Finite Group Databasebeta

← Group #13166570

Character table — Group #13166570

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size11222444444888888899121216161616161616161818182424242436363636363636363636484854545454727272108108108108
order12346334661233661212124448121212121212121221212242424242446881212121212128888624242888
χ1111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-11-1-1-1-1-1-111-1-1-1-11-1-111-1-1
χ311111111111111111111-1-111111111111-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-1
χ411111111111111111111-1-111111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-111111-1-1-1-111
χ5111111111111111111-1-11111111111-1-1-11111-1i−i-1i−iii−i−i11ii−i−i-1i−i-1-1i−i
χ6111111111111111111-1-11111111111-1-1-11111-1−ii-1−ii−i−iii11−i−iii-1−ii-1-1−ii
χ7111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1i−i-1i−iii−i−i-1-1−i−iii-1i−i11−ii
χ8111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1−ii-1−ii−i−iii-1-1ii−i−i-1−ii11i−i
χ91111111-11111111-111111-1-1-111-1-1-1-1111-1-1-1-1-1111-1-1111111-1-1-1-1-1-1-11-111
χ101111111-11111111-111111-1-1-111-1-1-1-1111-1-1-1-1-1-1-1111-1-1-1-1111111-1111-1-1-1
χ111111111-11111111-11111-11-1-111-1-1-1-11111111-1111-1-11111-1-11111-1-1-1-11-1-1
χ121111111-11111111-11111-11-1-111-1-1-1-11111111-1-1-1111-1-1-1-1-1-1-1-1-1-1-111-1111
χ131111111-11111111-111-1-11-1-1-111-1-1-1-1-1-1-1-1-1-1-11i−i-1−iiii−i−i11−i−iii1−ii-11i−i
χ141111111-11111111-111-1-11-1-1-111-1-1-1-1-1-1-1-1-1-1-11−ii-1i−i−i−iii11ii−i−i1i−i-11−ii
χ151111111-11111111-111-1-1-11-1-111-1-1-1-1-1-1-111111i−i-1−iiii−i−i-1-1ii−i−i1−ii1-1−ii
χ161111111-11111111-111-1-1-11-1-111-1-1-1-1-1-1-111111−ii-1i−i−i−iii-1-1−i−iii1i−i1-1i−i
χ17222-2222022-222220-2-2220000-2-20000-2220000000-2000000002-22-20000000
χ18222-2222022-222220-2-2220000-2-20000-2220000000-200000000-22-220000000
χ19222-2222022-222220-2-2-2-20000-2-200002-2-200000002000000002i−2i−2i2i0000000
χ20222-2222022-222220-2-2-2-20000-2-200002-2-20000000200000000−2i2i2i−2i0000000
χ2122-12-122222-1-1-1-1-1-122220022-1-1-1-1-1-12-1-10000222-122-1-1-1-1000000-1-1-10000
χ2222-12-122222-1-1-1-1-1-122220022-1-1-1-1-1-12-1-100002-2-2-1-2-21111000000-1110000
χ2322-12-122222-1-1-1-1-1-122-2-20022-1-1-1-1-1-1-2110000-22i−2i12i−2i−i−iii0000001−ii0000
χ2422-12-122222-1-1-1-1-1-122-2-20022-1-1-1-1-1-1-2110000-2−2i2i1−2i2iii−i−i0000001i−i0000
χ2522-12-122-222-1-1-1-1-11222200-2-2-1-111112-1-10000-222-1-2-2-1-1-1-10000001110000
χ2622-12-122-222-1-1-1-1-11222200-2-2-1-111112-1-10000-2-2-2-12211110000001-1-10000
χ2722-12-122-222-1-1-1-1-1122-2-200-2-2-1-11111-211000022i−2i1−2i2i−i−iii000000-1i−i0000
χ2822-12-122-222-1-1-1-1-1122-2-200-2-2-1-11111-21100002−2i2i12i−2iii−i−i000000-1−ii0000
χ29444441-241-241-21-241-200441-21-211-2-200011-2-200000000001-200000000000
χ30444441-241-241-21-241-200-4-41-21-211-2-2000-1-1220000000000-1200000000000
χ31444441-2-41-241-21-2-41-2004-4-121-2-1-122000-1-12200000000001-200000000000
χ32444441-2-41-241-21-2-41-200-44-121-2-1-12200011-2-20000000000-1200000000000
χ3344444-214-214-21-214-210044-21-21-2-211000-2-2110000000000-2100000000000
χ3444444-214-214-21-214-2100-4-4-21-21-2-21100022-1-100000000002-100000000000
χ3544444-21-4-214-21-21-4-21004-42-1-2122-1-100022-1-10000000000-2100000000000
χ3644444-21-4-214-21-21-4-2100-442-1-2122-1-1000-2-21100000000002-100000000000
χ3744-2-4-2440442-2-2-2-20-4-4440000220000-4-2-2000000020000000000000000000
χ3844-2-4-2440442-2-2-2-20-4-4-4-400002200004220000000-20000000000000000000
χ394-440-4440-4-4044-4-40004i−4i000000000004i−4i000000000000000000000000000
χ404-440-4440-4-4044-4-4000−4i4i00000000000−4i4i000000000000000000000000000
χ414-4-202440-4-40-2-2220004i−4i00000000000−2i2i0000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ220000000000000
χ424-4-202440-4-40-2-2220004i−4i00000000000−2i2i0000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ220000000000000
χ434-4-202440-4-40-2-222000−4i4i000000000002i−2i0000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ220000000000000
χ444-4-202440-4-40-2-222000−4i4i000000000002i−2i0000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ220000000000000
χ45888-882-402-4-82-42-40-24000000-240000000000000000000000000000000000
χ46888-88-420-42-8-42-4204-20000004-20000000000000000000000000000000000
χ4788-48-42-482-4-4-12-12-42-400002-4-12-1-122000000000000000000000000000000
χ4888-48-42-4-82-4-4-12-1242-40000-24-1211-2-2000000000000000000000000000000
χ4988-48-4-428-42-42-12-1-4-420000-422-122-1-1000000000000000000000000000000
χ5088-48-4-42-8-42-42-12-14-4200004-22-1-2-211000000000000000000000000000000
χ5188-4-8-42-402-44-12-120-240000001-2−3i33i300000000000000000000000000000000
χ5288-4-8-42-402-44-12-120-240000001-23i3−3i300000000000000000000000000000000
χ5388-4-8-4-420-4242-12-104-2000000-2100−3i33i3000000000000000000000000000000
χ5488-4-8-4-420-4242-12-104-2000000-21003i3−3i3000000000000000000000000000000
χ558-880-82-40-2402-4-2400000000000000000032−320000000000000000000000000
χ568-880-82-40-2402-4-24000000000000000000−32320000000000000000000000000
χ578-880-8-4204-20-424-20000000000000000000032−3200000000000000000000000
χ588-880-8-4204-20-424-200000000000000000000−323200000000000000000000000
χ5916-16-8084-80-480-242-4000000000000000000000000000000000000000000000
χ6016-16-808-8408-404-2-42000000000000000000000000000000000000000000000

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