Finite Group Databasebeta

← Group #13165188

Character table — Group #13165188

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122224444444466888888881212121212121212121212121818242424242424242424242424242424243636363636363636363636363636363654547272108108
order124436121233661212121288336612121212224466121224242424246666666121212121212122424688888812242424242424242488242444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111-11-111111111111-1-111-1-11-1-111-1-111111-1-1-1-111111-1-1-1-111-1-1-1-1
χ311111111111111111111111111-11-11-1-1-1-1111111-111-1-111-111-1-111111-1-111-1-11-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-1111111-1-111
χ51111111111111111-1-11111111111111111-1-1-1-11111111111111111-1-11-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111-1-1111111111-11-11111-1-1-1-1111-1-111-1-11-1-111-1-1-1-11-1-111-1-11-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111-1-111111111-11-11-1-1-1-1-1-1-1-111-111-1-111-111-1-111-1-1111-1-1-1-111111-1-1-1-1-1-1-1-111
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
χ911-1-111-1-11111-1-1-1-1i−i1111-1-1-1-111-1-111-1-1ii−i−i-111111111-1-1-1-1-1-1-1i−i-1i−ii−i1-11ii−i−i11-1-1i−ii−ii−i
χ1011-1-111-1-11111-1-1-1-1i−i1111-1-1-1-11-1-1111-1-1ii−i−i-111-1-111-1-1-111-1-111i−i-1i−i−ii-111ii−i−i-1-111i−i−ii−ii
χ1111-1-111-1-11111-1-1-1-1i−i1111-1-1-1-1-111-1-1-111ii−i−i-11-111-1-1111-1-111-1-1i−i-1−iii−i-111−i−iii-1-111i−ii−i−ii
χ1211-1-111-1-11111-1-1-1-1i−i1111-1-1-1-1-1-111-1-111ii−i−i-11-1-1-1-1-1-1-11111111i−i-1−ii−ii1-11−i−iii11-1-1i−i−iii−i
χ1311-1-111-1-11111-1-1-1-1−ii1111-1-1-1-111-1-111-1-1−i−iii-111111111-1-1-1-1-1-1-1−ii-1−ii−ii1-11−i−iii11-1-1−ii−ii−ii
χ1411-1-111-1-11111-1-1-1-1−ii1111-1-1-1-11-1-1111-1-1−i−iii-111-1-111-1-1-111-1-111−ii-1−iii−i-111−i−iii-1-111−iii−ii−i
χ1511-1-111-1-11111-1-1-1-1−ii1111-1-1-1-1-111-1-1-111−i−iii-11-111-1-1111-1-111-1-1−ii-1i−i−ii-111ii−i−i-1-111−ii−iii−i
χ1611-1-111-1-11111-1-1-1-1−ii1111-1-1-1-1-1-111-1-111−i−iii-11-1-1-1-1-1-1-11111111−ii-1i−ii−i1-11ii−i−i11-1-1−iii−i−ii
χ1722222222222222222222222222000000002222-2-20000000000000022-2000000-200000000-2-20000
χ182222222222222222-2-22222222200000000-2-2-2-2-2-200000000000000-2-2-2000000-200000000220000
χ192222-1-1-1-12222222200-1-1-1-1-1-1-1-122222222000022-1-12-1-1-1-1-1-12-1-1-1-100-1000022-10000-1-1-1-1000000
χ202222-1-1-1-12222222200-1-1-1-1-1-1-1-12-22-22222000022-11-2-1-111-11-2-1-11100-10000-2-2-100001111000000
χ212222-1-1-1-12222222200-1-1-1-1-1-1-1-1-22-22-2-2-2-20000221-1211-1-11-1211-1-100-10000-2-2-100001111000000
χ222222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-200002211-2111111-2111100-1000022-10000-1-1-1-1000000
χ2322-2-222-2-22222-2-2-2-22i−2i2222-2-2-2-2000000002i2i−2i−2i2-2000000000000002i−2i2000000-200000000−2i2i0000
χ2422-2-222-2-22222-2-2-2-2−2i2i2222-2-2-2-200000000−2i−2i2i2i2-200000000000000−2i2i2000000-2000000002i−2i0000
χ2522-2-2-1-1112222-2-2-2-200-1-1-1-1111122-2-222-2-20000-22-1-12-1-1-1-111-2111100100002-2-10000-1-111000000
χ2622-2-2-1-1112222-2-2-2-200-1-1-1-111112-2-2222-2-20000-22-11-2-1-1111-1211-1-10010000-22-1000011-1-1000000
χ2722-2-2-1-1112222-2-2-2-200-1-1-1-11111-222-2-2-2220000-221-1211-1-1-11-2-1-1110010000-22-1000011-1-1000000
χ2822-2-2-1-1112222-2-2-2-200-1-1-1-11111-2-222-2-2220000-2211-21111-1-12-1-1-1-100100002-2-10000-1-111000000
χ29444444441-21-211-2-2441-21-211-2-202020000-2-2-2-20002-100-1-102-100-1-111000220000000000000-1-100
χ30444444441-21-211-2-2441-21-211-2-20-20-20000-2-2-2-2000-2100110-21001111000-2-200000000000001100
χ31444444441-21-211-2-2-4-41-21-211-2-20202000022220002-100-1-102-100-1-1-1-1000-2-200000000000001100
χ32444444441-21-211-2-2-4-41-21-211-2-20-20-200002222000-2100110-210011-1-1000220000000000000-1-100
χ3344444444-21-21-2-21144-21-21-2-2112020-1-1-1-1111100200-1-100200-1-100-2-202200000-1-1-1-10000000000
χ3444444444-21-21-2-21144-21-21-2-211-20-201111111100-2001100-2001100-2-20-2-20000011110000000000
χ3544444444-21-21-2-211-4-4-21-21-2-2112020-1-1-1-1-1-1-1-100200-1-100200-1-100220-2-20000011110000000000
χ3644444444-21-21-2-211-4-4-21-21-2-211-20-201111-1-1-1-100-2001100-20011002202200000-1-1-1-10000000000
χ374444-2-2-2-24444444400-2-2-2-2-2-2-2-2000000000000-4-400000000000000002000000200000000000000
χ3844-4-444-4-41-21-2-1-1224i−4i1-21-2-1-122020-20000−2i−2i2i2i0002-100-1-10-210011i−i0002i−2i0000000000000−ii00
χ3944-4-444-4-41-21-2-1-1224i−4i1-21-2-1-1220-2020000−2i−2i2i2i000-21001102-100-1-1i−i000−2i2i0000000000000i−i00
χ4044-4-444-4-41-21-2-1-122−4i4i1-21-2-1-122020-200002i2i−2i−2i0002-100-1-10-210011−ii000−2i2i0000000000000i−i00
χ4144-4-444-4-41-21-2-1-122−4i4i1-21-2-1-1220-20200002i2i−2i−2i000-21001102-100-1-1−ii0002i−2i0000000000000−ii00
χ4244-4-444-4-4-21-2122-1-14i−4i-21-2122-1-120-20-1-111ii−i−i00200-1-100-2001100−2i2i02i−2i00000−i−iii0000000000
χ4344-4-444-4-4-21-2122-1-14i−4i-21-2122-1-1-202011-1-1ii−i−i00-2001100200-1-100−2i2i0−2i2i00000ii−i−i0000000000
χ4444-4-444-4-4-21-2122-1-1−4i4i-21-2122-1-120-20-1-111−i−iii00200-1-100-20011002i−2i0−2i2i00000ii−i−i0000000000
χ4544-4-444-4-4-21-2122-1-1−4i4i-21-2122-1-1-202011-1-1−i−iii00-2001100200-1-1002i−2i02i−2i00000−i−iii0000000000
χ4644-4-4-2-2224444-4-4-4-400-2-2-2-222220000000000004-40000000000000000-2000000200000000000000
χ474-44i−4i4-44i−4i44-4-44i−4i4i−4i0044-4-44i−4i4i−4i0000000000000000000000000000000000000000000000000000
χ484-44i−4i4-44i−4i-212-1−2i2ii−i00-212-1−2i2ii−i0000−i3i33−33ζ7+3ζ23−3ζ7−3ζ23−3ζ5−3ζ133ζ5+3ζ1300000−i3i3000003−3000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ494-44i−4i4-44i−4i-212-1−2i2ii−i00-212-1−2i2ii−i0000−i3i33−3−3ζ7−3ζ233ζ7+3ζ233ζ5+3ζ13−3ζ5−3ζ1300000−i3i3000003−3000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ504-44i−4i4-44i−4i-212-1−2i2ii−i00-212-1−2i2ii−i0000i3−i3−333ζ7+3ζ23−3ζ7−3ζ23−3ζ5−3ζ133ζ5+3ζ1300000i3−i300000−33000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ514-44i−4i4-44i−4i-212-1−2i2ii−i00-212-1−2i2ii−i0000i3−i3−33−3ζ7−3ζ233ζ7+3ζ233ζ5+3ζ13−3ζ5−3ζ1300000i3−i300000−33000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ524-44i−4i-22−2i2i44-4-44i−4i4i−4i00-2-222−2i2i−2i2i000000000000000000000000000000000000000000i6−i66−6000000
χ534-44i−4i-22−2i2i44-4-44i−4i4i−4i00-2-222−2i2i−2i2i000000000000000000000000000000000000000000−i6i6−66000000
χ544-4−4i4i4-4−4i4i44-4-4−4i4i−4i4i0044-4-4−4i4i−4i4i0000000000000000000000000000000000000000000000000000
χ554-4−4i4i4-4−4i4i-212-12i−2i−ii00-212-12i−2i−ii0000−i3i3−33−3ζ5−3ζ133ζ5+3ζ133ζ7+3ζ23−3ζ7−3ζ2300000−i3i300000−33000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ564-4−4i4i4-4−4i4i-212-12i−2i−ii00-212-12i−2i−ii0000−i3i3−333ζ5+3ζ13−3ζ5−3ζ13−3ζ7−3ζ233ζ7+3ζ2300000−i3i300000−33000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ574-4−4i4i4-4−4i4i-212-12i−2i−ii00-212-12i−2i−ii0000i3−i33−3−3ζ5−3ζ133ζ5+3ζ133ζ7+3ζ23−3ζ7−3ζ2300000i3−i3000003−3000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ584-4−4i4i4-4−4i4i-212-12i−2i−ii00-212-12i−2i−ii0000i3−i33−33ζ5+3ζ13−3ζ5−3ζ13−3ζ7−3ζ233ζ7+3ζ2300000i3−i3000003−3000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ594-4−4i4i-222i−2i44-4-4−4i4i−4i4i00-2-2222i−2i2i−2i000000000000000000000000000000000000000000i6−i6−66000000
χ604-4−4i4i-222i−2i44-4-4−4i4i−4i4i00-2-2222i−2i2i−2i000000000000000000000000000000000000000000−i6i66−6000000
χ618888-4-4-4-42-42-422-4-400-12-12-1-122040400000000000-2-200110-2-20011000000000000000000000000
χ628888-4-4-4-42-42-422-4-400-12-12-1-1220-40-4000000000002200-1-102200-1-1000000000000000000000000
χ638888-4-4-4-4-42-42-4-422002-12-122-1-14040-2-2-2-2000000-2001100-2001100000000000000000000000000
χ648888-4-4-4-4-42-42-4-422002-12-122-1-1-40-402222000000200-1-100200-1-100000000000000000000000000
χ6588-8-8-4-4442-42-4-2-24400-12-1211-2-2040-400000000000-2-2001102200-1-1000000000000000000000000
χ6688-8-8-4-4442-42-4-2-24400-12-1211-2-20-404000000000002200-1-10-2-20011000000000000000000000000
χ6788-8-8-4-444-42-4244-2-2002-12-1-2-21140-40-2-222000000-2001100200-1-100000000000000000000000000
χ6888-8-8-4-444-42-4244-2-2002-12-1-2-211-404022-2-2000000200-1-100-2001100000000000000000000000000
χ698-88i−8i8-88i−8i2-4-242i−2i−4i4i002-4-242i−2i−4i4i0000000000000000000000000000000000000000000000000000
χ708-88i−8i-44−4i4i2-4-242i−2i−4i4i00-121-2−ii2i−2i00000000000000000003-3000003i−3i000000000000000000000000
χ718-88i−8i-44−4i4i2-4-242i−2i−4i4i00-121-2−ii2i−2i0000000000000000000-3300000−3i3i000000000000000000000000
χ728-88i−8i-44−4i4i-424-2−4i4i2i−2i002-1-212i−2i−ii0000−2i32i323−23000000000i3−i300000−3300000000000000000000000000
χ738-88i−8i-44−4i4i-424-2−4i4i2i−2i002-1-212i−2i−ii00002i3−2i3−2323000000000−i3i3000003−300000000000000000000000000
χ748-8−8i8i8-8−8i8i2-4-24−2i2i4i−4i002-4-24−2i2i4i−4i0000000000000000000000000000000000000000000000000000
χ758-8−8i8i-444i−4i2-4-24−2i2i4i−4i00-121-2i−i−2i2i00000000000000000003-300000−3i3i000000000000000000000000
χ768-8−8i8i-444i−4i2-4-24−2i2i4i−4i00-121-2i−i−2i2i0000000000000000000-33000003i−3i000000000000000000000000
χ778-8−8i8i-444i−4i-424-24i−4i−2i2i002-1-21−2i2ii−i0000−2i32i3−2323000000000i3−i3000003−300000000000000000000000000
χ788-8−8i8i-444i−4i-424-24i−4i−2i2i002-1-21−2i2ii−i00002i3−2i323−23000000000−i3i300000−3300000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.