1-12-122-12-1-1-1-1-1-1-1-1-1-1-1-1-122002200-1-1-1-1-1-1-1-1000000000000
χ282222-12222222-12-12-12-1-122-1-122-1-1-1-1-12-122-12-1-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2-20011111111000000000000
χ292222-122-22-2-2-2-12-12-12-1-1-2-2-1-1-2-2-1-1-1-11-21-221211111-1-111-1-11100000000−i3i3−i3i3−i3i3−i3i3000000000000
χ302222-122-22-2-2-2-12-12-12-1-1-2-2-1-1-2-2-1-1-1-11-21-221211111-1-111-1-11100000000i3−i3i3−i3i3−i3i3−i3000000000000
χ312222-12-22-22-2-2-12-12-1211221122-1-1-1-11-21-2-2-1-2-1111111-1-111-1-100000000−i3i3−i3i3i3−i3i3−i3000000000000
χ322222-12-22-22-2-2-12-12-1211221122-1-1-1-11-21-2-2-1-2-1111111-1-111-1-100000000i3−i3i3−i3−i3i3−i3i3000000000000
χ332222-12-2-2-2-222-12-12-1211-2-211-2-2-1-1-1-1-12-12-21-21-1-1-1-1111111112200-2-200-1-1-1-11111000000000000
χ342222-12-2-2-2-222-12-12-1211-2-211-2-2-1-1-1-1-12-12-21-21-1-1-1-111111111-2-20022001111-1-1-1-1000000000000
χ352-2-22222i−2i−2i2i-22-2-222-2-22i2i−2i−2i−2i−2i2i2i22-2-2-2-2222i−2i−2i2i-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ362-2-2222−2i2i2i−2i-22-2-222-2-2−2i−2i2i2i2i2i−2i−2i22-2-2-2-222−2i2i2i−2i-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ372-2-222-12i2i−2i−2i2-2-212-1-212i2i−i−i−2i−2iii-1-1112-1-21−i2ii−2i-1-111−i−i−i−iiiii002i−2i002-200000000−i−iii-1-1110000
χ382-2-222-12i2i−2i−2i2-2-212-1-212i2i−i−i−2i−2iii-1-1112-1-21−i2ii−2i-1-111−i−i−i−iiiii00−2i2i00-2200000000ii−i−i11-1-10000
χ392-2-222-12i−2i−2i2i-22-212-1-212i2iii−2i−2i−i−i-1-111-212-1−i−2ii2i11-1-1−i−iiiii−i−i00000000000000003−3−33−i3i3i3−i30000
χ402-2-222-12i−2i−2i2i-22-212-1-212i2iii−2i−2i−i−i-1-111-212-1−i−2ii2i11-1-1−i−iiiii−i−i0000000000000000−333−3i3−i3−i3i30000
χ412-2-222-1−2i2i2i−2i-22-212-1-21−2i−2i−i−i2i2iii-1-111-212-1i2i−i−2i11-1-1ii−i−i−i−iii00000000000000003−3−33i3−i3−i3i30000
χ422-2-222-1−2i2i2i−2i-22-212-1-21−2i−2i−i−i2i2iii-1-111-212-1i2i−i−2i11-1-1ii−i−i−i−iii0000000000000000−333−3−i3i3i3−i30000
χ432-2-222-1−2i−2i2i2i2-2-212-1-21−2i−2iii2i2i−i−i-1-1112-1-21i−2i−i2i-1-111iiii−i−i−i−i002i−2i00-2200000000−i−iii11-1-10000
χ442-2-222-1−2i−2i2i2i2-2-212-1-21−2i−2iii2i2i−i−i-1-1112-1-21i−2i−i2i-1-111iiii−i−i−i−i00−2i2i002-200000000ii−i−i-1-1110000
χ452-2-22-122i2i−2i−2i2-21-2-121-2−i−i2i2iii−2i−2i-1-111-121-22i−i−2ii-1-111−i−i−i−iiiii2i−2i002-200−i−iii-1-111000000000000
χ462-2-22-122i2i−2i−2i2-21-2-121-2−i−i2i2iii−2i−2i-1-111-121-22i−i−2ii-1-111−i−i−i−iiiii−2i2i00-2200ii−i−i11-1-1000000000000
χ472-2-22-122i−2i−2i2i-221-2-121-2−i−i−2i−2iii2i2i-1-1111-2-122ii−2i−i11-1-1−i−iiiii−i−i000000003−3−33−i3i3i3−i3000000000000
χ482-2-22-122i−2i−2i2i-221-2-121-2−i−i−2i−2iii2i2i-1-1111-2-122ii−2i−i11-1-1−i−iiiii−i−i00000000−333−3i3−i3−i3i3000000000000
χ492-2-22-12−2i2i2i−2i-221-2-121-2ii2i2i−i−i−2i−2i-1-1111-2-12−2i−i2ii11-1-1ii−i−i−i−iii000000003−3−33i3−i3−i3i3000000000000
χ502-2-22-12−2i2i2i−2i-221-2-121-2ii2i2i−i−i−2i−2i-1-1111-2-12−2i−i2ii11-1-1ii−i−i−i−iii00000000−333−3−i3i3i3−i3000000000000
χ512-2-22-12−2i−2i2i2i2-21-2-121-2ii−2i−2i−i−i2i2i-1-111-121-2−2ii2i−i-1-111iiii−i−i−i−i2i−2i00-2200−i−iii11-1-1000000000000
χ522-2-22-12−2i−2i2i2i2-21-2-121-2ii−2i−2i−i−i2i2i-1-111-121-2−2ii2i−i-1-111iiii−i−i−i−i−2i2i002-200ii−i−i-1-111000000000000
χ534444-2-2444444-2-2-2-2-2-2-2-2-2-2-2-2-2-21111-2-2-2-2-2-2-2-21111111111110000000000000000000000000000
χ544444-2-24-44-4-4-4-2-2-2-2-2-2-2-222-2-22211112222-22-22-1-1-1-111-1-111-1-10000000000000000000000000000
χ554444-2-2-44-44-4-4-2-2-2-2-2-222-2-222-2-2111122222-22-2-1-1-1-1-1-111-1-1110000000000000000000000000000
χ564444-2-2-4-4-4-444-2-2-2-2-2-2222222221111-2-2-2-222221111-1-1-1-1-1-1-1-10000000000000000000000000000
χ5744-4-4440000004-4-4-4-44000000004-44-4000000000000000000000000000000000000000000000000
χ5844-4-44-200000042-42-4-20023−230023−23-22-220000000000000023−230023−230000000000000000000000000000
χ5944-4-44-200000042-42-4-200−232300−2323-22-2200000000000000−232300−23230000000000000000000000000000
χ6044-4-4-24000000-2-42-424−2i32i300−2i32i300-22-22000000000000−2i32i300−2i32i3000000000000000000000000000000
χ6144-4-4-24000000-2-42-4242i3−2i3002i3−2i300-22-220000000000002i3−2i3002i3−2i3000000000000000000000000000000
χ6244-4-4-2-2000000-22222-2−2i32i323−23−2i32i323−231-11-1000000003i−3i3i−3ii3−i3−33i3−i3−330000000000000000000000000000
χ6344-4-4-2-2000000-22222-2−2i32i3−2323−2i32i3−23231-11-100000000−3i3i−3i3ii3−i33−3i3−i33−30000000000000000000000000000
χ6444-4-4-2-2000000-22222-22i3−2i323−232i3−2i323−231-11-100000000−3i3i−3i3i−i3i3−33−i3i3−330000000000000000000000000000
χ6544-4-4-2-2000000-22222-22i3−2i3−23232i3−2i3−23231-11-1000000003i−3i3i−3i−i3i33−3−i3i33−30000000000000000000000000000
χ664-44-444000000-44-4-44-4000000004-4-44000000000000000000000000000000000000000000000000
χ674-44-44-2000000-4-2-424200−2i32i3002i3−2i3-222-200000000000000−2i32i3002i3−2i30000000000000000000000000000
χ684-44-44-2000000-4-2-4242002i3−2i300−2i32i3-222-2000000000000002i3−2i300−2i32i30000000000000000000000000000
χ694-44-4-24000000242-4-2-423−2300−232300-222-200000000000023−2300−2323000000000000000000000000000000
χ704-44-4-24000000242-4-2-4−23230023−2300-222-2000000000000−23230023−23000000000000000000000000000000
χ714-44-4-2-20000002-222-2223−23−2i32i3−23232i3−2i31-1-1100000000−3i3i3i−3i−33i3−i33−3−i3i30000000000000000000000000000
χ724-44-4-2-20000002-222-2223−232i3−2i3−2323−2i32i31-1-11000000003i−3i−3i3i−33−i3i33−3i3−i30000000000000000000000000000
χ734-44-4-2-20000002-222-22−2323−2i32i323−232i3−2i31-1-11000000003i−3i−3i3i3−3i3−i3−33−i3i30000000000000000000000000000
χ744-44-4-2-20000002-222-22−23232i3−2i323−23−2i32i31-1-1100000000−3i3i3i−3i3−3−i3i3−33i3−i30000000000000000000000000000
χ754-4-44-2-24i4i−4i−4i4-422-2-222−2i−2i−2i−2i2i2i2i2i11-1-1-2-222−2i−2i2i2i11-1-1iiii−i−i−i−i0000000000000000000000000000
χ764-4-44-2-24i−4i−4i4i-4422-2-222−2i−2i2i2i2i2i−2i−2i11-1-122-2-2−2i2i2i−2i-1-111ii−i−i−i−iii0000000000000000000000000000
χ774-4-44-2-2−4i4i4i−4i-4422-2-2222i2i−2i−2i−2i−2i2i2i11-1-122-2-22i−2i−2i2i-1-111−i−iiiii−i−i0000000000000000000000000000
χ784-4-44-2-2−4i−4i4i4i4-422-2-2222i2i2i2i−2i−2i−2i−2i11-1-1-2-2222i2i−2i−2i11-1-1−i−i−i−iiiii0000000000000000000000000000

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