Finite Group Databasebeta

← Group #13166027

Character table — Group #13166027

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222224444666666668888888888881212121216161616161616161616161618182424242424242424242424242424363636363636363636367272108108108108
order1222336666663666444412121212333666666666121212123336666666664412121212121212121212121212122288121224242424664488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111-1-111-1-1-1-11111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1
χ41111111111111111-1-111-1-1-1-11111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511-1-111-1-11-11-11-1-11i−i1-1ii−i−i111111-1-1-1-1-1-11-1-11111111-1-1-1-1-1-1i−i1-1iiiiii−i−i−i−i−i−i1-11-1i−i11-1-11-1i−ii−i
χ611-1-111-1-11-11-11-1-11i−i1-1ii−i−i111111-1-1-1-1-1-11-1-11111111-1-1-1-1-1-1i−i1-1iiiiii−i−i−i−i−i−i-11-11i−i-1-111-11−ii−ii
χ711-1-111-1-11-11-11-1-11−ii1-1−i−iii111111-1-1-1-1-1-11-1-11111111-1-1-1-1-1-1−ii1-1−i−i−i−i−i−iiiiiii1-11-1−ii11-1-11-1−ii−ii
χ811-1-111-1-11-11-11-1-11−ii1-1−i−iii111111-1-1-1-1-1-11-1-11111111-1-1-1-1-1-1−ii1-1−i−i−i−i−i−iiiiiii-11-11−ii-1-111-11i−ii−i
χ9222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000220000000000
χ102222222222222222-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2221111111111110000-2-20000000000
χ1122222-1-1-122-12-1-1-1-10022000022222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-100-1-1000000000000222200-1-1-1-1-1-10000
χ1222222-1-1-122-12-1-1-1-10022000022222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-100-1-1000000000000-2-2-2-2001111110000
χ132222-1222-1-12-1-1-1-1-12222-1-1-1-12-1-12-1-12-1-12-1-1-1-1222-1-12-1-122-1-1-1-122-1-122-1-1-1-122-1-1-1-10000-1-10000000000
χ142222-1222-1-12-1-1-1-1-12222-1-1-1-1-12-1-12-1-12-1-12-1-1-122-12-1-12-1-1-122-1-122-1-1-1-122-1-1-1-122-1-10000-1-10000000000
χ152222-1222-1-12-1-1-1-1-12222-1-1-1-1-1-12-1-12-1-12-1-12-1-122-1-12-1-12-1-1-1-12222-1-1-1-1-1-122-1-1-1-1220000-1-10000000000
χ162222-1222-1-12-1-1-1-1-1-2-22211112-1-12-1-12-1-12-1-1-1-1222-1-12-1-122-1-1-1-1-2-2-1-1-2-21111-2-211110000110000000000
χ172222-1222-1-12-1-1-1-1-1-2-2221111-12-1-12-1-12-1-12-1-1-122-12-1-12-1-1-122-1-1-2-2-1-111-2-21111-2-2110000110000000000
χ182222-1222-1-12-1-1-1-1-1-2-2221111-1-12-1-12-1-12-1-12-1-122-1-12-1-12-1-1-1-122-2-2-1-11111-2-21111-2-20000110000000000
χ1922-2-222-2-22-22-22-2-222i−2i2-22i2i−2i−2i-1-1-1-1-1-11111112-2-22-1-1-1-1-1-11111112i−2i2-2−i−i−i−i−i−iiiiiii00002i−2i0000000000
χ2022-2-222-2-22-22-22-2-22−2i2i2-2−2i−2i2i2i-1-1-1-1-1-11111112-2-22-1-1-1-1-1-1111111−2i2i2-2iiiiii−i−i−i−i−i−i0000−2i2i0000000000
χ2122-2-22-1112-2-1-2-111-1002-20000222222-2-2-2-2-2-22-21-1-1-1-1-1-1-111111100-110000000000002-22-200-1-111-110000
χ2222-2-22-1112-2-1-2-111-1002-20000222222-2-2-2-2-2-22-21-1-1-1-1-1-1-111111100-11000000000000-22-220011-1-11-10000
χ2322-2-2-12-2-2-1121-111-12i−2i2-2−i−iii2-1-12-1-1-211-211-11-222-1-12-1-1-2-211112i−2i-112i2i−i−i−i−i−2i−2iiiii0000−ii0000000000
χ2422-2-2-12-2-2-1121-111-12i−2i2-2−i−iii-12-1-12-11-211-21-11-22-12-1-12-111-2-2112i−2i-11−i−i2i2i−i−iii−2i−2iii0000−ii0000000000
χ2522-2-2-12-2-2-1121-111-12i−2i2-2−i−iii-1-12-1-1211-211-2-11-22-1-12-1-121111-2-22i−2i-11−i−i−i−i2i2iiiii−2i−2i0000−ii0000000000
χ2622-2-2-12-2-2-1121-111-1−2i2i2-2ii−i−i2-1-12-1-1-211-211-11-222-1-12-1-1-2-21111−2i2i-11−2i−2iiiii2i2i−i−i−i−i0000i−i0000000000
χ2722-2-2-12-2-2-1121-111-1−2i2i2-2ii−i−i-12-1-12-11-211-21-11-22-12-1-12-111-2-211−2i2i-11ii−2i−2iii−i−i2i2i−i−i0000i−i0000000000
χ2822-2-2-12-2-2-1121-111-1−2i2i2-2ii−i−i-1-12-1-1211-211-2-11-22-1-12-1-121111-2-2−2i2i-11iiii−2i−2i−i−i−i−i2i2i0000i−i0000000000
χ29333333333333333333-1-13333000000000000-1-1-1-1000000000000-1-1-1-100000000000011-1-1-1-1-1-1-1-11111-1-1
χ30333333333333333333-1-13333000000000000-1-1-1-1000000000000-1-1-1-1000000000000-1-111-1-11111-1-1-1-111
χ313333333333333333-3-3-1-1-3-3-3-3000000000000-1-1-1-100000000000011-1-100000000000011-1-111-1-1-1-111-1-111
χ323333333333333333-3-3-1-1-3-3-3-3000000000000-1-1-1-100000000000011-1-1000000000000-1-111111111-1-111-1-1
χ3333-3-333-3-33-33-33-3-333i−3i-113i3i−3i−3i000000000000-111-1000000000000−ii-110000000000001-1-11−ii-1-1111-1i−i−ii
χ3433-3-333-3-33-33-33-3-333i−3i-113i3i−3i−3i000000000000-111-1000000000000−ii-11000000000000-111-1−ii11-1-1-11−iii−i
χ3533-3-333-3-33-33-33-3-33−3i3i-11−3i−3i3i3i000000000000-111-1000000000000i−i-110000000000001-1-11i−i-1-1111-1−iii−i
χ3633-3-333-3-33-33-33-3-33−3i3i-11−3i−3i3i3i000000000000-111-1000000000000i−i-11000000000000-111-1i−i11-1-1-11i−i−ii
χ3744444-2-2-244-24-2-2-2-200440000-2-2-2-2-2-2-2-2-2-2-2-244-2-211111111111100-2-20000000000000000000000000000
χ384444-2-2-2-2-2-2-2-21111004400004-2-24-2-24-2-24-2-2-2-2-2-2-211-211-2-2111100110000000000000000000000000000
χ394444-2-2-2-2-2-2-2-2111100440000-24-2-24-2-24-2-24-2-2-2-2-21-211-2111-2-21100110000000000000000000000000000
χ404444-2-2-2-2-2-2-2-2111100440000-2-24-2-24-2-24-2-24-2-2-2-211-211-21111-2-200110000000000000000000000000000
χ4144-4-44-2224-4-2-4-222-2004-40000-2-2-2-2-2-22222224-42-2111111-1-1-1-1-1-100-220000000000000000000000000000
χ4244-4-4-2-222-22-221-1-11004-400004-2-24-2-2-422-422-222-2-211-21122-1-1-1-1001-10000000000000000000000000000
χ4344-4-4-2-222-22-221-1-11004-40000-24-2-24-22-422-42-222-21-211-21-1-122-1-1001-10000000000000000000000000000
χ4444-4-4-2-222-22-221-1-11004-40000-2-24-2-2422-422-4-222-211-211-2-1-1-1-122001-10000000000000000000000000000
χ454-44-4444-4-44-4-444-4-400000000111-1-1-1-1-1-11110000111-1-1-11-11-11-10000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i30000000000000000
χ464-44-4444-4-44-4-444-4-400000000111-1-1-1-1-1-11110000111-1-1-11-11-11-10000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i30000000000000000
χ474-44-4444-4-44-4-444-4-400000000-2-2-2222222-2-2-20000-2-2-2222-22-22-2200000000000000000000000000000000
χ484-44-44-2-22-442-4-2-22200000000-2-2-2222222-2-2-20000111-1-1-11-11-11-100000000000000000000006−66−6000000
χ494-44-44-2-22-442-4-2-22200000000-2-2-2222222-2-2-20000111-1-1-11-11-11-10000000000000000000000−66−66000000
χ504-44-4-244-42-2-42-2-2220000−2i32i3−2i32i311-2-1-12-1-1211-2000011-2-1-121-11-1-220000−i3i3i3−i300−i3i3i3−i3000000000000000000
χ514-44-4-244-42-2-42-2-2220000−2i32i3−2i32i31-21-12-1-12-11-2100001-21-12-11-1-221-10000i3−i300−i3i3i3−i300−i3i30000000000000000
χ524-44-4-244-42-2-42-2-2220000−2i32i3−2i32i3-2112-1-12-1-1-2110000-2112-1-1-221-11-1000000−i3i3i3−i300−i3i3i3−i30000000000000000
χ534-44-4-244-42-2-42-2-22200002i3−2i32i3−2i311-2-1-12-1-1211-2000011-2-1-121-11-1-220000i3−i3−i3i300i3−i3−i3i3000000000000000000
χ544-44-4-244-42-2-42-2-22200002i3−2i32i3−2i31-21-12-1-12-11-2100001-21-12-11-1-221-10000−i3i300i3−i3−i3i300i3−i30000000000000000
χ554-44-4-244-42-2-42-2-22200002i3−2i32i3−2i3-2112-1-12-1-1-2110000-2112-1-1-221-11-1000000i3−i3−i3i300i3−i3−i3i30000000000000000
χ564-4-4444-44-4-4-444-44-400000000111-1-1-1111-1-1-10000111-1-1-1-11-11-1100003−33−33−3−33−33−330000000000000000
χ574-4-4444-44-4-4-444-44-400000000111-1-1-1111-1-1-10000111-1-1-1-11-11-110000−33−33−333−33−33−30000000000000000
χ584-4-4444-44-4-4-444-44-400000000-2-2-2222-2-2-22220000-2-2-22222-22-22-200000000000000000000000000000000
χ594-4-444-22-2-4-424-22-2200000000-2-2-2222-2-2-22220000111-1-1-1-11-11-1100000000000000000000006−6−66000000
χ604-4-444-22-2-4-424-22-2200000000-2-2-2222-2-2-22220000111-1-1-1-11-11-110000000000000000000000−666−6000000
χ614-4-44-24-4422-4-2-22-22000023−23−232311-2-1-1211-2-1-12000011-2-1-12-11-112-200003−3−3300−333−3000000000000000000
χ624-4-44-24-4422-4-2-22-22000023−23−23231-21-12-11-21-12-100001-21-12-1-112-2-110000−33003−33−300−330000000000000000
χ634-4-44-24-4422-4-2-22-22000023−23−2323-2112-1-1-2112-1-10000-2112-1-12-2-11-110000003−3−3300−333−30000000000000000
χ644-4-44-24-4422-4-2-22-220000−232323−2311-2-1-1211-2-1-12000011-2-1-12-11-112-20000−333−3003−3−33000000000000000000
χ654-4-44-24-4422-4-2-22-220000−232323−231-21-12-11-21-12-100001-21-12-1-112-2-1100003−300−33−33003−30000000000000000
χ664-4-44-24-4422-4-2-22-220000−232323−23-2112-1-1-2112-1-10000-2112-1-12-2-11-11000000−333−3003−3−330000000000000000
χ6766666-3-3-366-36-3-3-3-300-2-20000000000000000-2-211000000000000001100000000000022-2-2001111-1-10000
χ6866666-3-3-366-36-3-3-3-300-2-20000000000000000-2-2110000000000000011000000000000-2-22200-1-1-1-1110000
χ696666-3666-3-36-3-3-3-3-366-2-2-3-3-3-300000000000011-2-2000000000000-2-2110000000000000000110000000000
χ706666-3666-3-36-3-3-3-3-3-6-6-2-2333300000000000011-2-200000000000022110000000000000000-1-10000000000
χ7166-6-66-3336-6-3-6-333-300-220000000000000000-22-11000000000000001-10000000000002-2-220011-1-1-110000
χ7266-6-66-3336-6-3-6-333-300-220000000000000000-22-11000000000000001-1000000000000-222-200-1-1111-10000
χ7366-6-6-36-6-6-3363-333-36i−6i-22−3i−3i3i3i0000000000001-12-2000000000000−2i2i1-10000000000000000i−i0000000000
χ7466-6-6-36-6-6-3363-333-3−6i6i-223i3i−3i−3i0000000000001-12-20000000000002i−2i1-10000000000000000−ii0000000000
χ758-88-88-4-44-884-8-4-44400000000222-2-2-2-2-2-22220000-1-1-1111-11-11-1100000000000000000000000000000000
χ768-88-8-4-4-444-44422-2-20000000022-4-2-24-2-2422-40000-1-1211-2-11-112-200000000000000000000000000000000
χ778-88-8-4-4-444-44422-2-2000000002-42-24-2-24-22-420000-12-11-21-112-2-1100000000000000000000000000000000
χ788-88-8-4-4-444-44422-2-200000000-4224-2-24-2-2-42200002-1-1-2112-2-11-1100000000000000000000000000000000
χ798-8-888-44-4-8-848-44-4400000000222-2-2-2222-2-2-20000-1-1-11111-11-11-100000000000000000000000000000000
χ808-8-88-4-44-4444-42-22-20000000022-4-2-2422-4-2-240000-1-1211-21-11-1-2200000000000000000000000000000000
χ818-8-88-4-44-4444-42-22-2000000002-42-24-22-42-24-20000-12-11-211-1-221-100000000000000000000000000000000
χ828-8-88-4-44-4444-42-22-200000000-4224-2-2-4224-2-200002-1-1-211-221-11-100000000000000000000000000000000
χ8312121212-6-6-6-6-6-6-6-6333300-4-40000000000000000222200000000000000-1-10000000000000000000000000000
χ841212-12-12-6-666-66-663-3-3300-4400000000000000002-2-2200000000000000-110000000000000000000000000000

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