Finite Group Databasebeta

← Group #10590358

Character table — Group #10590358

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111222222222222222222222244444444444444444444444412121212121212121212121212121212121212121212121236363636
order1222334444446666661212121212121212366612121212121212121212121212121212121212122244444466661212121212121212121212128888
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
χ5111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ6111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111
χ7111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111
χ8111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1
χ91-11-111i−ii−i1-1-11-11-1-1ii−i−iii−i−i11-1-11-1i−i1-1i−i11-1-1iiii−i−i−i−i1-11-1i−ii−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i
χ101-11-111i−ii−i1-1-11-11-1-1ii−i−iii−i−i11-1-11-1i−i1-1i−i11-1-1iiii−i−i−i−i1-1-11i−i−ii11-1-1ii−i−i-1-111−i−iii-11−ii
χ111-11-111i−ii−i1-1-11-11-1-1ii−i−iii−i−i11-1-11-1i−i1-1i−i11-1-1iiii−i−i−i−i-111-1−iii−i-1-111−i−iii11-1-1ii−i−i-11−ii
χ121-11-111i−ii−i1-1-11-11-1-1ii−i−iii−i−i11-1-11-1i−i1-1i−i11-1-1iiii−i−i−i−i-11-11−ii−ii-1-111−i−iii-1-111−i−iii1-1i−i
χ131-11-111−ii−ii1-1-11-11-1-1−i−iii−i−iii11-1-11-1−ii1-1−ii11-1-1−i−i−i−iiiii1-11-1−ii−ii11-1-1−i−iii11-1-1−i−iii1-1−ii
χ141-11-111−ii−ii1-1-11-11-1-1−i−iii−i−iii11-1-11-1−ii1-1−ii11-1-1−i−i−i−iiiii1-1-11−iii−i11-1-1−i−iii-1-111ii−i−i-11i−i
χ151-11-111−ii−ii1-1-11-11-1-1−i−iii−i−iii11-1-11-1−ii1-1−ii11-1-1−i−i−i−iiiii-111-1i−i−ii-1-111ii−i−i11-1-1−i−iii-11i−i
χ161-11-111−ii−ii1-1-11-11-1-1−i−iii−i−iii11-1-11-1−ii1-1−ii11-1-1−i−i−i−iiiii-11-11i−ii−i-1-111ii−i−i-1-111ii−i−i1-1−ii
χ1722222222-2-2-2-22222222222-2-2-2-22222-2-222-2-2-2-2-2-2-2-222-2-222-2-20000000000000000000000000000
χ18222222-2-222-2-2222222-2-2-2-222222222-2-2-2-2-2-222-2-2-2-2-2-222-2-2220000000000000000000000000000
χ1922222-12222222-1-122-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122002200-1-1-1-1-1-1-1-1000000000000
χ2022222-12222222-1-122-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2-20011111111000000000000
χ2122222-122-2-2-2-22-1-122-122221111-1-1-1-111-1-1-2-2-2-21111-1-111-1-11100000000−i3i3−i3i3−i3i3−i3i3000000000000
χ2222222-122-2-2-2-22-1-122-122221111-1-1-1-111-1-1-2-2-2-21111-1-111-1-11100000000i3−i3i3−i3i3−i3i3−i3000000000000
χ2322222-1-2-222-2-22-1-122-1-2-2-2-2-1-1-1-1-1-1-1-11111-2-222111111-1-111-1-100000000−i3i3−i3i3i3−i3i3−i3000000000000
χ2422222-1-2-222-2-22-1-122-1-2-2-2-2-1-1-1-1-1-1-1-11111-2-222111111-1-111-1-100000000i3−i3i3−i3−i3i3−i3i3000000000000
χ2522222-1-2-2-2-2222-1-122-1-2-2-2-21111-1-1-1-1-1-11122-2-2-1-1-1-1111111112200-2-200-1-1-1-11111000000000000
χ2622222-1-2-2-2-2222-1-122-1-2-2-2-21111-1-1-1-1-1-11122-2-2-1-1-1-111111111-2-20022001111-1-1-1-1000000000000
χ272222-12222222-122-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10022002200000000-1-1-1-1-1-1-1-10000
χ282222-12222222-122-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-200-2-200000000111111110000
χ292222-1222-2-2-2-2-122-1-12-1-1-1-1-2-2-2-2-1-1-1-1-2-22211111111-1-111-1-1110000000000000000−i3i3−i3i3−i3i3−i3i30000
χ302222-1222-2-2-2-2-122-1-12-1-1-1-1-2-2-2-2-1-1-1-1-2-22211111111-1-111-1-1110000000000000000i3−i3i3−i3i3−i3i3−i30000
χ312222-12-2-222-2-2-122-1-1211112222-1-1-1-1-2-2-2-211-1-1111111-1-111-1-10000000000000000−i3i3−i3i3i3−i3i3−i30000
χ322222-12-2-222-2-2-122-1-1211112222-1-1-1-1-2-2-2-211-1-1111111-1-111-1-10000000000000000i3−i3i3−i3−i3i3−i3i30000
χ332222-12-2-2-2-222-122-1-121111-2-2-2-2-1-1-1-122-2-2-1-111-1-1-1-111111111002200-2-200000000-1-1-1-111110000
χ342222-12-2-2-2-222-122-1-121111-2-2-2-2-1-1-1-122-2-2-1-111-1-1-1-11111111100-2-20022000000001111-1-1-1-10000
χ352-22-2222i−2i−2i2i-22-22-22-2-22i2i−2i−2i−2i−2i2i2i22-2-2-222i−2i-22−2i2i-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ362-22-222−2i2i2i−2i-22-22-22-2-2−2i−2i2i2i2i2i−2i−2i22-2-2-22−2i2i-222i−2i-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ372-22-22-12i−2i2i−2i2-2-2-112-212i2i−2i−2i−i−iii-1-111-11−ii2-22i−2i-1-111−i−i−i−iiiii2-2002i−2i00-1-111−i−iii000000000000
χ382-22-22-12i−2i2i−2i2-2-2-112-212i2i−2i−2i−i−iii-1-111-11−ii2-22i−2i-1-111−i−i−i−iiiii-2200−2i2i0011-1-1ii−i−i000000000000
χ392-22-22-12i−2i−2i2i-22-2-112-212i2i−2i−2iii−i−i-1-1111-1−ii-22−2i2i11-1-1−i−iiiii−i−i00000000−i3i3i3−i33−3−33000000000000
χ402-22-22-12i−2i−2i2i-22-2-112-212i2i−2i−2iii−i−i-1-1111-1−ii-22−2i2i11-1-1−i−iiiii−i−i00000000i3−i3−i3i3−333−3000000000000
χ412-22-22-1−2i2i2i−2i-22-2-112-21−2i−2i2i2i−i−iii-1-1111-1i−i-222i−2i11-1-1ii−i−i−i−iii00000000−i3i3i3−i3−333−3000000000000
χ422-22-22-1−2i2i2i−2i-22-2-112-21−2i−2i2i2i−i−iii-1-1111-1i−i-222i−2i11-1-1ii−i−i−i−iii00000000i3−i3−i3i33−3−33000000000000
χ432-22-22-1−2i2i−2i2i2-2-2-112-21−2i−2i2i2iii−i−i-1-111-11i−i2-2−2i2i-1-111iiii−i−i−i−i2-200−2i2i00-1-111ii−i−i000000000000
χ442-22-22-1−2i2i−2i2i2-2-2-112-21−2i−2i2i2iii−i−i-1-111-11i−i2-2−2i2i-1-111iiii−i−i−i−i-22002i−2i0011-1-1−i−iii000000000000
χ452-22-2-122i−2i2i−2i2-212-2-11-2−i−iii2i2i−2i−2i-1-1112-22i−2i-11−ii-1-111−i−i−i−iiiii002-2002i−2i00000000-1-111−i−iii0000
χ462-22-2-122i−2i2i−2i2-212-2-11-2−i−iii2i2i−2i−2i-1-1112-22i−2i-11−ii-1-111−i−i−i−iiiii00-2200−2i2i0000000011-1-1ii−i−i0000
χ472-22-2-122i−2i−2i2i-2212-2-11-2−i−iii−2i−2i2i2i-1-111-222i−2i1-1i−i11-1-1−i−iiiii−i−i0000000000000000−i3i3i3−i33−3−330000
χ482-22-2-122i−2i−2i2i-2212-2-11-2−i−iii−2i−2i2i2i-1-111-222i−2i1-1i−i11-1-1−i−iiiii−i−i0000000000000000i3−i3−i3i3−333−30000
χ492-22-2-12−2i2i2i−2i-2212-2-11-2ii−i−i2i2i−2i−2i-1-111-22−2i2i1-1−ii11-1-1ii−i−i−i−iii0000000000000000−i3i3i3−i3−333−30000
χ502-22-2-12−2i2i2i−2i-2212-2-11-2ii−i−i2i2i−2i−2i-1-111-22−2i2i1-1−ii11-1-1ii−i−i−i−iii0000000000000000i3−i3−i3i33−3−330000
χ512-22-2-12−2i2i−2i2i2-212-2-11-2ii−i−i−2i−2i2i2i-1-1112-2−2i2i-11i−i-1-111iiii−i−i−i−i002-200−2i2i00000000-1-111ii−i−i0000
χ522-22-2-12−2i2i−2i2i2-212-2-11-2ii−i−i−2i−2i2i2i-1-1112-2−2i2i-11i−i-1-111iiii−i−i−i−i00-22002i−2i0000000011-1-1−i−iii0000
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
χ544444-2-244-4-4-4-4-2-2-2-2-2-2-2-2-2-22222111122-2-22222-1-1-1-111-1-111-1-10000000000000000000000000000
χ554444-2-2-4-444-4-4-2-2-2-2-2-22222-2-2-2-21111222222-2-2-1-1-1-1-1-111-1-1110000000000000000000000000000
χ564444-2-2-4-4-4-444-2-2-2-2-2-2222222221111-2-222-2-2221111-1-1-1-1-1-1-1-10000000000000000000000000000
χ5744-4-4440000004-44-4-4-4000000004-44-4000000000000000000000000000000000000000000000000
χ5844-4-44-200000042-2-4-42000023−2323−23-22-220000000000000023−230023−230000000000000000000000000000
χ5944-4-44-200000042-2-4-420000−2323−2323-22-2200000000000000−232300−23230000000000000000000000000000
χ6044-4-4-24000000-2-4422-4−2i32i3−2i32i30000-22-22000000000000−2i32i300−2i32i3000000000000000000000000000000
χ6144-4-4-24000000-2-4422-42i3−2i32i3−2i30000-22-220000000000002i3−2i3002i3−2i3000000000000000000000000000000
χ6244-4-4-2-2000000-22-2222−2i32i3−2i32i323−2323−231-11-1000000003i−3i3i−3ii3−i3−33i3−i3−330000000000000000000000000000
χ6344-4-4-2-2000000-22-2222−2i32i3−2i32i3−2323−23231-11-100000000−3i3i−3i3ii3−i33−3i3−i33−30000000000000000000000000000
χ6444-4-4-2-2000000-22-22222i3−2i32i3−2i323−2323−231-11-100000000−3i3i−3i3i−i3i3−33−i3i3−330000000000000000000000000000
χ6544-4-4-2-2000000-22-22222i3−2i32i3−2i3−2323−23231-11-1000000003i−3i3i−3i−i3i33−3−i3i33−30000000000000000000000000000
χ664-44-4-2-24i−4i4i−4i4-42-22-222−2i−2i2i2i−2i−2i2i2i11-1-1-22−2i2i-22−2i2i11-1-1iiii−i−i−i−i0000000000000000000000000000
χ674-44-4-2-24i−4i−4i4i-442-22-222−2i−2i2i2i2i2i−2i−2i11-1-12-2−2i2i2-22i−2i-1-111ii−i−i−i−iii0000000000000000000000000000
χ684-44-4-2-2−4i4i4i−4i-442-22-2222i2i−2i−2i−2i−2i2i2i11-1-12-22i−2i2-2−2i2i-1-111−i−iiiii−i−i0000000000000000000000000000
χ694-44-4-2-2−4i4i−4i4i4-42-22-2222i2i−2i−2i2i2i−2i−2i11-1-1-222i−2i-222i−2i11-1-1−i−i−i−iiiii0000000000000000000000000000
χ704-4-4444000000-4-4-4-444000000004-4-44000000000000000000000000000000000000000000000000
χ714-4-444-2000000-422-44-20000−2i32i32i3−2i3-222-200000000000000−2i32i3002i3−2i30000000000000000000000000000
χ724-4-444-2000000-422-44-200002i3−2i3−2i32i3-222-2000000000000002i3−2i300−2i32i30000000000000000000000000000
χ734-4-44-240000002-4-42-2423−23−23230000-222-200000000000023−2300−2323000000000000000000000000000000
χ744-4-44-240000002-4-42-24−232323−230000-222-2000000000000−23230023−23000000000000000000000000000000
χ754-4-44-2-20000002222-2-223−23−2323−2i32i32i3−2i31-1-1100000000−3i3i3i−3i−33i3−i33−3−i3i30000000000000000000000000000
χ764-4-44-2-20000002222-2-223−23−23232i3−2i3−2i32i31-1-11000000003i−3i−3i3i−33−i3i33−3i3−i30000000000000000000000000000
χ774-4-44-2-20000002222-2-2−232323−23−2i32i32i3−2i31-1-11000000003i−3i−3i3i3−3i3−i3−33−i3i30000000000000000000000000000
χ784-4-44-2-20000002222-2-2−232323−232i3−2i3−2i32i31-1-1100000000−3i3i3i−3i3−3−i3i3−33i3−i30000000000000000000000000000

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