Finite Group Databasebeta

← Group #13166537

Character table — Group #13166537

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size11222444444668888888991216161616161616161818181818181824242424272727273636363636363636484854545454727272108108108
order123462336612883366612122246666661212466888824242424444424412242424241212448861212444
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-11111-1-1-1-11-1-11-1-1-1-111-1-1111-1-11-1-1
χ311111111111111111111-1-1111111111-1-1-1ii−i−i1111ii−i−i-1i−i-1ii−i−i11i−i-1-1-1i−i-1i−i
χ411111111111111111111-1-1111111111-1-1-1−i−iii1111−i−iii-1−ii-1−i−iii11−ii-1-1-1−ii-1−ii
χ511111111111-1-1111111111-1111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-1-1
χ611111111111-1-1111111111-111111111111-1-1-1-1-1-1-1-111111-1-11-1-1-1-1-1-111-1-11-1-1-111
χ711111111111-1-11111111-1-1-111111111-1-1-1ii−i−i-1-1-1-1−i−iii-1i−i-1ii−i−i-1-1−ii11-1i−i1−ii
χ811111111111-1-11111111-1-1-111111111-1-1-1−i−iii-1-1-1-1ii−i−i-1−ii-1−i−iii-1-1i−i11-1−ii1i−i
χ911111-1111111111-1111111-1-1-1-1-1-1-111111111111111111-1-1-111111-1-11111-1-1-1-1-1-1
χ1011111-1111111111-1111111-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1111-1-1-1-1-1-1-1-111-111-111
χ1111111-1111111111-11111-1-1-1-1-1-1-1-1-111-1-1-1ii−i−i1111ii−i−i1−ii-1ii−i−i-1-1i−i-1-11−ii1−ii
χ1211111-1111111111-11111-1-1-1-1-1-1-1-1-111-1-1-1−i−iii1111−i−iii1i−i-1−i−iii-1-1−ii-1-11i−i1i−i
χ1311111-111111-1-111-11111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1111
χ1411111-111111-1-111-11111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111-1111-1-1-1-11111-1-1-1111-1-1
χ1511111-111111-1-111-11111-1-11-1-1-1-1-1-111-1-1-1ii−i−i-1-1-1-1−i−iii1−ii-1ii−i−i11−ii111−ii-1i−i
χ1611111-111111-1-111-11111-1-11-1-1-1-1-1-111-1-1-1−i−iii-1-1-1-1ii−i−i1i−i-1−i−iii11i−i111i−i-1−ii
χ17222-2202222-20022022-2-2220000000-2-2-222000000002222000-2000000-2-200000000
χ18222-2202222-20022022-2-2220000000-2-2-22200000000-2-2-2-2000-20000002200000000
χ19222-2202222-20022022-2-2-2-20000000-2-22-2-2000000002i2i−2i−2i0002000000−2i2i00000000
χ20222-2202222-20022022-2-2-2-20000000-2-22-2-200000000−2i−2i2i2i00020000002i−2i00000000
χ2122-12-122222-100-1-1-1-1-12222022-1-1-1-1-1-12-1-1222200000000222-1-1-1-1-1000000-1-1-1000
χ2222-12-122222-100-1-1-1-1-12222022-1-1-1-1-1-12-1-1-2-2-2-2000000002-2-2-11111000000-111000
χ2322-12-122222-100-1-1-1-1-122-2-2022-1-1-1-1-1-1-2112i2i−2i−2i00000000-22i−2i1−i−iii0000001−ii000
χ2422-12-122222-100-1-1-1-1-122-2-2022-1-1-1-1-1-1-211−2i−2i2i2i00000000-2−2i2i1ii−i−i0000001i−i000
χ2522-12-1-22222-100-1-11-1-122220-2-21111-1-12-1-1222200000000-2-2-2-1-1-1-1-1000000111000
χ2622-12-1-22222-100-1-11-1-122220-2-21111-1-12-1-1-2-2-2-200000000-222-111110000001-1-1000
χ2722-12-1-22222-100-1-11-1-122-2-20-2-21111-1-1-2112i2i−2i−2i000000002−2i2i1−i−iii000000-1i−i000
χ2822-12-1-22222-100-1-11-1-122-2-20-2-21111-1-1-211−2i−2i2i2i0000000022i−2i1ii−i−i000000-1−ii000
χ292-220-2022-2-20−i2i2220-2-2002-20000000000-222−22−2−i2−i2i2i22i−2i2i−2i00002−22−20000−i2i2000000
χ302-220-2022-2-20−i2i2220-2-2002-20000000000-22−22−22−i2−i2i2i2−2i2i−2i2i0000−22−220000−i2i2000000
χ312-220-2022-2-20−i2i2220-2-200-2200000000002-2−i2i2i2−i2−i2−i2i2i22-2-220000−i2i2i2−i20000i2−i2000000
χ322-220-2022-2-20−i2i2220-2-200-2200000000002-2i2−i2−i2i2−i2−i2i2i2-222-20000i2−i2−i2i20000i2−i2000000
χ332-220-2022-2-20i2−i2220-2-2002-20000000000-222−22−2i2i2−i2−i2−2i2i−2i2i00002−22−20000i2−i2000000
χ342-220-2022-2-20i2−i2220-2-2002-20000000000-22−22−22i2i2−i2−i22i−2i2i−2i0000−22−220000i2−i2000000
χ352-220-2022-2-20i2−i2220-2-200-2200000000002-2−i2i2i2−i2i2i2−i2−i2-222-20000−i2i2i2−i20000−i2i2000000
χ362-220-2022-2-20i2−i2220-2-200-2200000000002-2i2−i2−i2i2i2i2−i2−i22-2-220000i2−i2−i2i20000−i2i2000000
χ374444441-21-24441-241-21-20041-211-2-21-200000001-21-20000000000001-20000000000
χ384444441-21-24-4-41-241-21-200-41-211-2-21-20000000-12-12000000000000-120000000000
χ39444444-21-21444-214-21-21004-21-2-211-210000000-21-21000000000000-210000000000
χ40444444-21-214-4-4-214-21-2100-4-21-2-211-2100000002-12-10000000000002-10000000000
χ4144444-41-21-24441-2-41-21-200-4-12-1-1221-200000001-21-2000000000000-120000000000
χ4244444-41-21-24-4-41-2-41-21-2004-12-1-1221-20000000-12-120000000000001-20000000000
χ4344444-4-21-21444-21-4-21-2100-42-122-1-1-210000000-21-210000000000002-10000000000
χ4444444-4-21-214-4-4-21-4-21-210042-122-1-1-2100000002-12-1000000000000-210000000000
χ4544-2-4-204444200-2-20-2-2-4-444000000022-4-2-200000000000000020000000000000000
χ4644-2-4-204444200-2-20-2-2-4-4-4-4000000022422000000000000000-20000000000000000
χ474-4-202044-4-4000-2-2022004-400000000002-222−2222−22000000000000−22−22000000000000
χ484-4-202044-4-4000-2-2022004-400000000002-2−2222−22220000000000002−22−2000000000000
χ494-4-202044-4-4000-2-202200-440000000000-22−2i22i22i2−2i2000000000000i2−i2−i2i2000000000000
χ504-4-202044-4-4000-2-202200-440000000000-222i2−2i2−2i22i2000000000000−i2i2i2−i2000000000000
χ51888-8802-42-4-8002-402-4-24000000000-2400000000000000000000000000000000000
χ52888-880-42-42-800-420-424-20000000004-200000000000000000000000000000000000
χ5388-48-482-42-4-400-12-4-122-40002-4-1-122-1200000000000000000000000000000000000
χ5488-48-48-42-42-4002-1-42-1-42000-4222-1-12-100000000000000000000000000000000000
χ5588-48-4-82-42-4-400-124-122-4000-2411-2-2-1200000000000000000000000000000000000
χ5688-48-4-8-42-42-4002-142-1-420004-2-2-2112-100000000000000000000000000000000000
χ5788-4-8-402-42-4400-120-12-2400000−3i33i3001-200000000000000000000000000000000000
χ5888-4-8-402-42-4400-120-12-24000003i3−3i3001-200000000000000000000000000000000000
χ5988-4-8-40-42-424002-102-14-20000000−3i33i3-2100000000000000000000000000000000000
χ6088-4-8-40-42-424002-102-14-200000003i3−3i3-2100000000000000000000000000000000000
χ618-880-802-4-240−4i24i22-40-2400000000000000000000−i22i2i2−2i2000000000000000000000000
χ628-880-802-4-2404i2−4i22-40-2400000000000000000000i2−2i2−i22i2000000000000000000000000
χ638-880-80-424-20−4i24i2-4204-2000000000000000000002i2−i2−2i2i2000000000000000000000000
χ648-880-80-424-204i2−4i2-4204-200000000000000000000−2i2i22i2−i2000000000000000000000000
χ6516-16-80804-8-48000-2402-4000000000000000000000000000000000000000000000000
χ6616-16-8080-848-40004-20-42000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).