Finite Group Databasebeta

← Group #13166547

Character table — Group #13166547

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112444448888889918181818183636362248888816161616161618183636363636727272336121212121224242424242427275454545454108108108
order1243346612121212121244244442883612331266121212121212121261212121262424224664661212121212124424444288
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111-1-1-1-11-1-111111111111111111-1-1-1-11-1-111111111111111111-1-1-1-11-1-1
χ311111111111111-1-1-1ii−i−i-1i−i11111111111111-1-1-1ii−i−i-1i−i11111111111111-1-1-1ii−i−i-1i−i
χ411111111111111-1-1-1−i−iii-1−ii11111111111111-1-1-1−i−iii-1−ii11111111111111-1-1-1−i−iii-1−ii
χ511111-11111-1-1-1-11111111-1-1-111111-11111-1-1-1-11111111-1-1-111111-11111-1-1-1-11111111-1-1-1
χ611111-11111-1-1-1-1111-1-1-1-1-11111111-11111-1-1-1-1111-1-1-1-1-11111111-11111-1-1-1-1111-1-1-1-1-111
χ711111-11111-1-1-1-1-1-1-1ii−i−i1−ii11111-11111-1-1-1-1-1-1-1ii−i−i1−ii11111-11111-1-1-1-1-1-1-1ii−i−i1−ii
χ811111-11111-1-1-1-1-1-1-1−i−iii1i−i11111-11111-1-1-1-1-1-1-1−i−iii1i−i11111-11111-1-1-1-1-1-1-1−i−iii1i−i
χ922-222022-2-2000022-2000000022-222022-2-2000022-2000000022-222022-2-2000022-20000000
χ1022-222022-2-20000-2-22000000022-222022-2-20000-2-22000000022-222022-2-20000-2-220000000
χ112-20220-2-20000002i−2i01+i−1−i1−i−1+i0002-20220-2-20000002i−2i01+i−1−i1−i−1+i0002-20220-2-20000002i−2i01+i−1−i1−i−1+i000
χ122-20220-2-20000002i−2i0−1−i1+i−1+i1−i0002-20220-2-20000002i−2i0−1−i1+i−1+i1−i0002-20220-2-20000002i−2i0−1−i1+i−1+i1−i000
χ132-20220-2-2000000−2i2i01−i−1+i1+i−1−i0002-20220-2-2000000−2i2i01−i−1+i1+i−1−i0002-20220-2-2000000−2i2i01−i−1+i1+i−1−i000
χ142-20220-2-2000000−2i2i0−1+i1−i−1−i1+i0002-20220-2-2000000−2i2i0−1+i1−i−1−i1+i0002-20220-2-2000000−2i2i0−1+i1−i−1−i1+i000
χ154441-241-21-211-2-200000000004441-241-21-211-2-200000000004441-241-21-211-2-20000000000
χ164441-2-41-21-2-1-12200000000004441-2-41-21-2-1-12200000000004441-2-41-21-2-1-1220000000000
χ17444-214-21-21-2-2110000000000444-214-21-21-2-2110000000000444-214-21-21-2-2110000000000
χ18444-21-4-21-2122-1-10000000000444-21-4-21-2122-1-10000000000444-21-4-21-2122-1-10000000000
χ1944-41-201-2-123-300000000000044-41-201-2-123-300000000000044-41-201-2-123-3000000000000
χ2044-41-201-2-12-3300000000000044-41-201-2-12-3300000000000044-41-201-2-12-33000000000000
χ2144-4-210-212-1003-3000000000044-4-210-212-1003-3000000000044-4-210-212-1003-30000000000
χ2244-4-210-212-100-33000000000044-4-210-212-100-33000000000044-4-210-212-100-330000000000
χ238-802-40-2400000000000000008-802-40-2400000000000000008-802-40-240000000000000000
χ248-80-4204-200000000000000008-80-4204-200000000000000008-80-4204-20000000000000000
χ25111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ2611111111111111111-1-1-1-11-1-111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111
χ2711111111111111-1-1-1ii−i−i-1i−i11111111111111-1-1-1ii−i−i-1i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1111−i−iii1−ii
χ2811111111111111-1-1-1−i−iii-1−ii11111111111111-1-1-1−i−iii-1−ii-1-1-1-1-1-1-1-1-1-1-1-1-1-1111ii−i−i1i−i
χ2911111-11111-1-1-1-11111111-1-1-111111-11111-1-1-1-11111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1111
χ3011111-11111-1-1-1-1111-1-1-1-1-11111111-11111-1-1-1-1111-1-1-1-1-111-1-1-1-1-11-1-1-1-11111-1-1-111111-1-1
χ3111111-11111-1-1-1-1-1-1-1ii−i−i1−ii11111-11111-1-1-1-1-1-1-1ii−i−i1−ii-1-1-1-1-11-1-1-1-11111111−i−iii-1i−i
χ3211111-11111-1-1-1-1-1-1-1−i−iii1i−i11111-11111-1-1-1-1-1-1-1−i−iii1i−i-1-1-1-1-11-1-1-1-11111111ii−i−i-1−ii
χ3322-222022-2-2000022-2000000022-222022-2-2000022-20000000-2-22-2-20-2-2220000-2-220000000
χ3422-222022-2-20000-2-22000000022-222022-2-20000-2-220000000-2-22-2-20-2-222000022-20000000
χ352-20220-2-20000002i−2i01+i−1−i1−i−1+i0002-20220-2-20000002i−2i01+i−1−i1−i−1+i000-220-2-2022000000−2i2i0−1−i1+i−1+i1−i000
χ362-20220-2-20000002i−2i0−1−i1+i−1+i1−i0002-20220-2-20000002i−2i0−1−i1+i−1+i1−i000-220-2-2022000000−2i2i01+i−1−i1−i−1+i000
χ372-20220-2-2000000−2i2i01−i−1+i1+i−1−i0002-20220-2-2000000−2i2i01−i−1+i1+i−1−i000-220-2-20220000002i−2i0−1+i1−i−1−i1+i000
χ382-20220-2-2000000−2i2i0−1+i1−i−1−i1+i0002-20220-2-2000000−2i2i0−1+i1−i−1−i1+i000-220-2-20220000002i−2i01−i−1+i1+i−1−i000
χ394441-241-21-211-2-200000000004441-241-21-211-2-20000000000-4-4-4-12-4-12-12-1-1220000000000
χ404441-2-41-21-2-1-12200000000004441-2-41-21-2-1-1220000000000-4-4-4-124-12-1211-2-20000000000
χ41444-214-21-21-2-2110000000000444-214-21-21-2-2110000000000-4-4-42-1-42-12-122-1-10000000000
χ42444-21-4-21-2122-1-10000000000444-21-4-21-2122-1-10000000000-4-4-42-142-12-1-2-2110000000000
χ4344-41-201-2-123-300000000000044-41-201-2-123-3000000000000-4-44-120-121-2-33000000000000
χ4444-41-201-2-12-3300000000000044-41-201-2-12-33000000000000-4-44-120-121-23-3000000000000
χ4544-4-210-212-1003-3000000000044-4-210-212-1003-30000000000-4-442-102-1-2100-330000000000
χ4644-4-210-212-100-33000000000044-4-210-212-100-330000000000-4-442-102-1-21003-30000000000
χ478-802-40-2400000000000000008-802-40-240000000000000000-880-2402-40000000000000000
χ488-80-4204-200000000000000008-80-4204-20000000000000000-8804-20-420000000000000000
χ49222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ5022222222222222222-2-2-2-22-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111000000000000000000000000
χ5122222222222222-2-2-22i2i−2i−2i-22i−2i-1-1-1-1-1-1-1-1-1-1-1-1-1-1111−i−iii1−ii000000000000000000000000
χ5222222222222222-2-2-2−2i−2i2i2i-2−2i2i-1-1-1-1-1-1-1-1-1-1-1-1-1-1111ii−i−i1i−i000000000000000000000000
χ5322222-22222-2-2-2-22222222-2-2-2-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1111000000000000000000000000
χ5422222-22222-2-2-2-2222-2-2-2-2-222-1-1-1-1-11-1-1-1-11111-1-1-111111-1-1000000000000000000000000
χ5522222-22222-2-2-2-2-2-2-22i2i−2i−2i2−2i2i-1-1-1-1-11-1-1-1-11111111−i−iii-1i−i000000000000000000000000
χ5622222-22222-2-2-2-2-2-2-2−2i−2i2i2i22i−2i-1-1-1-1-11-1-1-1-11111111ii−i−i-1−ii000000000000000000000000
χ5744-444044-4-4000044-40000000-2-22-2-20-2-2220000-2-220000000000000000000000000000000
χ5844-444044-4-40000-4-440000000-2-22-2-20-2-222000022-20000000000000000000000000000000
χ594-40440-4-40000004i−4i02+2i−2−2i2−2i−2+2i000-220-2-2022000000−2i2i0−1−i1+i−1+i1−i000000000000000000000000000
χ604-40440-4-40000004i−4i0−2−2i2+2i−2+2i2−2i000-220-2-2022000000−2i2i01+i−1−i1−i−1+i000000000000000000000000000
χ614-40440-4-4000000−4i4i02−2i−2+2i2+2i−2−2i000-220-2-20220000002i−2i0−1+i1−i−1−i1+i000000000000000000000000000
χ624-40440-4-4000000−4i4i0−2+2i2−2i−2−2i2+2i000-220-2-20220000002i−2i01−i−1+i1+i−1−i000000000000000000000000000
χ638882-482-42-422-4-40000000000-4-4-4-12-4-12-12-1-1220000000000000000000000000000000000
χ648882-4-82-42-4-2-2440000000000-4-4-4-124-12-1211-2-20000000000000000000000000000000000
χ65888-428-42-42-4-4220000000000-4-4-42-1-42-12-122-1-10000000000000000000000000000000000
χ66888-42-8-42-4244-2-20000000000-4-4-42-142-12-1-2-2110000000000000000000000000000000000
χ6788-82-402-4-246-6000000000000-4-44-120-121-2-33000000000000000000000000000000000000
χ6888-82-402-4-24-66000000000000-4-44-120-121-23-3000000000000000000000000000000000000
χ6988-8-420-424-2006-60000000000-4-442-102-1-2100-330000000000000000000000000000000000
χ7088-8-420-424-200-660000000000-4-442-102-1-21003-30000000000000000000000000000000000
χ7116-1604-80-480000000000000000-880-2402-40000000000000000000000000000000000000000
χ7216-160-8408-40000000000000000-8804-20-420000000000000000000000000000000000000000

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