Finite Group Databasebeta

← Group #13166546

Character table — Group #13166546

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size11222444444888888899121216161616161616161818182424242436363636363636363636484854545454727272108108108108
order12346233661233666121244486666661212212122424242444468812121212121288881224242888
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
χ911111-11111111-11111111-1-1-1-1-1-1-111111-1-1-1-1-1111-1-1111111-1-1-1-1-1-1-11-111
χ1011111-11111111-11111111-1-1-1-1-1-1-111111-1-1-1-1-1-1-1111-1-1-1-1111111-1111-1-1-1
χ1111111-11111111-1111111-11-1-1-1-1-1-1111111111-1111-1-11111-1-11111-1-1-1-11-1-1
χ1211111-11111111-1111111-11-1-1-1-1-1-1111111111-1-1-1111-1-1-1-1-1-1-1-1-1-1-111-1111
χ1311111-11111111-11111-1-11-1-1-1-1-1-1-111-1-1-1-1-1-1-11i−i-1−iiii−i−i11−i−iii1−ii-11i−i
χ1411111-11111111-11111-1-11-1-1-1-1-1-1-111-1-1-1-1-1-1-11−ii-1i−i−i−iii11ii−i−i1i−i-11−ii
χ1511111-11111111-11111-1-1-11-1-1-1-1-1-111-1-1-111111i−i-1−iiii−i−i-1-1ii−i−i1−ii1-1−ii
χ1611111-11111111-11111-1-1-11-1-1-1-1-1-111-1-1-111111−ii-1i−i−i−iii-1-1−i−iii1i−i1-1i−i
χ17222-2202222-222022-2-22200000000-2-2-2220000000-2000000002-22-20000000
χ18222-2202222-222022-2-22200000000-2-2-2220000000-200000000-22-220000000
χ19222-2202222-222022-2-2-2-200000000-2-22-2-200000002000000002i−2i−2i2i0000000
χ20222-2202222-222022-2-2-2-200000000-2-22-2-20000000200000000−2i2i2i−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
χ2522-12-1-22222-1-1-11-1-1222200-2-21111-1-12-1-10000-222-1-2-2-1-1-1-10000001110000
χ2622-12-1-22222-1-1-11-1-1222200-2-21111-1-12-1-10000-2-2-2-12211110000001-1-10000
χ2722-12-1-22222-1-1-11-1-122-2-200-2-21111-1-1-211000022i−2i1−2i2i−i−iii000000-1i−i0000
χ2822-12-1-22222-1-1-11-1-122-2-200-2-21111-1-1-21100002−2i2i12i−2iii−i−i000000-1−ii0000
χ294444441-21-241-241-21-200441-211-2-21-200011-2-200000000001-200000000000
χ304444441-21-241-241-21-200-4-41-211-2-21-2000-1-1220000000000-1200000000000
χ31444444-21-214-214-21-210044-21-2-211-21000-2-2110000000000-2100000000000
χ32444444-21-214-214-21-2100-4-4-21-2-211-2100022-1-100000000002-100000000000
χ3344444-41-21-241-2-41-21-2004-4-12-1-1221-2000-1-12200000000001-200000000000
χ3444444-41-21-241-2-41-21-200-44-12-1-1221-200011-2-20000000000-1200000000000
χ3544444-4-21-214-21-4-21-21004-42-122-1-1-2100022-1-10000000000-2100000000000
χ3644444-4-21-214-21-4-21-2100-442-122-1-1-21000-2-21100000000002-100000000000
χ3744-2-4-2044442-2-20-2-2-4-4440000000022-4-2-2000000020000000000000000000
χ3844-2-4-2044442-2-20-2-2-4-4-4-400000000224220000000-20000000000000000000
χ394-440-4044-4-40440-4-4004i−4i000000000004i−4i000000000000000000000000000
χ404-440-4044-4-40440-4-400−4i4i00000000000−4i4i000000000000000000000000000
χ414-4-202044-4-40-2-2022004i−4i00000000000−2i2i0000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ220000000000000
χ424-4-202044-4-40-2-2022004i−4i00000000000−2i2i0000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ220000000000000
χ434-4-202044-4-40-2-202200−4i4i000000000002i−2i0000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ220000000000000
χ444-4-202044-4-40-2-202200−4i4i000000000002i−2i0000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ220000000000000
χ45888-8802-42-4-82-402-4-240000000000-24000000000000000000000000000000
χ46888-880-42-42-8-420-424-200000000004-2000000000000000000000000000000
χ4788-48-482-42-4-4-12-4-122-400002-4-1-122-12000000000000000000000000000000
χ4888-48-48-42-42-42-1-42-1-420000-4222-1-12-1000000000000000000000000000000
χ4988-48-4-82-42-4-4-124-122-40000-2411-2-2-12000000000000000000000000000000
χ5088-48-4-8-42-42-42-142-1-4200004-2-2-2112-1000000000000000000000000000000
χ5188-4-8-402-42-44-120-12-24000000−3i33i3001-2000000000000000000000000000000
χ5288-4-8-402-42-44-120-12-240000003i3−3i3001-2000000000000000000000000000000
χ5388-4-8-40-42-4242-102-14-200000000−3i33i3-21000000000000000000000000000000
χ5488-4-8-40-42-4242-102-14-2000000003i3−3i3-21000000000000000000000000000000
χ558-880-802-4-2402-40-2400000000000000000−3i23i20000000000000000000000000
χ568-880-802-4-2402-40-24000000000000000003i2−3i20000000000000000000000000
χ578-880-80-424-20-4204-20000000000000000000−3i23i200000000000000000000000
χ588-880-80-424-20-4204-200000000000000000003i2−3i200000000000000000000000
χ5916-16-80804-8-480-2402-400000000000000000000000000000000000000000000
χ6016-16-8080-848-404-20-4200000000000000000000000000000000000000000000

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