Finite Group Databasebeta

← Group #10590581

Character table — Group #10590581

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111222222222244444444444444666666668888888812121212121212121212121212121212242436363636
order1222334466666634466612121212121212122244666612121212121212124444881212121212122424242412124488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1111111-1-1-1-1
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
χ5111111111111111-1-1111111-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111-1-1111111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ7111111111111111-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111
χ8111111111111111-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111111111-1-111-1-1
χ911-1-111-11-11-11-1-11i−i-11-1-11-1ii−i−i11-11-111-1-1i−i1-1ii−i−ii−ii−i1-11-1ii−i−i11-1-1i−ii−i1-1
χ1011-1-111-11-11-11-1-11i−i-11-1-11-1ii−i−i11-11-111-1-1i−i1-1ii−i−i−iii−i-111-1ii−i−i-1-111−ii−ii-11
χ1111-1-111-11-11-11-1-11i−i-11-1-11-1ii−i−i1-11-11-1-111i−i1-1ii−i−ii−i−ii1-1-11−i−iii11-1-1i−i−ii-11
χ1211-1-111-11-11-11-1-11i−i-11-1-11-1ii−i−i1-11-11-1-111i−i1-1ii−i−i−ii−ii-11-11−i−iii-1-111−iii−i1-1
χ1311-1-111-11-11-11-1-11−ii-11-1-11-1−i−iii11-11-111-1-1−ii1-1−i−iiii−i−ii-111-1−i−iii-1-111i−ii−i-11
χ1411-1-111-11-11-11-1-11−ii-11-1-11-1−i−iii11-11-111-1-1−ii1-1−i−iii−ii−ii1-11-1−i−iii11-1-1−ii−ii1-1
χ1511-1-111-11-11-11-1-11−ii-11-1-11-1−i−iii1-11-11-1-111−ii1-1−i−iiii−ii−i-11-11ii−i−i-1-111i−i−ii1-1
χ1611-1-111-11-11-11-1-11−ii-11-1-11-1−i−iii1-11-11-1-111−ii1-1−i−iii−iii−i1-1-11ii−i−i11-1-1−iii−i-11
χ17222222-2-2222222200222-2-2-20000-222-2-2222200-2-20000000000-2-200000000000000
χ18222222-2-2222222200222-2-2-20000-2-2-222-2-2-2-200-2-200000000002200000000000000
χ1922222-122-122-12-1-122-1-1-12-1-1-1-1-1-122222-1-1-1-122-1-1-1-1-1-1002200-1-1-1-1-1-10000000000
χ2022222-122-122-12-1-122-1-1-12-1-1-1-1-1-12-2-2-2-2111122-1-1-1-1-1-100-2-2001111110000000000
χ2122222-122-122-12-1-1-2-2-1-1-12-1-1111122222-1-1-1-1-2-2-1-1111100-2-200-1-111110000000000
χ2222222-122-122-12-1-1-2-2-1-1-12-1-111112-2-2-2-21111-2-2-1-1111100220011-1-1-1-10000000000
χ2322222-1-2-2-122-12-1-100-1-1-1-211−i3i3−i3i3-222-2-2-1-1-1-10011−i3i3−i3i300000011−i3i3−i3i30000000000
χ2422222-1-2-2-122-12-1-100-1-1-1-211−i3i3−i3i3-2-2-22211110011−i3i3−i3i3000000-1-1i3−i3i3−i30000000000
χ2522222-1-2-2-122-12-1-100-1-1-1-211i3−i3i3−i3-222-2-2-1-1-1-10011i3−i3i3−i300000011i3−i3i3−i30000000000
χ2622222-1-2-2-122-12-1-100-1-1-1-211i3−i3i3−i3-2-2-22211110011i3−i3i3−i3000000-1-1−i3i3−i3i30000000000
χ272222-12222-1-12-12-122-1-1-1-1222222-100000000-1-1-1-1-1-1-1-1220022000000-1-1-1-1-1-10000
χ282222-12222-1-12-12-122-1-1-1-1222222-100000000-1-1-1-1-1-1-1-1-2-200-2-20000001111110000
χ292222-12222-1-12-12-1-2-2-1-1-1-122-2-2-2-2-10000000011-1-111112200-2-20000001111-1-10000
χ302222-12222-1-12-12-1-2-2-1-1-1-122-2-2-2-2-10000000011-1-11111-2-20022000000-1-1-1-1110000
χ3122-2-2222-2-22-22-2-2200-22-22-220000-22-2-2222-2-200-220000000000-2200000000000000
χ3222-2-2222-2-22-22-2-2200-22-22-220000-2-222-2-2-22200-2200000000002-200000000000000
χ3322-2-22-12-212-2-1-21-1001-1121-13−3−33-22-2-22-1-111001-13−3−330000001-13−3−330000000000
χ3422-2-22-12-212-2-1-21-1001-1121-13−3−33-2-222-211-1-1001-13−3−33000000-11−333−30000000000
χ3522-2-22-12-212-2-1-21-1001-1121-1−333−3-22-2-22-1-111001-1−333−30000001-1−333−30000000000
χ3622-2-22-12-212-2-1-21-1001-1121-1−333−3-2-222-211-1-1001-1−333−3000000-113−3−330000000000
χ3722-2-22-1-2212-2-1-21-12i−2i1-11-2-11−i−iii22-22-2-1-1112i−2i-11−i−iii002i−2i00-11−i−iii0000000000
χ3822-2-22-1-2212-2-1-21-12i−2i1-11-2-11−i−iii2-22-2211-1-12i−2i-11−i−iii00−2i2i001-1ii−i−i0000000000
χ3922-2-22-1-2212-2-1-21-1−2i2i1-11-2-11ii−i−i22-22-2-1-111−2i2i-11ii−i−i00−2i2i00-11ii−i−i0000000000
χ4022-2-22-1-2212-2-1-21-1−2i2i1-11-2-11ii−i−i2-22-2211-1-1−2i2i-11ii−i−i002i−2i001-1−i−iii0000000000
χ4122-2-2-12-22-2-1121-2-12i−2i1-1112-22i2i−2i−2i-100000000−ii-11−i−iii2i−2i002-2000000-1-111−ii0000
χ4222-2-2-12-22-2-1121-2-12i−2i1-1112-22i2i−2i−2i-100000000−ii-11−i−iii−2i2i00-2200000011-1-1i−i0000
χ4322-2-2-12-22-2-1121-2-1−2i2i1-1112-2−2i−2i2i2i-100000000i−i-11ii−i−i2i−2i00-2200000011-1-1−ii0000
χ4422-2-2-12-22-2-1121-2-1−2i2i1-1112-2−2i−2i2i2i-100000000i−i-11ii−i−i−2i2i002-2000000-1-111i−i0000
χ454444-24-4-44-2-24-24-200-2-2-22-4-40000200000000002200000000000000000000000000
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
χ5044-4-4-244-4-4-2242-4-2002-22-2-440000200000000002-200000000000000000000000000
χ5144-4-4-2-24-42-22-222100-11-1-22-223−23−232320000000000-11−333−30000000000000000000000
χ5244-4-4-2-24-42-22-222100-11-1-22-2−232323−2320000000000-113−3−330000000000000000000000
χ5344-4-4-2-2-442-22-22214i−4i-11-12-22−2i−2i2i2i-200000000−2i2i1-1ii−i−i0000000000000000000000
χ5444-4-4-2-2-442-22-2221−4i4i-11-12-222i2i−2i−2i-2000000002i−2i1-1−i−iii0000000000000000000000
χ554-44-444004-4-4-44-44004-4-40000000000000000000000000000000000000000000000
χ564-44-44-200-2-4-4242-200-222000000000000−2i32i3−2i32i3000000000000000000000000000000
χ574-44-44-200-2-4-4242-200-2220000000000002i3−2i32i3−2i3000000000000000000000000000000
χ584-44-4-2400422-4-2-4-200-2220000000000000000000000000000000000006−66−6000000
χ594-44-4-2400422-4-2-4-200-222000000000000000000000000000000000000−66−66000000
χ604-4-444400-4-44-4-44400-4-440000000000000000000000000000000000000000000000
χ614-4-444-2002-442-4-2-20022-2000000000000−2i32i32i3−2i3000000000000000000000000000000
χ624-4-444-2002-442-4-2-20022-20000000000002i3−2i3−2i32i3000000000000000000000000000000
χ634-4-44-2400-42-2-424-20022-20000000000000000000000000000000000006−6−66000000
χ644-4-44-2400-42-2-424-20022-2000000000000000000000000000000000000−666−6000000
χ658-88-8-4-400-4444-442002-2-20000000000000000000000000000000000000000000000
χ668-8-88-4-40044-444-4200-2-220000000000000000000000000000000000000000000000

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