Finite Group Databasebeta

← Group #10591576

Character table — Group #10591576

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111222222222244444444444444666666668888888812121212121212121212121212121212242436363636
order12223344666666344666121212121212121244441212121212121212121212124444881212121212122424242412124488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1111111-1-1-1-1
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
χ5111111111111111-1-111111-1-1-1-11111111111-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111-1-111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ7111111111111111-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111
χ8111111111111111-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-111111111-1-111-1-1
χ911-1-1111-1-1-11-11-111-1-1-111-111-1-1-11i−ii−iii−i−i1-11-111-1-1i−i1-11-1i−iii−i−i11-1-11-1i−ii−i
χ1011-1-1111-1-1-11-11-111-1-1-111-111-1-1-11i−ii−iii−i−i1-11-111-1-1i−i-11-11i−iii−i−i-1-111-11−ii−ii
χ1111-1-1111-1-1-11-11-111-1-1-111-111-1-1-11−ii−ii−i−iii1-11-111-1-1−ii1-11-1−ii−i−iii11-1-11-1−ii−ii
χ1211-1-1111-1-1-11-11-111-1-1-111-111-1-1-11−ii−ii−i−iii1-11-111-1-1−ii-11-11−ii−i−iii-1-111-11i−ii−i
χ1311-1-1111-1-1-11-11-11-11-1-111-1-1-111-11i−ii−iii−i−i-111-1-1-111−ii1-1-11i−i−i−iii-1-1111-1i−i−ii
χ1411-1-1111-1-1-11-11-11-11-1-111-1-1-111-11i−ii−iii−i−i-111-1-1-111−ii-111-1i−i−i−iii11-1-1-11−iii−i
χ1511-1-1111-1-1-11-11-11-11-1-111-1-1-111-11−ii−ii−i−iii-111-1-1-111i−i1-1-11−iiii−i−i-1-1111-1−iii−i
χ1611-1-1111-1-1-11-11-11-11-1-111-1-1-111-11−ii−ii−i−iii-111-1-1-111i−i-111-1−iiii−i−i11-1-1-11i−i−ii
χ17222222-2-2222222200222-2-20000-2-222-2-2-2-2-2-200-2-200000000002200000000000000
χ18222222-2-2222222200222-2-20000-2-2-2-222222200-2-20000000000-2-200000000000000
χ1922222-12222-1-12-1-122-1-1-1-1-1-1-1-1-1222222-1-1-1-122-1-1-1-1-1-1220000-1-1-1-1-1-10000000000
χ2022222-12222-1-12-1-122-1-1-1-1-1-1-1-1-122-2-2-2-2111122-1-1-1-1-1-1-2-200001111110000000000
χ2122222-12222-1-12-1-1-2-2-1-1-1-1-11111222222-1-1-1-1-2-2-1-11111-2-20000-1-111110000000000
χ2222222-12222-1-12-1-1-2-2-1-1-1-1-1111122-2-2-2-21111-2-2-1-1111122000011-1-1-1-10000000000
χ2322222-1-2-222-1-12-1-100-1-1-111−i3i3−i3i3-2-222-2-211110011−i3i3−i3i3000000-1-1−i3i3−i3i30000000000
χ2422222-1-2-222-1-12-1-100-1-1-111−i3i3−i3i3-2-2-2-222-1-1-1-10011−i3i3−i3i300000011i3−i3i3−i30000000000
χ2522222-1-2-222-1-12-1-100-1-1-111i3−i3i3−i3-2-222-2-211110011i3−i3i3−i3000000-1-1i3−i3i3−i30000000000
χ2622222-1-2-222-1-12-1-100-1-1-111i3−i3i3−i3-2-2-2-222-1-1-1-10011i3−i3i3−i300000011−i3i3−i3i30000000000
χ272222-1222-1-122-12-122-1-1-1222222-1-100000000-1-1-1-1-1-1-1-1002222000000-1-1-1-1-1-10000
χ282222-1222-1-122-12-122-1-1-1222222-1-100000000-1-1-1-1-1-1-1-100-2-2-2-20000001111110000
χ292222-1222-1-122-12-1-2-2-1-1-122-2-2-2-2-1-10000000011-1-111110022-2-20000001111-1-10000
χ302222-1222-1-122-12-1-2-2-1-1-122-2-2-2-2-1-10000000011-1-1111100-2-222000000-1-1-1-1110000
χ3122-2-222-22-2-22-22-2200-2-22-2200002-22i−2i−2i2i−2i−2i2i2i00-2200000000002i−2i00000000000000
χ3222-2-222-22-2-22-22-2200-2-22-2200002-2−2i2i2i−2i2i2i−2i−2i00-220000000000−2i2i00000000000000
χ3322-2-22-12-2-2-2-1121-12-211-1-11-1-111-222i−2i2i−2i−i−iii2-2-11-1-1112i−2i0000−ii−i−iii0000000000
χ3422-2-22-12-2-2-2-1121-12-211-1-11-1-111-22−2i2i−2i2iii−i−i2-2-11-1-111−2i2i0000i−iii−i−i0000000000
χ3522-2-22-12-2-2-2-1121-1-2211-1-1111-1-1-222i−2i2i−2i−i−iii-22-1111-1-1−2i2i0000−iiii−i−i0000000000
χ3622-2-22-12-2-2-2-1121-1-2211-1-1111-1-1-22−2i2i−2i2iii−i−i-22-1111-1-12i−2i0000i−i−i−iii0000000000
χ3722-2-22-1-22-2-2-1121-10011-11-1−i3i3i3−i32-22i−2i−2i2iii−i−i001-1−i3i3i3−i3000000−ii3−3−330000000000
χ3822-2-22-1-22-2-2-1121-10011-11-1−i3i3i3−i32-2−2i2i2i−2i−i−iii001-1−i3i3i3−i3000000i−i−333−30000000000
χ3922-2-22-1-22-2-2-1121-10011-11-1i3−i3−i3i32-22i−2i−2i2iii−i−i001-1i3−i3−i3i3000000−ii−333−30000000000
χ4022-2-22-1-22-2-2-1121-10011-11-1i3−i3−i3i32-2−2i2i2i−2i−i−iii001-1i3−i3−i3i3000000i−i3−3−330000000000
χ4122-2-2-122-2112-2-1-2-12-211-12-222-2-21-100000000-11-11-1-111002-22-2000000-1-111-110000
χ4222-2-2-122-2112-2-1-2-12-211-12-222-2-21-100000000-11-11-1-11100-22-2200000011-1-11-10000
χ4322-2-2-122-2112-2-1-2-1-2211-12-2-2-2221-1000000001-1-1111-1-1002-2-2200000011-1-1-110000
χ4422-2-2-122-2112-2-1-2-1-2211-12-2-2-2221-1000000001-1-1111-1-100-222-2000000-1-1111-10000
χ454444-24-4-4-2-244-24-200-2-2-2-4-400002200000000002200000000000000000000000000
χ464444-2-244-2-2-2-2-2-2144111-2-2-2-2-2-2-2-200000000-2-21111110000000000000000000000
χ474444-2-244-2-2-2-2-2-21-4-4111-2-22222-2-2000000002211-1-1-1-10000000000000000000000
χ484444-2-2-4-4-2-2-2-2-2-210011122−2i32i3−2i32i3220000000000-1-1i3−i3i3−i30000000000000000000000
χ494444-2-2-4-4-2-2-2-2-2-2100111222i3−2i32i3−2i3220000000000-1-1−i3i3−i3i30000000000000000000000
χ5044-4-4-24-44224-4-2-4-20022-2-440000-2200000000002-200000000000000000000000000
χ5144-4-4-2-24-422-22-2214-4-1-11-22-2-2222-200000000-221-111-1-10000000000000000000000
χ5244-4-4-2-24-422-22-221-44-1-11-2222-2-22-2000000002-21-1-1-1110000000000000000000000
χ5344-4-4-2-2-4422-22-22100-1-112-2−2i32i32i3−2i3-220000000000-11i3−i3−i3i30000000000000000000000
χ5444-4-4-2-2-4422-22-22100-1-112-22i3−2i3−2i32i3-220000000000-11−i3i3i3−i30000000000000000000000
χ554-44-444004-4-4-4-444004-4-40000000000000000000000000000000000000000000000
χ564-44-44-2004-422-4-2-200-22200000000000023−2323−23000000000000000000000000000000
χ574-44-44-2004-422-4-2-200-222000000000000−2323−2323000000000000000000000000000000
χ584-44-4-2400-22-4-424-200-222000000000000000000000000000000000000i6−i6i6−i6000000
χ594-44-4-2400-22-4-424-200-222000000000000000000000000000000000000−i6i6−i6i6000000
χ604-4-444400-44-44-4-4400-44-40000000000000000000000000000000000000000000000
χ614-4-444-200-442-2-42-2002-22000000000000−2i32i32i3−2i3000000000000000000000000000000
χ624-4-444-200-442-2-42-2002-220000000000002i3−2i3−2i32i3000000000000000000000000000000
χ634-4-44-24002-2-442-4-2002-22000000000000000000000000000000000000i6−i6−i6i6000000
χ644-4-44-24002-2-442-4-2002-22000000000000000000000000000000000000−i6i6i6−i6000000
χ658-88-8-4-400-44444-42002-2-20000000000000000000000000000000000000000000000
χ668-8-88-4-4004-44-444200-22-20000000000000000000000000000000000000000000000

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