Finite Group Databasebeta

← Group #13167517

Character table — Group #13167517

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122224444444444488888888888888888888181818181818363636363636363636363636363636727272727272727272727272
order1222366633466666612123366666612121212121212121212121244121212124888812122424242424242424244466121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ51111111111-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1-11111-1-1-1-11-11-111-1-111-1-1
χ61111111111-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111
χ71111111111-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-1-1-111111-1-1111-1-1-1-111
χ81111111111-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-1-1-11111-111-1-1-11111-1-1
χ9222222222222222222222222222222222222222-2-2-2-2-2-2-20000-2-200000000000000000000
χ102222222222-2222222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2200002200000000000000000000
χ112222-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-122222-1-1-1-1-1-1-1-1-1-1000000000000
χ122222-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-12-2-2-2-2-1-111111111000000000000
χ132222-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-21111-200001133−3−333−3−3000000000000
χ142222-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-21111-2000011−3−333−3−333000000000000
χ152222-1-1-1-122-222222211-1-1-1-1-1-1-1-1-2-2-2-21111111122-1-1-1-1-222-2-211-1-1-1-11111000000000000
χ162222-1-1-1-122-222222211-1-1-1-1-1-1-1-1-2-2-2-21111111122-1-1-1-1-2-2-222111111-1-1-1-1000000000000
χ172222-1-1-1-122-222222211-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2111120000-1-133−3−3−3−333000000000000
χ182222-1-1-1-122-222222211-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2111120000-1-1−3−33333−3−3000000000000
χ192-2-222-22-2220-2-2-2-222002222-2-2-2-20000000000002-222-2-20002-20000002-22-2000000000000
χ202-2-222-22-2220-2-2-2-222002222-2-2-2-20000000000002-222-2-2000-22000000-22-22000000000000
χ212-2-222-22-2220-2-2-2-222002222-2-2-2-2000000000000-22-2-22202-200002-22-20000000000000000
χ222-2-222-22-2220-2-2-2-222002222-2-2-2-2000000000000-22-2-2220-220000-22-220000000000000000
χ232-2-22-11-11220-2-2-2-2223−3-1-1-1-1111100003333−3−3−3−32-2-1-1110002-23−33−3−33-11-11000000000000
χ242-2-22-11-11220-2-2-2-2223−3-1-1-1-1111100003333−3−3−3−32-2-1-111000-223−3−333−31-11-1000000000000
χ252-2-22-11-11220-2-2-2-2223−3-1-1-1-1111100003333−3−3−3−3-2211-1-102-200−33-11-11−333−3000000000000
χ262-2-22-11-11220-2-2-2-2223−3-1-1-1-1111100003333−3−3−3−3-2211-1-10-2200−331-11-13−3−33000000000000
χ272-2-22-11-11220-2-2-2-222−33-1-1-1-111110000−3−3−3−333332-2-1-1110002-2−33−333−3-11-11000000000000
χ282-2-22-11-11220-2-2-2-222−33-1-1-1-111110000−3−3−3−333332-2-1-111000-22−333−3−331-11-1000000000000
χ292-2-22-11-11220-2-2-2-222−33-1-1-1-111110000−3−3−3−33333-2211-1-102-2003−3-11-113−3−33000000000000
χ302-2-22-11-11220-2-2-2-222−33-1-1-1-111110000−3−3−3−33333-2211-1-10-22003−31-11-1−333−3000000000000
χ31444444441-241-21-2-21441-21-21-21-211-2-211-2-211-2-200000000000000000000000220000-1-1-1-1
χ32444444441-241-21-2-21441-21-21-21-211-2-211-2-211-2-200000000000000000000000-2-200001111
χ33444444441-2-41-21-2-21-4-41-21-21-21-2-1-122-1-122-1-122000000000000000000000002-20000-1-111
χ34444444441-2-41-21-2-21-4-41-21-21-21-2-1-122-1-122-1-12200000000000000000000000-22000011-1-1
χ3544444444-214-21-211-244-21-21-21-21-2-211-2-211-2-2110000000000000000000002200-1-1-1-10000
χ3644444444-214-21-211-244-21-21-21-21-2-211-2-211-2-211000000000000000000000-2-20011110000
χ3744444444-21-4-21-211-2-4-4-21-21-21-2122-1-122-1-122-1-10000000000000000000002-200-1-1110000
χ3844444444-21-4-21-211-2-4-4-21-21-21-2122-1-122-1-122-1-1000000000000000000000-220011-1-10000
χ3944-4-444-4-41-20-121-22-1001-2-12-121-23-3003-3003-300000000000000000000000000000003−33−3
χ4044-4-444-4-41-20-121-22-1001-2-12-121-23-3003-3003-30000000000000000000000000000000−33−33
χ4144-4-444-4-41-20-121-22-1001-2-12-121-2-3300-3300-3300000000000000000000000000000003−3−33
χ4244-4-444-4-41-20-121-22-1001-2-12-121-2-3300-3300-330000000000000000000000000000000−333−3
χ4344-4-444-4-4440-4-444-4-40044-4-4-4-444000000000000000000000000000000000000000000000
χ4444-4-4-2-222440-4-444-4-400-2-22222-2-20000000000000023−2323−23000000000000000000000000000
χ4544-4-4-2-222440-4-444-4-400-2-22222-2-200000000000000−2323−2323000000000000000000000000000
χ464-44-44-4-4444044-4-4-4-40044-4-444-4-4000000000000000000000000000000000000000000000
χ474-44-44-4-44-210-212-1-1200-212-1-212-1003i−3i003i−3i003i−3i0000000000000000000000000−i3i33−30000
χ484-44-44-4-44-210-212-1-1200-212-1-212-1003i−3i003i−3i003i−3i0000000000000000000000000i3−i3−330000
χ494-44-44-4-44-210-212-1-1200-212-1-212-100−3i3i00−3i3i00−3i3i0000000000000000000000000−i3i3−330000
χ504-44-44-4-44-210-212-1-1200-212-1-212-100−3i3i00−3i3i00−3i3i0000000000000000000000000i3−i33−30000
χ514-44-4-222-244044-4-4-4-400-2-222-2-2220000000000000023−23−2323000000000000000000000000000
χ524-44-4-222-244044-4-4-4-400-2-222-2-22200000000000000−232323−23000000000000000000000000000
χ538888-4-4-4-42-482-42-4-42-4-4-12-12-12-1222-4-4-1-122-1-122000000000000000000000000000000000
χ548888-4-4-4-42-4-82-42-4-4244-12-12-12-12-2-24411-2-211-2-2000000000000000000000000000000000
χ558888-4-4-4-4-428-42-422-4-4-42-12-12-12-1-4-42222-1-122-1-1000000000000000000000000000000000
χ568888-4-4-4-4-42-8-42-422-4442-12-12-12-144-2-2-2-211-2-211000000000000000000000000000000000
χ5788-8-888-8-8-4204-2-42-2400-424-24-2-42000000000000000000000000000000000000000000000
χ5888-8-8-4-4442-40-242-44-200-121-21-2-126-600-3300-3300000000000000000000000000000000000
χ5988-8-8-4-4442-40-242-44-200-121-21-2-12-66003-3003-300000000000000000000000000000000000
χ6088-8-8-4-444-4204-2-42-24002-1-21-212-1000000−3i33i3003i3−3i3000000000000000000000000000000000
χ6188-8-8-4-444-4204-2-42-24002-1-21-212-10000003i3−3i300−3i33i3000000000000000000000000000000000
χ628-88-88-8-882-402-4-244-2002-4-242-4-24000000000000000000000000000000000000000000000
χ638-88-8-444-42-402-4-244-200-121-2-121-2000033−3300−333300000000000000000000000000000000000
χ648-88-8-444-42-402-4-244-200-121-2-121-20000−33330033−3300000000000000000000000000000000000
χ658-88-8-444-4-420-424-2-24002-1-212-1-21006i−6i00−3i3i00−3i3i000000000000000000000000000000000
χ668-88-8-444-4-420-424-2-24002-1-212-1-2100−6i6i003i−3i003i−3i000000000000000000000000000000000
χ678-8-888-88-82-40-24-24-42002-42-4-24-24000000000000000000000000000000000000000000000
χ688-8-888-88-8-4204-24-22-400-42-424-24-2000000000000000000000000000000000000000000000
χ698-8-88-44-442-40-24-24-4243−43-12-121-21-2000033−23−23−3−32323000000000000000000000000000000000
χ708-8-88-44-442-40-24-24-42−4343-12-121-21-20000−3−3232333−23−23000000000000000000000000000000000
χ718-8-88-44-44-4204-24-22-443−432-12-1-21-210000−23−23332323−3−3000000000000000000000000000000000
χ728-8-88-44-44-4204-24-22-4−43432-12-1-21-2100002323−3−3−23−2333000000000000000000000000000000000

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