Finite Group Databasebeta

← Group #13166529

Character table — Group #13166529

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size112224444446688888888888991212121212161616161616181818242424242424363636363636363636365454727272108108108108108
order1234623366122433666666612124426666666612122121266661212444688121212122412242444488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-11-1-1-1-1-1-1111-1-11-1-1-1-1
χ3111111111111111111111111-1-111111111111-1-1-1111111-1i−i-1i−iii−i−i-1-1-1i−i-1i−ii−i
χ4111111111111111111111111-1-111111111111-1-1-1111111-1−ii-1−ii−i−iii-1-1-1−ii-1−ii−ii
χ511111111111-1-11111111111111-1-1-1-1-1111111111-1-1-1-1-1-11111111111-1-1111-1-1-1-1-1
χ611111111111-1-11111111111111-1-1-1-1-1111111111-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-11-1-1-11111
χ711111111111-1-111111111111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1i−i-1i−iii−i−i11-1i−i1−ii−ii
χ811111111111-1-111111111111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1−ii-1−ii−i−iii11-1−ii1i−ii−i
χ911111-1111111111-1-1-1-1-1111111-11111-1-1-1-111111-1-1-1-111-1111-1-1111111-1-1-1-111-1-1
χ1011111-1111111111-1-1-1-1-1111111-11111-1-1-1-111111-1-1-1-111-1-1-1111-1-1-1-111-111-1-1-111
χ1111111-1111111111-1-1-1-1-11111-1-1-11111-1-1-1-111-1-1-1-1-1-1-1111i−i-1−iiii−i−i-1-11−ii1i−i−ii
χ1211111-1111111111-1-1-1-1-11111-1-1-11111-1-1-1-111-1-1-1-1-1-1-1111−ii-1i−i−i−iii-1-11i−i1−iii−i
χ1311111-111111-1-111-1-1-1-1-11111111-1-1-1-1-1-1-1-1111111111-1-1-1111-1-11111-1-1-1-1-11-1-111
χ1411111-111111-1-111-1-1-1-1-11111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1111-1-1-1-1-1-1-111111-1-1
χ1511111-111111-1-111-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-111-1-1-11111-1-11i−i-1−iiii−i−i111−ii-1−iii−i
χ1611111-111111-1-111-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-111-1-1-11111-1-11−ii-1i−i−i−iii111i−i-1i−i−ii
χ17222-2202222-22-2220000022-2-222022220000-2-2-2220000-2-2000-2000000-2200000000
χ18222-2202222-22-2220000022-2-2-2-2022220000-2-22-2-20000-2-200020000002-200000000
χ19222-2202222-2-22220000022-2-2220-2-2-2-20000-2-2-222000022000-20000002-200000000
χ20222-2202222-2-22220000022-2-2-2-20-2-2-2-20000-2-22-2-20000220002000000-2200000000
χ2122-12-122222-100-1-1-12222-1-1222200000-1-1-1-1-1-12-1-1000000222-122-1-1-1-100-1-1-100000
χ2222-12-122222-100-1-1-12222-1-1222200000-1-1-1-1-1-12-1-10000002-2-2-1-2-2111100-11100000
χ2322-12-122222-100-1-1-12222-1-122-2-200000-1-1-1-1-1-1-211000000-22i−2i12i−2i−i−iii001−ii00000
χ2422-12-122222-100-1-1-12222-1-122-2-200000-1-1-1-1-1-1-211000000-2−2i2i1−2i2iii−i−i001i−i00000
χ2522-12-1-22222-100-1-11-2-2-2-2-1-12222000001111-1-12-1-1000000-222-1-2-2-1-1-1-10011100000
χ2622-12-1-22222-100-1-11-2-2-2-2-1-12222000001111-1-12-1-1000000-2-2-2-1221111001-1-100000
χ2722-12-1-22222-100-1-11-2-2-2-2-1-122-2-2000001111-1-1-21100000022i−2i1−2i2i−i−iii00-1i−i00000
χ2822-12-1-22222-100-1-11-2-2-2-2-1-122-2-2000001111-1-1-2110000002−2i2i12i−2iii−i−i00-1−ii00000
χ294444441-21-24441-2411-2-21-21-200411-2-211-2-21-200011-2-21-200000000000000000000
χ304444441-21-24-4-41-2411-2-21-21-200-4-1-12211-2-21-2000-1-122-1200000000000000000000
χ31444444-21-21444-214-2-211-21-21004-2-211-2-211-21000-2-211-2100000000000000000000
χ32444444-21-214-4-4-214-2-211-21-2100-422-1-1-2-211-2100022-1-12-100000000000000000000
χ3344444-41-21-24441-2-4-1-1221-21-200-411-2-2-1-1221-2000-1-1221-200000000000000000000
χ3444444-41-21-24-4-41-2-4-1-1221-21-2004-1-122-1-1221-200011-2-2-1200000000000000000000
χ3544444-4-21-21444-21-422-1-1-21-2100-4-2-21122-1-1-2100022-1-1-2100000000000000000000
χ3644444-4-21-214-4-4-21-422-1-1-21-2100422-1-122-1-1-21000-2-2112-100000000000000000000
χ37444-4401-21-2-44-41-203-3001-2-1200011-2-23-300-120003-300-1200000000000000000000
χ38444-4401-21-2-44-41-20-33001-2-1200011-2-2-3300-12000-3300-1200000000000000000000
χ39444-4401-21-2-4-441-203-3001-2-12000-1-1223-300-12000-33001-200000000000000000000
χ40444-4401-21-2-4-441-20-33001-2-12000-1-122-3300-120003-3001-200000000000000000000
χ41444-440-21-21-44-4-210003-3-212-1000-2-211003-32-1000003-32-100000000000000000000
χ42444-440-21-21-44-4-21000-33-212-1000-2-21100-332-100000-332-100000000000000000000
χ43444-440-21-21-4-44-210003-3-212-100022-1-1003-32-100000-33-2100000000000000000000
χ44444-440-21-21-4-44-21000-33-212-100022-1-100-332-1000003-3-2100000000000000000000
χ4544-2-4-204444200-2-200000-2-2-4-44400000000022-4-2-200000000020000000000000000
χ4644-2-4-204444200-2-200000-2-2-4-4-4-400000000022422000000000-20000000000000000
χ474-440-4044-4-40004400000-4-4004i−4i0000000000004i−4i00000000000000000000000000
χ484-440-4044-4-40004400000-4-400−4i4i000000000000−4i4i00000000000000000000000000
χ494-4-202044-4-4000-2-20000022004i−4i000000000000−2i2i000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ110000000000
χ504-4-202044-4-4000-2-20000022004i−4i000000000000−2i2i000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ110000000000
χ514-4-202044-4-4000-2-2000002200−4i4i0000000000002i−2i000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ110000000000
χ524-4-202044-4-4000-2-2000002200−4i4i0000000000002i−2i000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ110000000000
χ5388-48-482-42-4-400-12-422-4-4-122-40000000-1-122-1200000000000000000000000000000
χ5488-48-48-42-42-4002-1-4-4-4222-1-42000000022-1-12-100000000000000000000000000000
χ5588-48-4-82-42-4-400-124-2-244-122-4000000011-2-2-1200000000000000000000000000000
χ5688-48-4-8-42-42-4002-1444-2-22-1-420000000-2-2112-100000000000000000000000000000
χ5788-4-8-402-42-4400-1206-600-12-240000000-33001-200000000000000000000000000000
χ5888-4-8-402-42-4400-120-6600-12-2400000003-3001-200000000000000000000000000000
χ5988-4-8-40-42-424002-10006-62-14-2000000000-33-2100000000000000000000000000000
χ6088-4-8-40-42-424002-1000-662-14-20000000003-3-2100000000000000000000000000000
χ618-880-802-4-240002-400000-24000006-60000000000000000000000000000000000000
χ628-880-802-4-240002-400000-2400000-660000000000000000000000000000000000000
χ638-880-80-424-2000-42000004-200000006-600000000000000000000000000000000000
χ648-880-80-424-2000-42000004-20000000-6600000000000000000000000000000000000
χ6516-16-80804-8-48000-24000002-400000000000000000000000000000000000000000000
χ6616-16-8080-848-40004-200000-4200000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.