Finite Group Databasebeta

← Group #13165523

Character table — Group #13165523

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122224444444466888888881212121212121212121212121818242424242424242424242424242424243636363636363636363636363636363654547272108108
order122236663366666644336666662222666612121212446666666666666612124444881212121212122424242444121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1
χ311111111111111111111111111-1-111-1-1-1-1111111-1-11111-1-1-1-1111111-1-111-1-11-1-1-1-11-1-1-1-11111-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-1-1-11111111-1-111
χ51111111111111111-1-11111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1
χ61111111111111111-1-11111111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11-1-1-1-11-1-1-1-1-1-11111
χ71111111111111111-1-111111111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ81111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1
χ911-1-11-1-111111-1-1-1-1i−i1111-1-1-1-11-11-111-1-1ii−i−i1-11-11-11-111-1-111-1-1i−ii−ii−i1-1-1ii−i−i111-1-1i−ii−ii−i
χ1011-1-11-1-111111-1-1-1-1i−i1111-1-1-1-11-1-1111-1-1ii−i−i1-11-1-11-1111-1-1-1-111i−ii−i−ii-11-1ii−i−i1-1-111i−i−ii−ii
χ1111-1-11-1-111111-1-1-1-1i−i1111-1-1-1-1-111-1-1-111ii−i−i1-1-111-11-1-1-11111-1-1i−i−iii−i-11-1−i−iii1-1-111i−ii−i−ii
χ1211-1-11-1-111111-1-1-1-1i−i1111-1-1-1-1-11-11-1-111ii−i−i1-1-11-11-11-1-111-1-111i−i−ii−ii1-1-1−i−iii111-1-1i−i−iii−i
χ1311-1-11-1-111111-1-1-1-1−ii1111-1-1-1-11-11-111-1-1−i−iii1-11-11-11-111-1-111-1-1−ii−ii−ii1-1-1−i−iii111-1-1−ii−ii−ii
χ1411-1-11-1-111111-1-1-1-1−ii1111-1-1-1-11-1-1111-1-1−i−iii1-11-1-11-1111-1-1-1-111−ii−iii−i-11-1−i−iii1-1-111−iii−ii−i
χ1511-1-11-1-111111-1-1-1-1−ii1111-1-1-1-1-111-1-1-111−i−iii1-1-111-11-1-1-11111-1-1−iii−i−ii-11-1ii−i−i1-1-111−ii−iii−i
χ1611-1-11-1-111111-1-1-1-1−ii1111-1-1-1-1-11-11-1-111−i−iii1-1-11-11-11-1-111-1-111−iii−ii−i1-1-1ii−i−i111-1-1−iii−i−ii
χ1722222222222222222222222222000000002222-2-20000000000000022000000-20000-20000-2-20000
χ182222222222222222-2-22222222200000000-2-2-2-2-2-200000000000000-2-2000000-20000-20000220000
χ192222-1-1-1-12222222200-1-1-1-1-1-1-1-122222222000022-1-1-1-122-1-1-1-1-1-1-1-100000022-10000-1-1-1-1-1000000
χ202222-1-1-1-12222222200-1-1-1-1-1-1-1-122-2-22222000022-1-111-2-2-1-1-1-11111000000-2-2-10000-11111000000
χ212222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-222-2-2-2-200002211-1-1221111-1-1-1-1000000-2-2-10000-11111000000
χ222222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-20000221111-2-21111111100000022-10000-1-1-1-1-1000000
χ2322-2-22-2-222222-2-2-2-22i−2i2222-2-2-2-2000000002i2i−2i−2i-22000000000000002i−2i00000020000-20000−2i2i0000
χ2422-2-22-2-222222-2-2-2-2−2i2i2222-2-2-2-200000000−2i−2i2i2i-2200000000000000−2i2i00000020000-200002i−2i0000
χ2522-2-2-111-12222-2-2-2-200-1-1-1-111112-22-222-2-200002-2-11-112-2-1-111-1-1110000002-210000-1-1-111000000
χ2622-2-2-111-12222-2-2-2-200-1-1-1-111112-2-2222-2-200002-2-111-1-22-1-11111-1-1000000-2210000-111-1-1000000
χ2722-2-2-111-12222-2-2-2-200-1-1-1-11111-222-2-2-22200002-21-1-112-211-1-1-1-111000000-2210000-111-1-1000000
χ2822-2-2-111-12222-2-2-2-200-1-1-1-11111-22-22-2-22200002-21-11-1-2211-1-111-1-10000002-210000-1-1-111000000
χ29444444441-21-21-2-21441-21-211-2-22200-1-1-1-1111100220000-1-1-1-10000-2-22200000-1-1-1-100000000000
χ30444444441-21-21-2-21441-21-211-2-2-2-2001111111100-2-2000011110000-2-2-2-200000111100000000000
χ31444444441-21-21-2-21-4-41-21-211-2-22200-1-1-1-1-1-1-1-100220000-1-1-1-1000022-2-200000111100000000000
χ32444444441-21-21-2-21-4-41-21-211-2-2-2-2001111-1-1-1-100-2-2000011110000222200000-1-1-1-100000000000
χ3344444444-21-21-211-244-21-21-2-21100220000-2-2-2-2000022-1-10000-1-1-1-111002200000000000000-1-100
χ3444444444-21-21-211-244-21-21-2-21100-2-20000-2-2-2-20000-2-211000011111100-2-2000000000000001100
χ3544444444-21-21-211-2-4-4-21-21-2-211002200002222000022-1-10000-1-1-1-1-1-100-2-2000000000000001100
χ3644444444-21-21-211-2-4-4-21-21-2-21100-2-2000022220000-2-21100001111-1-1002200000000000000-1-100
χ374444-2-2-2-24444444400-2-2-2-2-2-2-2-2000000000000-4-400000000000000000000002000020000000000
χ3844-4-44-4-441-21-2-122-14i−4i1-21-2-1-1222-200-1-111ii−i−i002-20000-1-1110000−2i2i2i−2i00000−i−iii00000000000
χ3944-4-44-4-441-21-2-122-14i−4i1-21-2-1-122-220011-1-1ii−i−i00-22000011-1-10000−2i2i−2i2i00000ii−i−i00000000000
χ4044-4-44-4-441-21-2-122-1−4i4i1-21-2-1-1222-200-1-111−i−iii002-20000-1-11100002i−2i−2i2i00000ii−i−i00000000000
χ4144-4-44-4-441-21-2-122-1−4i4i1-21-2-1-122-220011-1-1−i−iii00-22000011-1-100002i−2i2i−2i00000−i−iii00000000000
χ4244-4-44-4-44-21-212-1-124i−4i-21-2122-1-1002-20000−2i−2i2i2i00002-2-110000-1-111i−i002i−2i00000000000000−ii00
χ4344-4-44-4-44-21-212-1-124i−4i-21-2122-1-100-220000−2i−2i2i2i0000-221-1000011-1-1i−i00−2i2i00000000000000i−i00
χ4444-4-44-4-44-21-212-1-12−4i4i-21-2122-1-1002-200002i2i−2i−2i00002-2-110000-1-111−ii00−2i2i00000000000000i−i00
χ4544-4-44-4-44-21-212-1-12−4i4i-21-2122-1-100-2200002i2i−2i−2i0000-221-1000011-1-1−ii002i−2i00000000000000−ii00
χ4644-4-4-222-24444-4-4-4-400-2-2-2-22222000000000000-440000000000000000000000-2000020000000000
χ474-44-444-4-41-2-12-1-221001-2-121-12-20000−i3i3−i3i33-33-300000000−i3i3−i3i30000000000000−i3i3−i3i300000000000
χ484-44-444-4-41-2-12-1-221001-2-121-12-20000−i3i3−i3i3-33-3300000000−i3i3−i3i30000000000000i3−i3i3−i300000000000
χ494-44-444-4-41-2-12-1-221001-2-121-12-20000i3−i3i3−i33-33-300000000i3−i3i3−i30000000000000i3−i3i3−i300000000000
χ504-44-444-4-41-2-12-1-221001-2-121-12-20000i3−i3i3−i3-33-3300000000i3−i3i3−i30000000000000−i3i3−i3i300000000000
χ514-44-444-4-444-4-4-44-440044-4-44-4-440000000000000000000000000000000000000000000000000000
χ524-44-4-2-22244-4-4-44-4400-2-222-222-2000000000000000000000000000000000000000000i6−i6i6−i6000000
χ534-44-4-2-22244-4-4-44-4400-2-222-222-2000000000000000000000000000000000000000000−i6i6−i6i6000000
χ544-4-444-44-41-2-1212-2-1001-2-12-11-220000−i3i3i3−i33i−3i−3i3i00000000−i3i3i3−i300000000000003−3−3300000000000
χ554-4-444-44-41-2-1212-2-1001-2-12-11-220000−i3i3i3−i3−3i3i3i−3i00000000−i3i3i3−i30000000000000−333−300000000000
χ564-4-444-44-41-2-1212-2-1001-2-12-11-220000i3−i3−i3i33i−3i−3i3i00000000i3−i3−i3i30000000000000−333−300000000000
χ574-4-444-44-41-2-1212-2-1001-2-12-11-220000i3−i3−i3i3−3i3i3i−3i00000000i3−i3−i3i300000000000003−3−3300000000000
χ584-4-444-44-444-4-44-44-40044-4-4-444-40000000000000000000000000000000000000000000000000000
χ594-4-44-22-2244-4-44-44-400-2-2222-2-22000000000000000000000000000000000000000000i6−i6−i6i6000000
χ604-4-44-22-2244-4-44-44-400-2-2222-2-22000000000000000000000000000000000000000000−i6i6i6−i6000000
χ618888-4-4-4-42-42-42-4-4200-12-12-1-1224400-2-2-2-2000000-2-2000011110000000000000000000000000000
χ628888-4-4-4-42-42-42-4-4200-12-12-1-122-4-4002222000000220000-1-1-1-10000000000000000000000000000
χ638888-4-4-4-4-42-42-422-4002-12-122-1-10044000000000000-2-2-2-200001111000000000000000000000000
χ648888-4-4-4-4-42-42-422-4002-12-122-1-100-4-400000000000022220000-1-1-1-1000000000000000000000000
χ6588-8-8-444-42-42-4-244-200-12-1211-2-24-400-2-222000000-22000011-1-10000000000000000000000000000
χ6688-8-8-444-42-42-4-244-200-12-1211-2-2-440022-2-20000002-20000-1-1110000000000000000000000000000
χ6788-8-8-444-4-42-424-2-24002-12-1-2-211004-4000000000000-22-22000011-1-1000000000000000000000000
χ6888-8-8-444-4-42-424-2-24002-12-1-2-21100-440000000000002-22-20000-1-111000000000000000000000000
χ698-88-888-8-8-424-242-2-400-424-2-44-220000000000000000000000000000000000000000000000000000
χ708-88-8-4-4442-4-24-2-44200-121-2-11-220000−2i32i3−2i32i3000000000000i3−i3i3−i30000000000000000000000000000
χ718-88-8-4-4442-4-24-2-44200-121-2-11-2200002i3−2i32i3−2i3000000000000−i3i3−i3i30000000000000000000000000000
χ728-88-8-4-444-424-242-2-4002-1-212-21-10000000000000000000000003-33-3000000000000000000000000
χ738-88-8-4-444-424-242-2-4002-1-212-21-1000000000000000000000000-33-33000000000000000000000000
χ748-8-888-88-8-424-2-4-22400-424-24-42-20000000000000000000000000000000000000000000000000000
χ758-8-88-44-442-4-2424-4-200-121-21-12-20000−2i32i32i3−2i3000000000000i3−i3−i3i30000000000000000000000000000
χ768-8-88-44-442-4-2424-4-200-121-21-12-200002i3−2i3−2i32i3000000000000−i3i3i3−i30000000000000000000000000000
χ778-8-88-44-44-424-2-4-224002-1-21-22-110000000000000000000000003-3-33000000000000000000000000
χ788-8-88-44-44-424-2-4-224002-1-21-22-11000000000000000000000000-333-3000000000000000000000000

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