Finite Group Databasebeta

← Group #13167595

Character table — Group #13167595

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122224444444444488888888888888888888181818181818363636363636363636363636363636727272727272727272727272
order122236662336666666633666666666666666666441212121248888121224242424242424242244666612121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ511111111-111-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1
χ611111111-111-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111
χ711111111-111-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-1-1-111111-1-1111-1-1-1-111
χ811111111-111-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-1-1-11111-111-1-1-11111-1-1
χ9222222222222222222222222222222222222222-2-2-2-2-2-2-20000-2-200000000000000000000
χ1022222222-222-2-222222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2200002200000000000000000000
χ112222-1-1-1-1222-1-1222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122222-1-1-1-1-1-1-1-1-1-1000000000000
χ122222-1-1-1-1222-1-1222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-12-2-2-2-2-1-111111111000000000000
χ132222-1-1-1-1222-1-1222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21111-200001133−3−333−3−3000000000000
χ142222-1-1-1-1222-1-1222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21111-2000011−3−333−3−333000000000000
χ152222-1-1-1-1-22211222222-1-1-2-2-2-2-1-1-1-1-1-11111111122-1-1-1-1-222-2-211-1-1-1-11111000000000000
χ162222-1-1-1-1-22211222222-1-1-2-2-2-2-1-1-1-1-1-11111111122-1-1-1-1-2-2-222111111-1-1-1-1000000000000
χ172222-1-1-1-1-22211222222-1-1-2-2-2-2-1-1-1-1-1-111111111-2-2111120000-1-133−3−3−3−333000000000000
χ182222-1-1-1-1-22211222222-1-1-2-2-2-2-1-1-1-1-1-111111111-2-2111120000-1-1−3−33333−3−3000000000000
χ1922-2-22-2-220220022-2-2-2-222000022-2-2-2-2000000002-222-2-20002i−2i0000002i−2i2i−2i000000000000
χ2022-2-22-2-220220022-2-2-2-222000022-2-2-2-2000000002-222-2-2000−2i2i000000−2i2i−2i2i000000000000
χ2122-2-22-2-220220022-2-2-2-222000022-2-2-2-200000000-22-2-22202-200002-22-20000000000000000
χ2222-2-22-2-220220022-2-2-2-222000022-2-2-2-200000000-22-2-2220-220000-22-220000000000000000
χ2322-2-2-111-1022−i3i322-2-2-2-2-1-10000-1-11111−i3−i3−i3−i3i3i3i3i32-2-1-1110002i−2i−i3i33−3−33−ii−ii000000000000
χ2422-2-2-111-1022−i3i322-2-2-2-2-1-10000-1-11111−i3−i3−i3−i3i3i3i3i32-2-1-111000−2i2i−i3i3−333−3i−ii−i000000000000
χ2522-2-2-111-1022−i3i322-2-2-2-2-1-10000-1-11111−i3−i3−i3−i3i3i3i3i3-2211-1-102-200i3−i3-11-11−i3i3i3−i3000000000000
χ2622-2-2-111-1022−i3i322-2-2-2-2-1-10000-1-11111−i3−i3−i3−i3i3i3i3i3-2211-1-10-2200i3−i31-11-1i3−i3−i3i3000000000000
χ2722-2-2-111-1022i3−i322-2-2-2-2-1-10000-1-11111i3i3i3i3−i3−i3−i3−i32-2-1-1110002i−2ii3−i3−333−3−ii−ii000000000000
χ2822-2-2-111-1022i3−i322-2-2-2-2-1-10000-1-11111i3i3i3i3−i3−i3−i3−i32-2-1-111000−2i2ii3−i33−3−33i−ii−i000000000000
χ2922-2-2-111-1022i3−i322-2-2-2-2-1-10000-1-11111i3i3i3i3−i3−i3−i3−i3-2211-1-102-200−i3i3-11-11i3−i3−i3i3000000000000
χ3022-2-2-111-1022i3−i322-2-2-2-2-1-10000-1-11111i3i3i3i3−i3−i3−i3−i3-2211-1-10-2200−i3i31-11-1−i3i3i3−i3000000000000
χ314444444441-2441-21-21-21-211-2-21-211-2-211-2-211-2-2000000000000000000000020200-1-100-1-1
χ324444444441-2441-21-21-21-211-2-21-211-2-211-2-211-2-20000000000000000000000-20-200110011
χ33444444444-2144-21-21-21-21-2-211-21-2-211-2-211-2-2110000000000000000000002020-1-100-1-100
χ34444444444-2144-21-21-21-21-2-211-21-2-211-2-211-2-211000000000000000000000-20-2011001100
χ3544444444-41-2-4-41-21-21-21-2-1-1221-211-2-2-1-122-1-122000000000000000000000020-200-1-10011
χ3644444444-41-2-4-41-21-21-21-2-1-1221-211-2-2-1-122-1-1220000000000000000000000-202001100-1-1
χ3744444444-4-21-4-4-21-21-21-2122-1-1-21-2-21122-1-122-1-100000000000000000000020-20-1-1001100
χ3844444444-4-21-4-4-21-21-21-2122-1-1-21-2-21122-1-122-1-1000000000000000000000-20201100-1-100
χ394-44-444-4-401-200-12-1-2121-23-300-121-12-23-3003-300000000000000000000000000000−i3i300−i3i3
χ404-44-444-4-401-200-12-1-2121-23-300-121-12-23-3003-300000000000000000000000000000i3−i300i3−i3
χ414-44-444-4-401-200-12-1-2121-2-3300-121-12-2-3300-3300000000000000000000000000000−i3i300i3−i3
χ424-44-444-4-401-200-12-1-2121-2-3300-121-12-2-3300-3300000000000000000000000000000i3−i300−i3i3
χ434-44-444-4-404400-4-4-444-4440000-4-44-4-4400000000000000000000000000000000000000000
χ444-44-4-2-22204400-4-4-444-4-2-2000022-222-2000000000023−2323−23000000000000000000000000000
χ454-44-4-2-22204400-4-4-444-4-2-2000022-222-20000000000−2323−2323000000000000000000000000000
χ464-4-444-44-404400-4-44-4-44440000-4-4-444-400000000000000000000000000000000000000000
χ474-4-444-44-40-21002-1-2-121-21003-32-12-21-1003-3003-30000000000000000000000000−i3i300−i3i300
χ484-4-444-44-40-21002-1-2-121-21003-32-12-21-1003-3003-30000000000000000000000000i3−i300i3−i300
χ494-4-444-44-40-21002-1-2-121-2100-332-12-21-100-3300-330000000000000000000000000−i3i300i3−i300
χ504-4-444-44-40-21002-1-2-121-2100-332-12-21-100-3300-330000000000000000000000000i3−i300−i3i300
χ514-4-44-22-2204400-4-44-4-44-2-20000222-2-22000000000023−23−2323000000000000000000000000000
χ524-4-44-22-2204400-4-44-4-44-2-20000222-2-220000000000−232323−23000000000000000000000000000
χ538888-4-4-4-482-4-4-42-42-42-4-1222-4-4-12-1-122-1-122-1-122000000000000000000000000000000000
χ548888-4-4-4-48-42-4-4-42-42-422-1-4-4222-122-1-122-1-122-1-1000000000000000000000000000000000
χ558888-4-4-4-4-82-4442-42-42-4-12-2-244-12-1-12211-2-211-2-2000000000000000000000000000000000
χ568888-4-4-4-4-8-4244-42-42-422-144-2-22-122-1-1-2-211-2-211000000000000000000000000000000000
χ5788-8-88-8-8802-4002-4-24-242-400002-4-2-24400000000000000000000000000000000000000000
χ5888-8-88-8-880-4200-424-24-2-420000-4244-2-200000000000000000000000000000000000000000
χ5988-8-8-444-402-4−4i34i32-4-24-24-120000-1211-2-2−i3−i32i32i3i3i3−2i3−2i3000000000000000000000000000000000
χ6088-8-8-444-402-44i3−4i32-4-24-24-120000-1211-2-2i3i3−2i3−2i3−i3−i32i32i3000000000000000000000000000000000
χ6188-8-8-444-40-42−4i34i3-424-24-22-100002-1-2-2112i32i3−i3−i3−2i3−2i3i3i3000000000000000000000000000000000
χ6288-8-8-444-40-424i3−4i3-424-24-22-100002-1-2-211−2i3−2i3i3i32i32i3−i3−i3000000000000000000000000000000000
χ638-88-888-8-80-42004-242-4-2-4200004-2-44-2200000000000000000000000000000000000000000
χ648-88-8-4-44402-400-24-2-424-126-6001-2-11-22-3300-3300000000000000000000000000000000000
χ658-88-8-4-44402-400-24-2-424-12-66001-2-11-223-3003-300000000000000000000000000000000000
χ668-88-8-4-4440-42004-242-4-22-10000-212-21-100−3i33i3003i3−3i3000000000000000000000000000000000
χ678-88-8-4-4440-42004-242-4-22-10000-212-21-1003i3−3i300−3i33i3000000000000000000000000000000000
χ688-8-888-88-802-400-2424-2-42-40000-24-22-4400000000000000000000000000000000000000000
χ698-8-88-44-4402-400-2424-2-4-1200001-21-12-2−3i33i3003i3−3i300000000000000000000000000000000000
χ708-8-88-44-4402-400-2424-2-4-1200001-21-12-23i3−3i300−3i33i300000000000000000000000000000000000
χ718-8-88-44-440-42004-2-4-2422-1006-6-21-22-1100-3300-33000000000000000000000000000000000
χ728-8-88-44-440-42004-2-4-2422-100-66-21-22-11003-3003-3000000000000000000000000000000000

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