Finite Group Databasebeta

← Group #13166527

Character table — Group #13166527

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112223344444468888888888899121212121216161616161618181818181818242424242424272736363636363636365454545454727272108108108
order12346442336612233666666612122241212121266661212466888866121212124424412242424242888861212444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1111111111-1-11-1-1-1-11-1-1-1-11-1-11-1-1
χ31111111111111111111111111-1-111111111111-1-1-1ii−i−i111111-1-1-1i−i-1ii−i−i-1ii−i−i-1i−i-1i−i
χ41111111111111111111111111-1-111111111111-1-1-1−i−iii111111-1-1-1−ii-1−i−iii-1−i−iii-1−ii-1−ii
χ51111111-111111111-1-1-1-1-1111111-11111-1-1-1-111111111111-1-1-1-111-1-1-11111111111-1-1-1-1-1-1
χ61111111-111111111-1-1-1-1-1111111-11111-1-1-1-111111-1-1-1-111-1-1-1-111-1111-1-1-1-11-1-1-1-1-111-111
χ71111111-111111111-1-1-1-1-11111-1-1-11111-1-1-1-111-1-1-1ii−i−i11-1-1-1-1-1-11−ii-1ii−i−i-1ii−i−i1−ii1−ii
χ81111111-111111111-1-1-1-1-11111-1-1-11111-1-1-1-111-1-1-1−i−iii11-1-1-1-1-1-11i−i-1−i−iii-1−i−iii1i−i1i−i
χ911111-1-1111111-11111111111111-1-1-1-1-11111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1111-1-1-1
χ1011111-1-1111111-11111111111111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-111111-1-1-111
χ1111111-1-1111111-111111111111-1-1-1-1-1-1-1111111-1-1-1ii−i−i-1-1-1-1-1-111-1i−i-1ii−i−i1−i−iii-1i−i1−ii
χ1211111-1-1111111-111111111111-1-1-1-1-1-1-1111111-1-1-1−i−iii-1-1-1-1-1-111-1−ii-1−i−iii1ii−i−i-1−ii1i−i
χ1311111-1-1-111111-111-1-1-1-1-11111111-1-1-1-1-1-1-1-1111111111-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1-1111
χ1411111-1-1-111111-111-1-1-1-1-11111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111-1-1-1111-1-1-1-1-11111-1111-1-1
χ1511111-1-1-111111-111-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-111-1-1-1ii−i−i-1-11111111−ii-1ii−i−i1−i−iii1−ii-1i−i
χ1611111-1-1-111111-111-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-111-1-1-1−i−iii-1-11111111i−i-1−i−iii1ii−i−i1i−i-1−ii
χ17222-222202222-2-2220000022-2-222022220000-2-2-2220000-2-2000022000-20000-20000000000
χ18222-222202222-2-2220000022-2-2-2-2022220000-2-22-2-20000-2-20000-2-20002000020000000000
χ19222-22-2-202222-22220000022-2-2220-2-2-2-20000-2-2-2220000220000-2-2000-2000020000000000
χ20222-22-2-202222-22220000022-2-2-2-20-2-2-2-20000-2-22-2-200002200002200020000-20000000000
χ2122-12-10022222-10-1-1-12222-1-1222200000-1-1-1-1-1-12-1-1222200000000222-1-1-1-1-100000-1-1-1000
χ2222-12-10022222-10-1-1-12222-1-1222200000-1-1-1-1-1-12-1-1-2-2-2-2000000002-2-2-1111100000-111000
χ2322-12-10022222-10-1-1-12222-1-122-2-200000-1-1-1-1-1-1-2112i2i−2i−2i00000000-22i−2i1−i−iii000001−ii000
χ2422-12-10022222-10-1-1-12222-1-122-2-200000-1-1-1-1-1-1-211−2i−2i2i2i00000000-2−2i2i1ii−i−i000001i−i000
χ2522-12-100-22222-10-1-11-2-2-2-2-1-12222000001111-1-12-1-1222200000000-2-2-2-1-1-1-1-100000111000
χ2622-12-100-22222-10-1-11-2-2-2-2-1-12222000001111-1-12-1-1-2-2-2-200000000-222-11111000001-1-1000
χ2722-12-100-22222-10-1-11-2-2-2-2-1-122-2-2000001111-1-1-2112i2i−2i−2i000000002−2i2i1−i−iii00000-1i−i000
χ2822-12-100-22222-10-1-11-2-2-2-2-1-122-2-2000001111-1-1-211−2i−2i2i2i0000000022i−2i1ii−i−i00000-1−ii000
χ292-220-22i−2i022-2-2002200000-2-2002-202i2i−2i−2i0000000-222−22−20000002i−2i00002−22−20i2−i2i2−i2000000
χ302-220-22i−2i022-2-2002200000-2-2002-202i2i−2i−2i0000000-22−22−220000002i−2i0000−22−220−i2i2−i2i2000000
χ312-220-22i−2i022-2-2002200000-2-200-2202i2i−2i−2i00000002-2i2−i2−i2i2000000−2i2i0000i2−i2−i2i20−222−2000000
χ322-220-22i−2i022-2-2002200000-2-200-2202i2i−2i−2i00000002-2−i2i2i2−i2000000−2i2i0000−i2i2i2−i202−2−22000000
χ332-220-2−2i2i022-2-2002200000-2-2002-20−2i−2i2i2i0000000-222−22−2000000−2i2i00002−22−20−i2i2−i2i2000000
χ342-220-2−2i2i022-2-2002200000-2-2002-20−2i−2i2i2i0000000-22−22−22000000−2i2i0000−22−220i2−i2i2−i2000000
χ352-220-2−2i2i022-2-2002200000-2-200-220−2i−2i2i2i00000002-2i2−i2−i2i20000002i−2i0000i2−i2−i2i202−2−22000000
χ362-220-2−2i2i022-2-2002200000-2-200-220−2i−2i2i2i00000002-2−i2i2i2−i20000002i−2i0000−i2i2i2−i20−222−2000000
χ37444444441-21-2441-2411-2-21-21-20041-21-211-2-21-200000001-211-2-2000000000000000000000
χ3844444444-21-2144-214-2-211-21-21004-21-21-2-211-210000000-21-2-211000000000000000000000
χ394444444-41-21-2441-2-4-1-1221-21-200-41-21-2-1-1221-200000001-2-1-122000000000000000000000
χ404444444-4-21-2144-21-422-1-1-21-2100-4-21-2122-1-1-210000000-2122-1-1000000000000000000000
χ4144444-4-441-21-24-41-2411-2-21-21-200-4-12-1211-2-21-20000000-12-1-122000000000000000000000
χ4244444-4-44-21-214-4-214-2-211-21-2100-42-12-1-2-211-2100000002-122-1-1000000000000000000000
χ4344444-4-4-41-21-24-41-2-4-1-1221-21-2004-12-12-1-1221-20000000-1211-2-2000000000000000000000
χ4444444-4-4-4-21-214-4-21-422-1-1-21-210042-12-122-1-1-2100000002-1-2-211000000000000000000000
χ45444-444401-21-2-4-41-203-3001-2-120001-21-23-300-120000000-123-300000000000000000000000
χ46444-444401-21-2-4-41-20-33001-2-120001-21-2-3300-120000000-12-3300000000000000000000000
χ47444-44440-21-21-4-4-210003-3-212-1000-21-21003-32-100000002-1003-3000000000000000000000
χ48444-44440-21-21-4-4-21000-33-212-1000-21-2100-332-100000002-100-33000000000000000000000
χ49444-44-4-401-21-2-441-203-3001-2-12000-12-123-300-1200000001-2-3300000000000000000000000
χ50444-44-4-401-21-2-441-20-33001-2-12000-12-12-3300-1200000001-23-300000000000000000000000
χ51444-44-4-40-21-21-44-210003-3-212-10002-12-1003-32-10000000-2100-33000000000000000000000
χ52444-44-4-40-21-21-44-21000-33-212-10002-12-100-332-10000000-21003-3000000000000000000000
χ5344-2-4-2000444420-2-200000-2-2-4-44400000000022-4-2-20000000000000002000000000000000
χ5444-2-4-2000444420-2-200000-2-2-4-4-4-400000000022422000000000000000-2000000000000000
χ554-4-20200044-4-400-2-20000022004-40000000000002-222−2222−22000000000000−22−2200000000000
χ564-4-20200044-4-400-2-20000022004-40000000000002-2−2222−22220000000000002−22−200000000000
χ574-4-20200044-4-400-2-2000002200-44000000000000-222i2−2i2−2i22i2000000000000−i2i2i2−i200000000000
χ584-4-20200044-4-400-2-2000002200-44000000000000-22−2i22i22i2−2i2000000000000i2−i2−i2i200000000000
χ5988-48-40082-42-4-40-12-422-4-4-122-40000000-1-122-120000000000000000000000000000000000
χ6088-48-4008-42-42-402-1-4-4-4222-1-42000000022-1-12-10000000000000000000000000000000000
χ6188-48-400-82-42-4-40-124-2-244-122-4000000011-2-2-120000000000000000000000000000000000
χ6288-48-400-8-42-42-402-1444-2-22-1-420000000-2-2112-10000000000000000000000000000000000
χ6388-4-8-40002-42-440-1206-600-12-240000000-33001-20000000000000000000000000000000000
χ6488-4-8-40002-42-440-120-6600-12-2400000003-3001-20000000000000000000000000000000000
χ6588-4-8-4000-42-42402-10006-62-14-2000000000-33-210000000000000000000000000000000000
χ6688-4-8-4000-42-42402-1000-662-14-20000000003-3-210000000000000000000000000000000000
χ678-880-88i−8i02-4-24002-400000-24000002i−4i−2i4i0000000000000000000000000000000000000000
χ688-880-88i−8i0-424-200-42000004-200000−4i2i4i−2i0000000000000000000000000000000000000000
χ698-880-8−8i8i02-4-24002-400000-2400000−2i4i2i−4i0000000000000000000000000000000000000000
χ708-880-8−8i8i0-424-200-42000004-2000004i−2i−4i2i0000000000000000000000000000000000000000
χ7116-16-8080004-8-4800-24000002-40000000000000000000000000000000000000000000000000
χ7216-16-808000-848-4004-200000-420000000000000000000000000000000000000000000000000

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