Finite Group Databasebeta

← Group #13166022

Character table — Group #13166022

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222224444666666668888888888881212121216161616161616161616161618182424242424242424242424242424363636363636363636367272108108108108
order122233666666366644441212121233366666666612121212333666666666441212121212121212121212121212448812122424242412124488
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
χ51-1-1111-111-1-1-11-1-11i−i-11ii−i−i111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1i−i1-1iiiiii−i−i−i−i−i−ii−ii−ii−iii−i−ii−i1-11-1
χ61-1-1111-111-1-1-11-1-11i−i-11ii−i−i111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1i−i1-1iiiiii−i−i−i−i−i−i−ii−iii−i−i−iii−ii-11-11
χ71-1-1111-111-1-1-11-1-11−ii-11−i−iii111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1−ii1-1−i−i−i−i−i−iiiiiiii−ii−i−iiii−i−ii−i-11-11
χ81-1-1111-111-1-1-11-1-11−ii-11−i−iii111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1−ii1-1−i−i−i−i−i−iiiiiii−ii−ii−ii−i−iii−ii1-11-1
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
χ1122222-122-1-1-12-1-1-1-12222-1-1-1-12-1-12-1-12-1-12-1-12-1-122-1-12-1-122-1-1-1-122-1-122-1-1-1-122-1-1-1-10000-1-10000000000
χ1222222-122-1-1-12-1-1-1-12222-1-1-1-1-12-1-12-1-12-1-12-12-1-12-12-1-12-1-1-122-1-122-1-1-1-122-1-1-1-122-1-10000-1-10000000000
χ1322222-122-1-1-12-1-1-1-12222-1-1-1-1-1-12-1-12-1-12-1-122-1-12-1-12-1-12-1-1-1-12222-1-1-1-1-1-122-1-1-1-1220000-1-10000000000
χ1422222-122-1-1-12-1-1-1-1-2-22211112-1-12-1-12-1-12-1-12-1-122-1-12-1-122-1-1-1-1-2-2-1-1-2-21111-2-211110000110000000000
χ1522222-122-1-1-12-1-1-1-1-2-2221111-12-1-12-1-12-1-12-12-1-12-12-1-12-1-1-122-1-1-2-2-1-111-2-21111-2-2110000110000000000
χ1622222-122-1-1-12-1-1-1-1-2-2221111-1-12-1-12-1-12-1-122-1-12-1-12-1-12-1-1-1-122-2-2-1-11111-2-21111-2-20000110000000000
χ172222-12-1-1222-1-1-1-1-100220000222222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-100-1-1000000000000222200-1-1-1-1-1-10000
χ182222-12-1-1222-1-1-1-1-100220000222222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-100-1-1000000000000-2-2-2-2001111110000
χ192-2-2222-222-2-2-22-2-222i−2i-222i2i−2i−2i-1-1-1-1-1-111111122-2-2-1-1-1-1-1-11111112i−2i2-2−i−i−i−i−i−iiiiiii00002i−2i0000000000
χ202-2-2222-222-2-2-22-2-22−2i2i-22−2i−2i2i2i-1-1-1-1-1-111111122-2-2-1-1-1-1-1-1111111−2i2i2-2iiiiii−i−i−i−i−i−i0000−2i2i0000000000
χ212-2-222-1-22-111-2-111-12i−2i-22−i−iii2-1-12-1-1-211-2112-11-22-1-12-1-1-2-211112i−2i-112i2i−i−i−i−i−2i−2iiiii0000−ii0000000000
χ222-2-222-1-22-111-2-111-12i−2i-22−i−iii-12-1-12-11-211-212-11-2-12-1-12-111-2-2112i−2i-11−i−i2i2i−i−iii−2i−2iii0000−ii0000000000
χ232-2-222-1-22-111-2-111-12i−2i-22−i−iii-1-12-1-1211-211-22-11-2-1-12-1-121111-2-22i−2i-11−i−i−i−i2i2iiiii−2i−2i0000−ii0000000000
χ242-2-222-1-22-111-2-111-1−2i2i-22ii−i−i2-1-12-1-1-211-2112-11-22-1-12-1-1-2-21111−2i2i-11−2i−2iiiii2i2i−i−i−i−i0000i−i0000000000
χ252-2-222-1-22-111-2-111-1−2i2i-22ii−i−i-12-1-12-11-211-212-11-2-12-1-12-111-2-211−2i2i-11ii−2i−2iii−i−i2i2i−i−i0000i−i0000000000
χ262-2-222-1-22-111-2-111-1−2i2i-22ii−i−i-1-12-1-1211-211-22-11-2-1-12-1-121111-2-2−2i2i-11iiii−2i−2i−i−i−i−i2i2i0000i−i0000000000
χ272-2-22-121-12-2-21-111-100-220000222222-2-2-2-2-2-2-12-21-1-1-1-1-1-111111100-110000000000002i−2i2i−2i00−i−iii−ii0000
χ282-2-22-121-12-2-21-111-100-220000222222-2-2-2-2-2-2-12-21-1-1-1-1-1-111111100-11000000000000−2i2i−2i2i00ii−i−ii−i0000
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
χ333-3-3333-333-3-3-33-3-333i−3i1-13i3i−3i−3i000000000000-1-111000000000000−ii-11000000000000i−i−ii−ii−i−iiii−i1-1-11
χ343-3-3333-333-3-3-33-3-333i−3i1-13i3i−3i−3i000000000000-1-111000000000000−ii-11000000000000−iii−i−iiii−i−i−ii-111-1
χ353-3-3333-333-3-3-33-3-33−3i3i1-1−3i−3i3i3i000000000000-1-111000000000000i−i-11000000000000i−i−iii−i−i−iiii−i-111-1
χ363-3-3333-333-3-3-33-3-33−3i3i1-1−3i−3i3i3i000000000000-1-111000000000000i−i-11000000000000−iii−ii−iii−i−i−ii1-1-11
χ374444-24-2-2444-2-2-2-2-200440000-2-2-2-2-2-2-2-2-2-2-2-2-244-211111111111100-2-20000000000000000000000000000
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
χ4144-4-4444-4-4-44-444-4-400000000111-1-1-1111-1-1-10000111-1-1-11-11-11-100003−33−33−33−33−33−30000000000000000
χ4244-4-4444-4-4-44-444-4-400000000111-1-1-1111-1-1-10000111-1-1-11-11-11-10000−33−33−33−33−33−330000000000000000
χ4344-4-4444-4-4-44-444-4-400000000-2-2-2222-2-2-22220000-2-2-2222-22-22-2200000000000000000000000000000000
χ4444-4-44-24-422-2-4-2-222000023−2323−2311-2-1-1211-2-1-12000011-2-1-121-11-1-2200003−3−33003−3−33000000000000000000
χ4544-4-44-24-422-2-4-2-222000023−2323−231-21-12-11-21-12-100001-21-12-11-1-221-10000−33003−3−33003−30000000000000000
χ4644-4-44-24-422-2-4-2-222000023−2323−23-2112-1-1-2112-1-10000-2112-1-1-221-11-10000003−3−33003−3−330000000000000000
χ4744-4-44-24-422-2-4-2-2220000−2323−232311-2-1-1211-2-1-12000011-2-1-121-11-1-220000−333−300−333−3000000000000000000
χ4844-4-44-24-422-2-4-2-2220000−2323−23231-21-12-11-21-12-100001-21-12-11-1-221-100003−300−333−300−330000000000000000
χ4944-4-44-24-422-2-4-2-2220000−2323−2323-2112-1-1-2112-1-10000-2112-1-1-221-11-1000000−333−300−333−30000000000000000
χ5044-4-4-24-22-4-442-2-22200000000-2-2-2222-2-2-22220000111-1-1-11-11-11-10000000000000000000000i6−i6i6−i6000000
χ5144-4-4-24-22-4-442-2-22200000000-2-2-2222-2-2-22220000111-1-1-11-11-11-10000000000000000000000−i6i6−i6i6000000
χ524-44-444-4-4-44-444-44-400000000111-1-1-1-1-1-11110000111-1-1-1-11-11-110000−i3i3−i3i3−i3i3i3−i3i3−i3i3−i30000000000000000
χ534-44-444-4-4-44-444-44-400000000111-1-1-1-1-1-11110000111-1-1-1-11-11-110000i3−i3i3−i3i3−i3−i3i3−i3i3−i3i30000000000000000
χ544-44-444-4-4-44-444-44-400000000-2-2-2222222-2-2-20000-2-2-22222-22-22-200000000000000000000000000000000
χ554-44-44-2-4-42-224-22-220000−2i32i32i3−2i311-2-1-12-1-1211-2000011-2-1-12-11-112-20000−i3i3i3−i300i3−i3−i3i3000000000000000000
χ564-44-44-2-4-42-224-22-220000−2i32i32i3−2i31-21-12-1-12-11-2100001-21-12-1-112-2-110000i3−i300−i3i3−i3i300i3−i30000000000000000
χ574-44-44-2-4-42-224-22-220000−2i32i32i3−2i3-2112-1-12-1-1-2110000-2112-1-12-2-11-11000000−i3i3i3−i300i3−i3−i3i30000000000000000
χ584-44-44-2-4-42-224-22-2200002i3−2i3−2i32i311-2-1-12-1-1211-2000011-2-1-12-11-112-20000i3−i3−i3i300−i3i3i3−i3000000000000000000
χ594-44-44-2-4-42-224-22-2200002i3−2i3−2i32i31-21-12-1-12-11-2100001-21-12-1-112-2-110000−i3i300i3−i3i3−i300−i3i30000000000000000
χ604-44-44-2-4-42-224-22-2200002i3−2i3−2i32i3-2112-1-12-1-1-2110000-2112-1-12-2-11-11000000i3−i3−i3i300−i3i3i3−i30000000000000000
χ614-44-4-2422-44-4-2-22-2200000000-2-2-2222222-2-2-20000111-1-1-1-11-11-1100000000000000000000006−6−66000000
χ624-44-4-2422-44-4-2-22-2200000000-2-2-2222222-2-2-20000111-1-1-1-11-11-110000000000000000000000−666−6000000
χ634-4-44-242-24-4-42-222-200-440000-2-2-2-2-2-2222222-24-42111111-1-1-1-1-1-100-220000000000000000000000000000
χ644-4-44-2-22-2-22221-1-1100-4400004-2-24-2-2-422-422-2-222-211-21122-1-1-1-1001-10000000000000000000000000000
χ654-4-44-2-22-2-22221-1-1100-440000-24-2-24-22-422-42-2-2221-211-21-1-122-1-1001-10000000000000000000000000000
χ664-4-44-2-22-2-22221-1-1100-440000-2-24-2-2422-422-4-2-22211-211-2-1-1-1-122001-10000000000000000000000000000
χ6766666-366-3-3-36-3-3-3-366-2-2-3-3-3-3000000000000-211-2000000000000-2-2110000000000000000110000000000
χ6866666-366-3-3-36-3-3-3-3-6-6-2-23333000000000000-211-200000000000022110000000000000000-1-10000000000
χ696666-36-3-3666-3-3-3-3-300-2-200000000000000001-2-21000000000000001100000000000022-2-2001111-1-10000
χ706666-36-3-3666-3-3-3-3-300-2-200000000000000001-2-210000000000000011000000000000-2-22200-1-1-1-1110000
χ716-6-666-3-66-333-6-333-36i−6i2-2−3i−3i3i3i000000000000-21-12000000000000−2i2i1-10000000000000000i−i0000000000
χ726-6-666-3-66-333-6-333-3−6i6i2-23i3i−3i−3i000000000000-21-120000000000002i−2i1-10000000000000000−ii0000000000
χ736-6-66-363-36-6-63-333-3002-200000000000000001-22-1000000000000001-10000000000002i−2i−2i2i00ii−i−i−ii0000
χ746-6-66-363-36-6-63-333-3002-200000000000000001-22-1000000000000001-1000000000000−2i2i2i−2i00−i−iiii−i0000
χ7588-8-8-48-44-8-884-4-44400000000222-2-2-2222-2-2-20000-1-1-1111-11-11-1100000000000000000000000000000000
χ7688-8-8-4-4-4444-4422-2-20000000022-4-2-2422-4-2-240000-1-1211-2-11-112-200000000000000000000000000000000
χ7788-8-8-4-4-4444-4422-2-2000000002-42-24-22-42-24-20000-12-11-21-112-2-1100000000000000000000000000000000
χ7888-8-8-4-4-4444-4422-2-200000000-4224-2-2-4224-2-200002-1-1-2112-2-11-1100000000000000000000000000000000
χ798-88-8-4844-88-8-4-44-4400000000222-2-2-2-2-2-22220000-1-1-11111-11-11-100000000000000000000000000000000
χ808-88-8-4-4444-44-42-22-20000000022-4-2-24-2-2422-40000-1-1211-21-11-1-2200000000000000000000000000000000
χ818-88-8-4-4444-44-42-22-2000000002-42-24-2-24-22-420000-12-11-211-1-221-100000000000000000000000000000000
χ828-88-8-4-4444-44-42-22-200000000-4224-2-24-2-2-42200002-1-1-211-221-11-100000000000000000000000000000000
χ8312121212-6-6-6-6-6-6-6-6333300-4-40000000000000000222200000000000000-1-10000000000000000000000000000
χ8412-12-1212-6-66-6-66663-3-33004-4000000000000000022-2-200000000000000-110000000000000000000000000000

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