Finite Group Databasebeta

← Group #13166025

Character table — Group #13166025

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222224444666666668888888888881212121216161616161616161616161618182424242424242424242424242424363636363636363636367272108108108108
order1222336666663666444412121212333666666666121212123336666666662212121212121212121212121212124466882424242412124488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111-1-11-1-1-1-11111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1
χ411111111111111111-1-11-1-1-1-11111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51-11-111-1-1-111-11-1-1111-1-111-1-1111-1-1-1-1-1-111111-1-1111111-1-1-1-1-1-11-11-1111111-1-1-1-1-1-1i−i1-1i−iii−i−ii−ii−ii−i
χ61-11-111-1-1-111-11-1-1111-1-111-1-1111-1-1-1-1-1-111111-1-1111111-1-1-1-1-1-11-11-1111111-1-1-1-1-1-1−ii1-1−ii−i−iii−ii−ii−ii
χ71-11-111-1-1-111-11-1-111-11-1-1-111111-1-1-1-1-1-111111-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1111111i−i-11i−iii−i−ii−i−ii−ii
χ81-11-111-1-1-111-11-1-111-11-1-1-111111-1-1-1-1-1-111111-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1111111−ii-11−ii−i−iii−iii−ii−i
χ9222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10022000000000000
χ1022222222222222222-2-22-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-22211111111111100-2-2000000000000
χ1122222-12-1-12-12-1-1-1-12222-1-1-1-12-1-122-1-1-1-12-1-12-1-122-1-12-1-122-1-1-1-122-1-122-1-1-1-122-1-1-1-100-1-1000000000000
χ1222222-12-1-12-12-1-1-1-12222-1-1-1-1-12-1-1-122-1-1-12-12-1-12-12-1-12-1-1-122-1-122-1-1-1-122-1-1-1-122-1-100-1-1000000000000
χ1322222-12-1-12-12-1-1-1-12222-1-1-1-1-1-12-1-1-1-122-1-122-1-12-1-12-1-12-1-1-1-12222-1-1-1-1-1-122-1-1-1-12200-1-1000000000000
χ1422222-12-1-12-12-1-1-1-12-2-2211112-1-122-1-1-1-12-1-12-1-122-1-12-1-122-1-1-1-1-2-2-1-1-2-21111-2-211110011000000000000
χ1522222-12-1-12-12-1-1-1-12-2-221111-12-1-1-122-1-1-12-12-1-12-12-1-12-1-1-122-1-1-2-2-1-111-2-21111-2-2110011000000000000
χ1622222-12-1-12-12-1-1-1-12-2-221111-1-12-1-1-1-122-1-122-1-12-1-12-1-12-1-1-1-122-2-2-1-11111-2-21111-2-20011000000000000
χ172222-12-122-12-1-1-1-1-120020000222222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-100-1-1000000000000220022-1-1-1-1-1-10000
χ182222-12-122-12-1-1-1-1-120020000222222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-100-1-1000000000000-2-200-2-21111110000
χ192-22-222-2-2-222-22-2-2222-2-222-2-2-1-1-1111111-1-1-122-2-2-1-1-1-1-1-11111112-22-2-1-1-1-1-1-1111111002-2000000000000
χ202-22-222-2-2-222-22-2-222-22-2-2-222-1-1-1111111-1-1-122-2-2-1-1-1-1-1-1111111-222-2111111-1-1-1-1-1-100-22000000000000
χ212-22-22-1-2112-1-2-111-122-2-2-1-1112-1-1-2-211112-1-12-11-22-1-12-1-1-2-211112-2-1122-1-1-1-1-2-2111100-11000000000000
χ222-22-22-1-2112-1-2-111-122-2-2-1-111-12-111-2-211-12-12-11-2-12-1-12-111-2-2112-2-11-1-122-1-111-2-21100-11000000000000
χ232-22-22-1-2112-1-2-111-122-2-2-1-111-1-121111-2-2-1-122-11-2-1-12-1-121111-2-22-2-11-1-1-1-1221111-2-200-11000000000000
χ242-22-22-1-2112-1-2-111-12-22-211-1-12-1-1-2-211112-1-12-11-22-1-12-1-1-2-21111-22-11-2-2111122-1-1-1-1001-1000000000000
χ252-22-22-1-2112-1-2-111-12-22-211-1-1-12-111-2-211-12-12-11-2-12-1-12-111-2-211-22-1111-2-211-1-122-1-1001-1000000000000
χ262-22-22-1-2112-1-2-111-12-22-211-1-1-1-121111-2-2-1-122-11-2-1-12-1-121111-2-2-22-111111-2-2-1-1-1-122001-1000000000000
χ272-22-2-121-2-2-121-111-1200-20000222-2-2-2-2-2-2222-12-21-1-1-1-1-1-111111100-110000000000002i−2i002i−2i−i−iii−ii0000
χ282-22-2-121-2-2-121-111-1200-20000222-2-2-2-2-2-2222-12-21-1-1-1-1-1-111111100-11000000000000−2i2i00−2i2iii−i−ii−i0000
χ293333333333333333-133-13333000000000000-1-1-1-1000000000000-1-1-1-100000000000011-1-1-1-1-1-1-1-11111-1-1
χ303333333333333333-133-13333000000000000-1-1-1-1000000000000-1-1-1-1000000000000-1-1-1-1111111-1-1-1-111
χ313333333333333333-1-3-3-1-3-3-3-3000000000000-1-1-1-100000000000011-1-10000000000001111-1-1-1-1-1-111-1-111
χ323333333333333333-1-3-3-1-3-3-3-3000000000000-1-1-1-100000000000011-1-1000000000000-1-111111111-1-111-1-1
χ333-33-333-3-3-333-33-3-33-13-3133-3-3000000000000-1-111000000000000-11-11000000000000i−i-11−ii−i−iiii−ii−i−ii
χ343-33-333-3-3-333-33-3-33-13-3133-3-3000000000000-1-111000000000000-11-11000000000000−ii-11i−iii−i−i−ii−iii−i
χ353-33-333-3-3-333-33-3-33-1-331-3-333000000000000-1-1110000000000001-1-11000000000000i−i1-1−ii−i−iiii−i−iii−i
χ363-33-333-3-3-333-33-3-33-1-331-3-333000000000000-1-1110000000000001-1-11000000000000−ii1-1i−iii−i−i−iii−i−ii
χ374444-24-244-24-2-2-2-2-240040000-2-2-2-2-2-2-2-2-2-2-2-2-244-211111111111100-2-20000000000000000000000000000
χ384444-2-2-2-2-2-2-2-21111400400004-2-244-2-2-2-24-2-2-2-2-2-2-211-211-2-2111100110000000000000000000000000000
χ394444-2-2-2-2-2-2-2-2111140040000-24-2-2-244-2-2-24-2-2-2-2-21-211-2111-2-21100110000000000000000000000000000
χ404444-2-2-2-2-2-2-2-2111140040000-2-24-2-2-2-244-2-24-2-2-2-211-211-21111-2-200110000000000000000000000000000
χ4144-4-44444-4-4-4-444-4-4000000001111-11-11-1-1-1-10000111-1-1-11-11-11-100003−33−33−33−33−33−30000000000000000
χ4244-4-44444-4-4-4-444-4-4000000001111-11-11-1-1-1-10000111-1-1-11-11-11-10000−33−33−33−33−33−330000000000000000
χ4344-4-44444-4-4-4-444-4-400000000-2-2-2-22-22-222220000-2-2-2222-22-22-2200000000000000000000000000000000
χ4444-4-44-24-22-42-4-2-222000023−2323−2311-21-11-1-22-1-12000011-2-1-121-11-1-2200003−3−33003−3−33000000000000000000
χ4544-4-44-24-22-42-4-2-222000023−2323−231-211-1-221-1-12-100001-21-12-11-1-221-10000−33003−3−33003−30000000000000000
χ4644-4-44-24-22-42-4-2-222000023−2323−23-211-221-11-12-1-10000-2112-1-1-221-11-10000003−3−33003−3−330000000000000000
χ4744-4-44-24-22-42-4-2-2220000−2323−232311-21-11-1-22-1-12000011-2-1-121-11-1-220000−333−300−333−3000000000000000000
χ4844-4-44-24-22-42-4-2-2220000−2323−23231-211-1-221-1-12-100001-21-12-11-1-221-100003−300−333−300−330000000000000000
χ4944-4-44-24-22-42-4-2-2220000−2323−2323-211-221-11-12-1-10000-2112-1-1-221-11-1000000−333−300−333−30000000000000000
χ5044-4-4-24-24-42-42-2-22200000000-2-2-2-22-22-222220000111-1-1-11-11-11-10000000000000000000000i6−i6i6−i6000000
χ5144-4-4-24-24-42-42-2-22200000000-2-2-2-22-22-222220000111-1-1-11-11-11-10000000000000000000000−i6i6−i6i6000000
χ524-44-4-242-4-4-242-222-2400-40000-2-2-2222222-2-2-2-24-42111111-1-1-1-1-1-100-220000000000000000000000000000
χ534-44-4-2-2222-2-221-1-11400-400004-2-2-4-422224-2-2-2-222-211-21122-1-1-1-1001-10000000000000000000000000000
χ544-44-4-2-2222-2-221-1-11400-40000-24-222-4-422-24-2-2-2221-211-21-1-122-1-1001-10000000000000000000000000000
χ554-44-4-2-2222-2-221-1-11400-40000-2-242222-4-4-2-24-2-22211-211-2-1-1-1-122001-10000000000000000000000000000
χ564-4-4444-4-44-4-444-44-400000000111-11-11-11-1-1-10000111-1-1-1-11-11-1100003−33−33−3−33−33−330000000000000000
χ574-4-4444-4-44-4-444-44-400000000111-11-11-11-1-1-10000111-1-1-1-11-11-110000−33−33−333−33−33−30000000000000000
χ584-4-4444-4-44-4-444-44-400000000-2-2-22-22-22-22220000-2-2-22222-22-22-200000000000000000000000000000000
χ594-4-444-2-42-2-424-22-22000023−23−232311-2-11-112-2-1-12000011-2-1-12-11-112-200003−3−3300−333−3000000000000000000
χ604-4-444-2-42-2-424-22-22000023−23−23231-21-112-2-11-12-100001-21-12-1-112-2-110000−33003−33−300−330000000000000000
χ614-4-444-2-42-2-424-22-22000023−23−2323-2112-2-11-112-1-10000-2112-1-12-2-11-110000003−3−3300−333−30000000000000000
χ624-4-444-2-42-2-424-22-220000−232323−2311-2-11-112-2-1-12000011-2-1-12-11-112-20000−333−3003−3−33000000000000000000
χ634-4-444-2-42-2-424-22-220000−232323−231-21-112-2-11-12-100001-21-12-1-112-2-1100003−300−33−33003−30000000000000000
χ644-4-444-2-42-2-424-22-220000−232323−23-2112-2-11-112-1-10000-2112-1-12-2-11-11000000−333−3003−3−330000000000000000
χ654-4-44-242-442-4-2-22-2200000000-2-2-22-22-22-22220000111-1-1-1-11-11-1100000000000000000000006−6−66000000
χ664-4-44-242-442-4-2-22-2200000000-2-2-22-22-22-22220000111-1-1-1-11-11-110000000000000000000000−666−6000000
χ6766666-36-3-36-36-3-3-3-3-266-2-3-3-3-3000000000000-211-2000000000000-2-2110000000000000011000000000000
χ6866666-36-3-36-36-3-3-3-3-2-6-6-23333000000000000-211-2000000000000221100000000000000-1-1000000000000
χ696666-36-366-36-3-3-3-3-3-200-200000000000000001-2-2100000000000000110000000000002200-2-21111-1-10000
χ706666-36-366-36-3-3-3-3-3-200-200000000000000001-2-210000000000000011000000000000-2-20022-1-1-1-1110000
χ716-66-66-3-6336-3-6-333-3-26-62-3-333000000000000-21-12000000000000-221-1000000000000001-1000000000000
χ726-66-66-3-6336-3-6-333-3-2-66233-3-3000000000000-21-120000000000002-21-100000000000000-11000000000000
χ736-66-6-363-6-6-363-333-3-200200000000000000001-22-1000000000000001-10000000000002i−2i00−2i2iii−i−i−ii0000
χ746-66-6-363-6-6-363-333-3-200200000000000000001-22-1000000000000001-1000000000000−2i2i002i−2i−i−iiii−i0000
χ7588-8-8-48-48-84-84-4-444000000002222-22-22-2-2-2-20000-1-1-1111-11-11-1100000000000000000000000000000000
χ7688-8-8-4-4-4-4444422-2-20000000022-42-22-2-44-2-240000-1-1211-2-11-112-200000000000000000000000000000000
χ7788-8-8-4-4-4-4444422-2-2000000002-422-2-442-2-24-20000-12-11-21-112-2-1100000000000000000000000000000000
χ7888-8-8-4-4-4-4444422-2-200000000-422-442-22-24-2-200002-1-1-2112-2-11-1100000000000000000000000000000000
χ798-8-88-484-884-8-4-44-4400000000222-22-22-22-2-2-20000-1-1-11111-11-11-100000000000000000000000000000000
χ808-8-88-4-444-444-42-22-20000000022-4-22-224-4-2-240000-1-1211-21-11-1-2200000000000000000000000000000000
χ818-8-88-4-444-444-42-22-2000000002-42-224-4-22-24-20000-12-11-211-1-221-100000000000000000000000000000000
χ828-8-88-4-444-444-42-22-200000000-4224-4-22-224-2-200002-1-1-211-221-11-100000000000000000000000000000000
χ8312121212-6-6-6-6-6-6-6-63333-400-40000000000000000222200000000000000-1-10000000000000000000000000000
χ8412-1212-12-6-6666-6-663-3-33-4004000000000000000022-2-200000000000000-110000000000000000000000000000

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