Finite Group Databasebeta

← Group #10590589

Character table — Group #10590589

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111222222222244444444444444666666668888888812121212121212121212121212121212242436363636
order1222334466666634466612121212121212124444121212121212121212121212224466668812122424242412122288
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1111111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111-1-1111111-1-1-1-1111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1
χ6111111111111111-1-1111111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111
χ7111111111111111-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111
χ8111111111111111-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-11111-1-111-1-1
χ911-1-1111-111-1-1-1-11i−i-11-11-1-1ii−i−i1i−ii−iii−i−ii−i1-1ii−i−i1-1i−i11-1-11-1i−i11-1-1i−i1-1i−i
χ1011-1-1111-111-1-1-1-11i−i-11-11-1-1ii−i−i1i−ii−iii−i−ii−i1-1ii−i−i1-1−ii11-1-1-11i−i-1-111−ii-11−ii
χ1111-1-1111-111-1-1-1-11i−i-11-11-1-1ii−i−i1−ii−ii−i−iiii−i1-1ii−i−i-11i−i-1-1111-1−ii11-1-1i−i-11−ii
χ1211-1-1111-111-1-1-1-11i−i-11-11-1-1ii−i−i1−ii−ii−i−iiii−i1-1ii−i−i-11−ii-1-111-11−ii-1-111−ii1-1i−i
χ1311-1-1111-111-1-1-1-11−ii-11-11-1-1−i−iii1i−ii−iii−i−i−ii1-1−i−iii-11i−i-1-111-11i−i-1-111i−i1-1−ii
χ1411-1-1111-111-1-1-1-11−ii-11-11-1-1−i−iii1i−ii−iii−i−i−ii1-1−i−iii-11−ii-1-1111-1i−i11-1-1−ii-11i−i
χ1511-1-1111-111-1-1-1-11−ii-11-11-1-1−i−iii1−ii−ii−i−iii−ii1-1−i−iii1-1i−i11-1-1-11−ii-1-111i−i-11i−i
χ1611-1-1111-111-1-1-1-11−ii-11-11-1-1−i−iii1−ii−ii−i−iii−ii1-1−i−iii1-1−ii11-1-11-1−ii11-1-1−ii1-1−ii
χ17222222-2-2222222200222-2-2-20000-222-2-2222200-2-200000000000000-2-20000000000
χ18222222-2-2222222200222-2-2-20000-2-2-222-2-2-2-200-2-200000000000000220000000000
χ1922222-1222-12-1-12-122-1-1-1-12-1-1-1-1-122222-1-1-1-122-1-1-1-1-1-12200-1-1-1-100-1-10000000000
χ2022222-1222-12-1-12-122-1-1-1-12-1-1-1-1-12-2-2-2-2111122-1-1-1-1-1-1-2-200111100110000000000
χ2122222-1222-12-1-12-1-2-2-1-1-1-12-1111122222-1-1-1-1-2-2-1-11111-2-200111100-1-10000000000
χ2222222-1222-12-1-12-1-2-2-1-1-1-12-111112-2-2-2-21111-2-2-1-111112200-1-1-1-100110000000000
χ2322222-1-2-22-12-1-12-100-1-1-11-21−i3i3−i3i3-222-2-2-1-1-1-10011−i3i3−i3i30000−i3i3−i3i300110000000000
χ2422222-1-2-22-12-1-12-100-1-1-11-21−i3i3−i3i3-2-2-22211110011−i3i3−i3i30000i3−i3i3−i300-1-10000000000
χ2522222-1-2-22-12-1-12-100-1-1-11-21i3−i3i3−i3-222-2-2-1-1-1-10011i3−i3i3−i30000i3−i3i3−i300110000000000
χ2622222-1-2-22-12-1-12-100-1-1-11-21i3−i3i3−i3-2-2-22211110011i3−i3i3−i30000−i3i3−i3i300-1-10000000000
χ272222-1222-12-122-1-122-1-1-12-122222-100000000-1-1-1-1-1-1-1-1002200002200-1-1-1-1-1-10000
χ282222-1222-12-122-1-122-1-1-12-122222-100000000-1-1-1-1-1-1-1-100-2-20000-2-2001111110000
χ292222-1222-12-122-1-1-2-2-1-1-12-12-2-2-2-2-10000000011-1-1111100220000-2-2001111-1-10000
χ302222-1222-12-122-1-1-2-2-1-1-12-12-2-2-2-2-10000000011-1-1111100-2-200002200-1-1-1-1110000
χ3122-2-222-2222-2-2-2-2200-22-2-2220000-22i−2i−2i2i2i2i−2i−2i00-2200000000000000−2i2i0000000000
χ3222-2-222-2222-2-2-2-2200-22-2-2220000-2−2i2i2i−2i−2i−2i2i2i00-22000000000000002i−2i0000000000
χ3322-2-22-12-22-1-211-2-12i−2i1-11-1-21−i−iii22i−2i2i−2i−i−iii2i−2i-11−i−iii2-200-1-11100−ii0000000000
χ3422-2-22-12-22-1-211-2-12i−2i1-11-1-21−i−iii2−2i2i−2i2iii−i−i2i−2i-11−i−iii-220011-1-100i−i0000000000
χ3522-2-22-12-22-1-211-2-1−2i2i1-11-1-21ii−i−i22i−2i2i−2i−i−iii−2i2i-11ii−i−i-220011-1-100−ii0000000000
χ3622-2-22-12-22-1-211-2-1−2i2i1-11-1-21ii−i−i2−2i2i−2i2iii−i−i−2i2i-11ii−i−i2-200-1-11100i−i0000000000
χ3722-2-22-1-222-1-211-2-1001-1112-13−3−33-22i−2i−2i2i−i−iii001-13−3−330000−i3i3i3−i300i−i0000000000
χ3822-2-22-1-222-1-211-2-1001-1112-13−3−33-2−2i2i2i−2iii−i−i001-13−3−330000i3−i3−i3i300−ii0000000000
χ3922-2-22-1-222-1-211-2-1001-1112-1−333−3-22i−2i−2i2i−i−iii001-1−333−30000i3−i3−i3i300i−i0000000000
χ4022-2-22-1-222-1-211-2-1001-1112-1−333−3-2−2i2i2i−2iii−i−i001-1−333−30000−i3i3i3−i300−ii0000000000
χ4122-2-2-122-2-121-2-21-12i−2i1-1121-22i2i−2i−2i-100000000−ii-11−i−iii002i−2i00002-200-1-111−ii0000
χ4222-2-2-122-2-121-2-21-12i−2i1-1121-22i2i−2i−2i-100000000−ii-11−i−iii00−2i2i0000-220011-1-1i−i0000
χ4322-2-2-122-2-121-2-21-1−2i2i1-1121-2−2i−2i2i2i-100000000i−i-11ii−i−i002i−2i0000-220011-1-1−ii0000
χ4422-2-2-122-2-121-2-21-1−2i2i1-1121-2−2i−2i2i2i-100000000i−i-11ii−i−i00−2i2i00002-200-1-111i−i0000
χ454444-24-4-4-24-244-2-200-2-2-2-42-40000200000000002200000000000000000000000000
χ464444-2-244-2-2-2-2-2-2144111-2-2-2-2-2-2-2-200000000-2-21111110000000000000000000000
χ474444-2-244-2-2-2-2-2-21-4-4111-2-2-22222-2000000002211-1-1-1-10000000000000000000000
χ484444-2-2-4-4-2-2-2-2-2-2100111222−2i32i3−2i32i320000000000-1-1i3−i3i3−i30000000000000000000000
χ494444-2-2-4-4-2-2-2-2-2-21001112222i3−2i32i3−2i320000000000-1-1−i3i3−i3i30000000000000000000000
χ5044-4-4-24-44-242-4-42-2002-22-4-240000200000000002-200000000000000000000000000
χ5144-4-4-2-24-4-2-2222214i−4i-11-1-222−2i−2i2i2i-200000000−2i2i1-1ii−i−i0000000000000000000000
χ5244-4-4-2-24-4-2-222221−4i4i-11-1-2222i2i−2i−2i-2000000002i−2i1-1−i−iii0000000000000000000000
χ5344-4-4-2-2-44-2-22222100-11-12-2-223−23−232320000000000-11−333−30000000000000000000000
χ5444-4-4-2-2-44-2-22222100-11-12-2-2−232323−2320000000000-113−3−330000000000000000000000
χ554-44-44400-4-44-44-4400-4-440000000000000000000000000000000000000000000000
χ564-44-44-200-4242-2-4-20022-2000000000000−2i32i3−2i32i3000000000000000000000000000000
χ574-44-44-200-4242-2-4-20022-20000000000002i3−2i32i3−2i3000000000000000000000000000000
χ584-44-4-24002-4-2-442-20022-20000000000000000000000000000000000006−66−6000000
χ594-44-4-24002-4-2-442-20022-2000000000000000000000000000000000000−66−66000000
χ604-4-444400-4-4-44-444004-4-40000000000000000000000000000000000000000000000
χ614-4-444-200-42-4-224-200-22200000000000023−23−2323000000000000000000000000000000
χ624-4-444-200-42-4-224-200-222000000000000−232323−23000000000000000000000000000000
χ634-4-44-24002-424-4-2-200-2220000000000000000000000000000000000006−6−66000000
χ644-4-44-24002-424-4-2-200-222000000000000000000000000000000000000−666−6000000
χ658-88-8-4-40044-44-44200-2-220000000000000000000000000000000000000000000000
χ668-8-88-4-400444-44-42002-2-20000000000000000000000000000000000000000000000

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