Finite Group Databasebeta

← Group #13165519

Character table — Group #13165519

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122224444444466888888881212121212121212121212121818242424242424242424242424242424243636363636363636363636363636363654547272108108
order122236663366666644336666664444121212121212121244121212121212121212121212121212124444881212121212122424242444121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1-1-1
χ311111111111111111111111111-1-1111111-1-1-1-111-1-1111111-1-1-1-1111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-1
χ411111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111111-1-111
χ51111111111111111-1-1111111111111-1-1-1-1111111111111-1-111111111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1
χ61111111111111111-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11-1-1-1-11-1-1-1-1-1-11111
χ71111111111111111-1-111111111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-111
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
χ911-1-11-1-1111-111-1-1-1i−i11-1-1-1-1111-11-1ii−i−i11-1-11-11-11-11-1i−i11-1-111-1-1i−ii−i1-1-1ii−i−i111-1-1i−ii−ii−i
χ1011-1-11-1-1111-111-1-1-1i−i11-1-1-1-1111-1-11ii−i−i11-1-11-11-1-11-11i−i11-1-1-1-111−iii−i-11-1ii−i−i1-1-111i−i−ii−ii
χ1111-1-11-1-1111-111-1-1-1i−i11-1-1-1-111-111-1ii−i−i-1-1111-1-111-11-1i−i-1-11111-1-1i−i−ii-11-1−i−iii1-1-111i−ii−i−ii
χ1211-1-11-1-1111-111-1-1-1i−i11-1-1-1-111-11-11ii−i−i-1-1111-1-11-11-11i−i-1-111-1-111−ii−ii1-1-1−i−iii111-1-1i−i−iii−i
χ1311-1-11-1-1111-111-1-1-1−ii11-1-1-1-1111-11-1−i−iii11-1-11-11-11-11-1−ii11-1-111-1-1−ii−ii1-1-1−i−iii111-1-1−ii−ii−ii
χ1411-1-11-1-1111-111-1-1-1−ii11-1-1-1-1111-1-11−i−iii11-1-11-11-1-11-11−ii11-1-1-1-111i−i−ii-11-1−i−iii1-1-111−iii−ii−i
χ1511-1-11-1-1111-111-1-1-1−ii11-1-1-1-111-111-1−i−iii-1-1111-1-111-11-1−ii-1-11111-1-1−iii−i-11-1ii−i−i1-1-111−ii−iii−i
χ1611-1-11-1-1111-111-1-1-1−ii11-1-1-1-111-11-11−i−iii-1-1111-1-11-11-11−ii-1-111-1-111i−ii−i1-1-1ii−i−i111-1-1−iii−i−ii
χ1722222222222222222222222222000022220000-2-20000002200000000000000-20000-20000-2-20000
χ182222222222222222-2-2222222220000-2-2-2-20000-2-2000000-2-200000000000000-20000-20000220000
χ192222-1-1-1-12222222200-1-1-1-1-1-1-1-122220000222222-1-1-1-12200-1-1-1-1-1-1-1-1000022-10000-1-1-1-1-1000000
χ202222-1-1-1-12222222200-1-1-1-1-1-1-1-122-2-20000222222-1-111-2-200-1-1-1-111110000-2-2-10000-11111000000
χ212222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-2220000-2-2-2-22211-1-122001111-1-1-1-10000-2-2-10000-11111000000
χ222222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-2-2-20000-2-2-2-2221111-2-20011111111000022-10000-1-1-1-1-1000000
χ2322-2-22-2-2222-222-2-2-22i−2i22-2-2-2-22200002i2i−2i−2i0000-220000002i−2i0000000000000020000-20000−2i2i0000
χ2422-2-22-2-2222-222-2-2-2−2i2i22-2-2-2-2220000−2i−2i2i2i0000-22000000−2i2i0000000000000020000-200002i−2i0000
χ2522-2-2-111-122-222-2-2-200-1-11111-1-12-22-2000022-2-22-2-11-112-200-1-111-1-11100002-210000-1-1-111000000
χ2622-2-2-111-122-222-2-2-200-1-11111-1-12-2-22000022-2-22-2-111-1-2200-1-11111-1-10000-2210000-111-1-1000000
χ2722-2-2-111-122-222-2-2-200-1-11111-1-1-222-20000-2-2222-21-1-112-20011-1-1-1-1110000-2210000-111-1-1000000
χ2822-2-2-111-122-222-2-2-200-1-11111-1-1-22-220000-2-2222-21-11-1-220011-1-111-1-100002-210000-1-1-111000000
χ29444444441-211-2-2-21441-211-2-21-20022-2-2-2-20000000022-1-1110000-1-1-1-1220000000000000000-1-100
χ30444444441-211-2-2-21441-211-2-21-200-2-2-2-2-2-200000000-2-2111100001111-2-200000000000000001100
χ31444444441-211-2-2-21-4-41-211-2-21-2002222220000000022-1-1-1-10000-1-1-1-1-2-200000000000000001100
χ32444444441-211-2-2-21-4-41-211-2-21-200-2-2222200000000-2-211-1-100001111220000000000000000-1-100
χ3344444444-21-2-2111-244-21-2-211-2122001111-1-1-1-100220000-2-2-1-1-1-100000022000-1-1-1-100000000000
χ3444444444-21-2-2111-244-21-2-211-21-2-2001111111100-2-20000-2-21111000000-2-2000111100000000000
χ3544444444-21-2-2111-2-4-4-21-2-211-212200-1-1-1-1-1-1-1-10022000022-1-1-1-1000000-2-2000111100000000000
χ3644444444-21-2-2111-2-4-4-21-2-211-21-2-200-1-1-1-1111100-2-2000022111100000022000-1-1-1-100000000000
χ374444-2-2-2-24444444400-2-2-2-2-2-2-2-2000000000000-4-400000000000000000000002000020000000000
χ3844-4-44-4-441-2-11-222-14i−4i1-2-1-1221-2002-2−2i−2i2i2i000000002-2-11i−i0000-1-1112i−2i0000000000000000−ii00
χ3944-4-44-4-441-2-11-222-14i−4i1-2-1-1221-200-22−2i−2i2i2i00000000-221-1i−i000011-1-1−2i2i0000000000000000i−i00
χ4044-4-44-4-441-2-11-222-1−4i4i1-2-1-1221-2002-22i2i−2i−2i000000002-2-11−ii0000-1-111−2i2i0000000000000000i−i00
χ4144-4-44-4-441-2-11-222-1−4i4i1-2-1-1221-200-222i2i−2i−2i00000000-221-1−ii000011-1-12i−2i0000000000000000−ii00
χ4244-4-44-4-44-212-21-1-124i−4i-2122-1-1-212-200ii−i−i-1-111002-20000−2i2i-1-1110000002i−2i000−i−iii00000000000
χ4344-4-44-4-44-212-21-1-124i−4i-2122-1-1-21-2200ii−i−i11-1-100-220000−2i2i11-1-1000000−2i2i000ii−i−i00000000000
χ4444-4-44-4-44-212-21-1-12−4i4i-2122-1-1-212-200−i−iii-1-111002-200002i−2i-1-111000000−2i2i000ii−i−i00000000000
χ4544-4-44-4-44-212-21-1-12−4i4i-2122-1-1-21-2200−i−iii11-1-100-2200002i−2i11-1-10000002i−2i000−i−iii00000000000
χ4644-4-4-222-244-444-4-4-400-2-22222-2-2000000000000-440000000000000000000000-2000020000000000
χ474-44-444-4-444-4-4-44-4400444-44-4-4-40000000000000000000000000000000000000000000000000000
χ484-44-444-4-4-2122-11-1-200-21-221-12-100003-33-33−33−300000000003−33−3000000000003−33−300000000000
χ494-44-444-4-4-2122-11-1-200-21-221-12-100003-33-3−33−330000000000−33−3300000000000−33−3300000000000
χ504-44-444-4-4-2122-11-1-200-21-221-12-10000-33-333−33−300000000003−33−300000000000−33−3300000000000
χ514-44-444-4-4-2122-11-1-200-21-221-12-10000-33-33−33−330000000000−33−33000000000003−33−300000000000
χ524-44-4-2-22244-4-4-44-4400-2-2-22-2222000000000000000000000000000000000000000000i6−i6i6−i6000000
χ534-44-4-2-22244-4-4-44-4400-2-2-22-2222000000000000000000000000000000000000000000−i6i6−i6i6000000
χ544-4-444-44-4444-4-4-44-40044-44-44-4-40000000000000000000000000000000000000000000000000000
χ554-4-444-44-4-21-22-1-11200-212-2-112-100003i−3i−3i3i3−3−3300000000003−3−3300000000000i3−i3−i3i300000000000
χ564-4-444-44-4-21-22-1-11200-212-2-112-100003i−3i−3i3i−333−30000000000−333−300000000000−i3i3i3−i300000000000
χ574-4-444-44-4-21-22-1-11200-212-2-112-10000−3i3i3i−3i3−3−3300000000003−3−3300000000000−i3i3i3−i300000000000
χ584-4-444-44-4-21-22-1-11200-212-2-112-10000−3i3i3i−3i−333−30000000000−333−300000000000i3−i3−i3i300000000000
χ594-4-44-22-22444-4-4-44-400-2-22-22-222000000000000000000000000000000000000000000i6−i6−i6i6000000
χ604-4-44-22-22444-4-4-44-400-2-22-22-222000000000000000000000000000000000000000000−i6i6i6−i6000000
χ618888-4-4-4-42-422-4-4-4200-12-1-122-120044000000000000-2-2-2-200000011110000000000000000000000
χ628888-4-4-4-42-422-4-4-4200-12-1-122-1200-4-40000000000002222000000-1-1-1-10000000000000000000000
χ638888-4-4-4-4-42-4-4222-4002-122-1-12-144000000-2-2-2-200-2-2000000111100000000000000000000000000
χ648888-4-4-4-4-42-4-4222-4002-122-1-12-1-4-400000022220022000000-1-1-1-100000000000000000000000000
χ6588-8-8-444-42-4-22-444-200-1211-2-2-12004-4000000000000-22-2200000011-1-10000000000000000000000
χ6688-8-8-444-42-4-22-444-200-1211-2-2-1200-440000000000002-22-2000000-1-1110000000000000000000000
χ6788-8-8-444-4-424-42-2-24002-1-2-2112-14-4000000-2-22200-2200000011-1-100000000000000000000000000
χ6888-8-8-444-4-424-42-2-24002-1-2-2112-1-4400000022-2-2002-2000000-1-11100000000000000000000000000
χ698-88-888-8-82-4-2-24-442002-42-2-44-240000000000000000000000000000000000000000000000000000
χ708-88-8-4-4442-4-2-24-44200-12-112-21-2000000000000000000000000003i−3i3i−3i0000000000000000000000
χ718-88-8-4-4442-4-2-24-44200-12-112-21-200000000000000000000000000−3i3i−3i3i0000000000000000000000
χ728-88-8-4-444-4244-22-2-4002-12-2-11-210000000023−2323−230000000000−33−3300000000000000000000000000
χ738-88-8-4-444-4244-22-2-4002-12-2-11-2100000000−2323−232300000000003−33−300000000000000000000000000
χ748-8-888-88-82-42-244-4-2002-4-224-4-240000000000000000000000000000000000000000000000000000
χ758-8-88-44-442-42-244-4-200-121-1-221-2000000000000000000000000003i−3i−3i3i0000000000000000000000
χ768-8-88-44-442-42-244-4-200-121-1-221-200000000000000000000000000−3i3i3i−3i0000000000000000000000
χ778-8-88-44-44-42-44-2-224002-1-221-1-210000000023−23−23230000000000−333−300000000000000000000000000
χ788-8-88-44-44-42-44-2-224002-1-221-1-2100000000−232323−2300000000003−3−3300000000000000000000000000

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