Finite Group Databasebeta

← Group #13166274

Character table — Group #13166274

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size112224444444488888888888888888888889912121818183636363636363636484848485454545472727272108108108108
order12346336681224243366121212121212242424242424242424242424442221212688888242466668888242424244444
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1
χ31111111111111111111111111111111111111-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111-1-111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111
χ511111111111111111111111111111111111-1-111-1-1-1-1-1ii−i−i-1-11111ii−i−iii−i−i-1-1i−i
χ611111111111111111111111111111111111-1-111-1-1-1-1-1−i−iii-1-11111−i−iii−i−iii-1-1−ii
χ711111111111111111111111111111111111-1-1-1-1-1-1-1-1-1ii−i−i-1-1-1-1-1-1−i−iiiii−i−i11−ii
χ811111111111111111111111111111111111-1-1-1-1-1-1-1-1-1−i−iii-1-1-1-1-1-1ii−i−i−i−iii11i−i
χ9111111111-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111-11111-11-11-1-1-111-1-111111-11-11-1-1-1
χ10111111111-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111-11111-1-11-11-1-111-1-1-1-1-1-1-11-111-111
χ11111111111-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-111111-11-11-1-1-1-1-111-1-1-1-11-11-1-1111
χ12111111111-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-111111-1-11-11-1-1-1-1111111-11-11-11-1-1
χ13111111111-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-11i−i−ii1111-1-1ii−i−ii−i−ii-11−ii
χ14111111111-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-11−iii−i1111-1-1−i−iii−iii−i-11i−i
χ15111111111-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11i−i−ii11-1-111−i−iiii−i−ii1-1i−i
χ16111111111-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11−iii−i11-1-111ii−i−i−iii−i1-1−ii
χ17222-2222220-2002222-2-2-2-2-2-20000000000002200-222-2000000000002-22-200000000
χ18222-2222220-2002222-2-2-2-2-2-20000000000002200-222-200000000000-22-2200000000
χ19222-2222220-2002222-2-2-2-2-2-2000000000000-2-2002-2-22000000000002i−2i−2i2i00000000
χ20222-2222220-2002222-2-2-2-2-2-2000000000000-2-2002-2-2200000000000−2i2i2i−2i00000000
χ2122-12-122222-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-122002-1-1-122222-1-100000000-1-1-1-10000
χ2222-12-122222-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-122002-1-1-12-2-2-2-2-1-10000000011110000
χ2322-12-122222-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-200-2111-22i2i−2i−2i1100000000−i−iii0000
χ2422-12-122222-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-200-2111-2−2i−2i2i2i1100000000ii−i−i0000
χ2522-12-12222-2-111-1-1-1-122-1-1-1-1-2-2-2-21111111122002-1-1-1-22-22-21100000000-11-110000
χ2622-12-12222-2-111-1-1-1-122-1-1-1-1-2-2-2-21111111122002-1-1-1-2-22-2211000000001-11-10000
χ2722-12-12222-2-111-1-1-1-122-1-1-1-1-2-2-2-211111111-2-200-211122i−2i−2i2i-1-100000000−iii−i0000
χ2822-12-12222-2-111-1-1-1-122-1-1-1-1-2-2-2-211111111-2-200-21112−2i2i2i−2i-1-100000000i−i−ii0000
χ29444441-21-244441-21-21-211-2-211-2-21111-2-2-2-20044000000000001-21-2000000000000
χ30444441-21-244441-21-21-211-2-211-2-21111-2-2-2-200-4-400000000000-12-12000000000000
χ31444441-21-2-44-4-41-21-21-211-2-2-1-122-1-1-1-12222004-4000000000001-2-12000000000000
χ32444441-21-2-44-4-41-21-21-211-2-2-1-122-1-1-1-1222200-4400000000000-121-2000000000000
χ3344444-21-214444-21-21-21-2-211-2-211-2-2-2-21111004400000000000-21-21000000000000
χ3444444-21-214444-21-21-21-2-211-2-211-2-2-2-2111100-4-4000000000002-12-1000000000000
χ3544444-21-21-44-4-4-21-21-21-2-21122-1-12222-1-1-1-1004-400000000000-212-1000000000000
χ3644444-21-21-44-4-4-21-21-21-2-21122-1-12222-1-1-1-100-44000000000002-1-21000000000000
χ3744-2-4-244440200-2-2-2-2-4-422220000000000004400-4-2-2200000000000000000000000
χ3844-2-4-244440200-2-2-2-2-4-42222000000000000-4-400422-200000000000000000000000
χ394-440-444-4-4000044-4-40000000000000000004i−4i0004i−4i000000000000000000000000
χ404-440-444-4-4000044-4-4000000000000000000−4i4i000−4i4i000000000000000000000000
χ414-4-20244-4-4006−6-2-222000000000066−6−666−6−64i−4i000−2i2i000000i6−i60000000000000000
χ424-4-20244-4-4006−6-2-222000000000066−6−666−6−6−4i4i0002i−2i000000−i6i60000000000000000
χ434-4-20244-4-400−66-2-2220000000000−6−666−6−6664i−4i000−2i2i000000−i6i60000000000000000
χ444-4-20244-4-400−66-2-2220000000000−6−666−6−666−4i4i0002i−2i000000i6−i60000000000000000
χ45888-882-42-40-8002-42-4-24-2-2440000000000000000000000000000000000000000000
χ46888-88-42-420-800-42-424-244-2-20000000000000000000000000000000000000000000
χ4788-48-42-42-48-4-4-4-12-122-4-1-12222-4-4-1-1-1-122220000000000000000000000000000000
χ4888-48-42-42-4-8-444-12-122-4-1-122-2-2441111-2-2-2-20000000000000000000000000000000
χ4988-48-4-42-428-4-4-42-12-1-4222-1-1-4-4222222-1-1-1-10000000000000000000000000000000
χ5088-48-4-42-42-8-4442-12-1-4222-1-144-2-2-2-2-2-211110000000000000000000000000000000
χ5188-4-8-42-42-40400-12-12-2411-2-2000033−3333−3300000000000000000000000000000000000
χ5288-4-8-42-42-40400-12-12-2411-2-20000−3333−333300000000000000000000000000000000000
χ5388-4-8-4-42-4204002-12-14-2-2-2110000000033−3333−330000000000000000000000000000000
χ5488-4-8-4-42-4204002-12-14-2-2-21100000000−3333−33330000000000000000000000000000000
χ558-880-82-4-2400002-4-2400000032−320032−32−323200000000000000000000000000000000000
χ568-880-82-4-2400002-4-24000000−323200−323232−3200000000000000000000000000000000000
χ578-880-8-424-20000-424-20000000032−32000032−32−32320000000000000000000000000000000
χ588-880-8-424-20000-424-200000000−32320000−323232−320000000000000000000000000000000
χ598-8-4042-4-240026−26-121-20033−330032−32002ζ5−2ζ7+ζ13−ζ23−ζ5+ζ7−2ζ13+2ζ23−2ζ5+2ζ7−ζ13+ζ23ζ5−ζ7+2ζ13−2ζ23−6−6660000000000000000000000000000000
χ608-8-4042-4-240026−26-121-200−333300−323200−ζ5+ζ7−2ζ13+2ζ232ζ5−2ζ7+ζ13−ζ23ζ5−ζ7+2ζ13−2ζ23−2ζ5+2ζ7−ζ13+ζ23−6−6660000000000000000000000000000000
χ618-8-4042-4-2400−2626-121-20033−3300−323200−2ζ5+2ζ7−ζ13+ζ23ζ5−ζ7+2ζ13−2ζ232ζ5−2ζ7+ζ13−ζ23−ζ5+ζ7−2ζ13+2ζ2366−6−60000000000000000000000000000000
χ628-8-4042-4-2400−2626-121-200−33330032−3200ζ5−ζ7+2ζ13−2ζ23−2ζ5+2ζ7−ζ13+ζ23−ζ5+ζ7−2ζ13+2ζ232ζ5−2ζ7+ζ13−ζ2366−6−60000000000000000000000000000000
χ638-8-404-424-20026−262-1-21000033−330032−32−6−6662ζ5−2ζ7+ζ13−ζ23−ζ5+ζ7−2ζ13+2ζ23−2ζ5+2ζ7−ζ13+ζ23ζ5−ζ7+2ζ13−2ζ230000000000000000000000000000000
χ648-8-404-424-20026−262-1-210000−333300−3232−6−666−ζ5+ζ7−2ζ13+2ζ232ζ5−2ζ7+ζ13−ζ23ζ5−ζ7+2ζ13−2ζ23−2ζ5+2ζ7−ζ13+ζ230000000000000000000000000000000
χ658-8-404-424-200−26262-1-21000033−3300−323266−6−6−2ζ5+2ζ7−ζ13+ζ23ζ5−ζ7+2ζ13−2ζ232ζ5−2ζ7+ζ13−ζ23−ζ5+ζ7−2ζ13+2ζ230000000000000000000000000000000
χ668-8-404-424-200−26262-1-210000−33330032−3266−6−6ζ5−ζ7+2ζ13−2ζ23−2ζ5+2ζ7−ζ13+ζ23−ζ5+ζ7−2ζ13+2ζ232ζ5−2ζ7+ζ13−ζ230000000000000000000000000000000

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