Finite Group Databasebeta

← Group #10591430

Character table — Group #10591430

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111222222222244444444444444666666668888888812121212121212121212121212121212242436363636
order12223344666666223666666612121212444412121212666666121222448812121212121224242424664488
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
χ511111111111111-1-11-1-1-1-1111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1
χ611111111111111-1-11-1-1-1-1111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ711111111111111-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-111
χ811111111111111-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111111111-1-111-1-1
χ911-1-1111-1-1-111-1-11-1111-1-1-1-111-1-11i−ii−iii−i−i1-111-1-11-11-1i−i1-1i−iii−i−i11-1-11-1i−ii−i
χ1011-1-1111-1-1-111-1-11-1111-1-1-1-111-1-11i−ii−iii−i−i1-111-1-11-1-11i−i-11i−iii−i−i-1-111-11−ii−ii
χ1111-1-1111-1-1-111-1-11-1111-1-1-1-111-1-11−ii−ii−i−iii1-111-1-11-11-1−ii1-1−ii−i−iii11-1-11-1−ii−ii
χ1211-1-1111-1-1-111-1-11-1111-1-1-1-111-1-11−ii−ii−i−iii1-111-1-11-1-11−ii-11−ii−i−iii-1-111-11i−ii−i
χ1311-1-1111-1-1-111-1-1-111-1-111-1-111-1-11i−ii−iii−i−i-11-1-1111-11-1−ii-11i−i−i−iii-1-1111-1i−i−ii
χ1411-1-1111-1-1-111-1-1-111-1-111-1-111-1-11i−ii−iii−i−i-11-1-1111-1-11−ii1-1i−i−i−iii11-1-1-11−iii−i
χ1511-1-1111-1-1-111-1-1-111-1-111-1-111-1-11−ii−ii−i−iii-11-1-1111-11-1i−i-11−iiii−i−i-1-1111-1−iii−i
χ1611-1-1111-1-1-111-1-1-111-1-111-1-111-1-11−ii−ii−i−iii-11-1-1111-1-11i−i1-1−iiii−i−i11-1-1-11i−i−ii
χ17222222-2-22222220020000222-2-2-2-222-2-22222000000-2-2000000-2-200000000000000
χ18222222-2-22222220020000222-2-2-2-2-2-222-2-2-2-2000000-2-20000002200000000000000
χ1922222-122-1-12-12222-12222-1-1-122-1-100000000-1-1-1-1-1-1-1-1220022000000-1-1-1-1-1-10000
χ2022222-122-1-12-12222-12222-1-1-122-1-100000000-1-1-1-1-1-1-1-1-2-200-2-20000001111110000
χ2122222-122-1-12-122-2-2-1-2-2-2-2-1-1-122-1-100000000111111-1-12200-2-20000001111-1-10000
χ2222222-122-1-12-122-2-2-1-2-2-2-2-1-1-122-1-100000000111111-1-1-2-20022000000-1-1-1-1110000
χ232222-122222-12-1-122-1-1-1-1-1-1-1-1-1-1222222-1-1-1-122-1-1-1-1-1-1002200-1-1-1-1-1-10000000000
χ242222-122222-12-1-122-1-1-1-1-1-1-1-1-1-122-2-2-2-2111122-1-1-1-1-1-100-2-2001111110000000000
χ252222-122222-12-1-1-2-2-11111-1-1-1-1-1222222-1-1-1-1-2-21111-1-100-2-200-1-111110000000000
χ262222-122222-12-1-1-2-2-11111-1-1-1-1-122-2-2-2-21111-2-21111-1-100220011-1-1-1-10000000000
χ272222-12-2-222-12-1-100-1−i3i3−i3i3-1-1-111-2-222-2-2-1-1-1-100−i3i3−i3i31100000011−i3i3−i3i30000000000
χ282222-12-2-222-12-1-100-1−i3i3−i3i3-1-1-111-2-2-2-222111100−i3i3−i3i311000000-1-1i3−i3i3−i30000000000
χ292222-12-2-222-12-1-100-1i3−i3i3−i3-1-1-111-2-222-2-2-1-1-1-100i3−i3i3−i31100000011i3−i3i3−i30000000000
χ302222-12-2-222-12-1-100-1i3−i3i3−i3-1-1-111-2-2-2-222111100i3−i3i3−i311000000-1-1−i3i3−i3i30000000000
χ3122-2-222-22-2-222-2-20020000-2-22-222-22i−2i−2i2i2i2i−2i−2i000000-22000000−2i2i00000000000000
χ3222-2-222-22-2-222-2-20020000-2-22-222-2−2i2i2i−2i−2i−2i2i2i000000-220000002i−2i00000000000000
χ3322-2-22-12-2112-1-2-22-2-122-2-211-12-21-100000000-11-1-111-112-2002-2000000-1-111-110000
χ3422-2-22-12-2112-1-2-22-2-122-2-211-12-21-100000000-11-1-111-11-2200-2200000011-1-11-10000
χ3522-2-22-12-2112-1-2-2-22-1-2-22211-12-21-1000000001-111-1-1-112-200-2200000011-1-1-110000
χ3622-2-22-12-2112-1-2-2-22-1-2-22211-12-21-1000000001-111-1-1-11-22002-2000000-1-1111-10000
χ3722-2-2-122-2-2-2-12112-2-1-1-11111-1-11-222i−2i2i−2i−i−iii2-2-1-111-11002i−2i00−ii−i−iii0000000000
χ3822-2-2-122-2-2-2-12112-2-1-1-11111-1-11-22−2i2i−2i2iii−i−i2-2-1-111-1100−2i2i00i−iii−i−i0000000000
χ3922-2-2-122-2-2-2-1211-22-111-1-111-1-11-222i−2i2i−2i−i−iii-2211-1-1-1100−2i2i00−iiii−i−i0000000000
χ4022-2-2-122-2-2-2-1211-22-111-1-111-1-11-22−2i2i−2i2iii−i−i-2211-1-1-11002i−2i00i−i−i−iii0000000000
χ4122-2-2-12-22-2-2-121100-1−i3i3i3−i311-11-12-22i−2i−2i2i−i−iii00−i3i3i3−i31-1000000i−i3−3−330000000000
χ4222-2-2-12-22-2-2-121100-1−i3i3i3−i311-11-12-2−2i2i2i−2iii−i−i00−i3i3i3−i31-1000000−ii−333−30000000000
χ4322-2-2-12-22-2-2-121100-1i3−i3−i3i311-11-12-22i−2i−2i2i−i−iii00i3−i3−i3i31-1000000i−i−333−30000000000
χ4422-2-2-12-22-2-2-121100-1i3−i3−i3i311-11-12-2−2i2i2i−2iii−i−i00i3−i3−i3i31-1000000−ii3−3−330000000000
χ4544444-2-4-4-2-24-24400-20000-2-2-2-4-42200000000000000220000000000000000000000
χ464444-2-244-2-2-2-2-2-2441-2-2-2-2111-2-2-2-200000000-2-21111110000000000000000000000
χ474444-2-244-2-2-2-2-2-2-4-412222111-2-2-2-20000000022-1-1-1-1110000000000000000000000
χ484444-2-2-4-4-2-2-2-2-2-2001−2i32i3−2i32i311122220000000000i3−i3i3−i3-1-10000000000000000000000
χ494444-2-2-4-4-2-2-2-2-2-20012i3−2i32i3−2i311122220000000000−i3i3−i3i3-1-10000000000000000000000
χ5044-4-44-2-44224-2-4-400-2000022-2-44-22000000000000002-20000000000000000000000
χ5144-4-4-2-24-422-2-2224-41-2-222-1-11-222-200000000-2211-1-11-10000000000000000000000
χ5244-4-4-2-24-422-2-222-44122-2-2-1-11-222-2000000002-2-1-1111-10000000000000000000000
χ5344-4-4-2-2-4422-2-222001−2i32i32i3−2i3-1-112-2-220000000000i3−i3−i3i3-110000000000000000000000
χ5444-4-4-2-2-4422-2-2220012i3−2i3−2i32i3-1-112-2-220000000000−i3i3i3−i3-110000000000000000000000
χ554-44-444004-4-4-4-4400400004-4-4000000000000000000000000000000000000000000
χ564-44-44-200-22-42-4400-20000-22200000000000000000000000000000000i6−i6i6−i6000000
χ574-44-44-200-22-42-4400-20000-22200000000000000000000000000000000−i6i6−i6i6000000
χ584-44-4-24004-42-42-200-20000-22200000000−2i32i3−2i32i3000000000000000000000000000000
χ594-44-4-24004-42-42-200-20000-222000000002i3−2i32i3−2i3000000000000000000000000000000
χ604-4-444400-44-4-44-40040000-44-4000000000000000000000000000000000000000000
χ614-4-444-2002-2-424-400-200002-2200000000000000000000000000000000i6−i6−i6i6000000
χ624-4-444-2002-2-424-400-200002-2200000000000000000000000000000000−i6i6i6−i6000000
χ634-4-44-2400-442-4-2200-200002-220000000023−23−2323000000000000000000000000000000
χ644-4-44-2400-442-4-2200-200002-2200000000−232323−23000000000000000000000000000000
χ658-88-8-4-400-44444-400200002-2-2000000000000000000000000000000000000000000
χ668-8-88-4-4004-444-440020000-22-2000000000000000000000000000000000000000000

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