Finite Group Databasebeta

← Group #13165410

Character table — Group #13165410

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122224444444466888888889999121212121212121212121212181818181818181824242424242424242424242424242424363636363636363654545454545472727272
order12223666336666664433666666222244441212121212121212444466661212121212121212121212121212121244441212121244444412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111
χ3111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ51111111111111111-1-11111111111111111111111111111111111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111-1-111111111111111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111-1-1111111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-111
χ81111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111
χ91-11-11-11-111-1-11-11-1i−i111-1-1-11-11-1-111-1i−i11-1-1ii−i−iii−i−i11-1-11-1i−ii−ii−i11-1-1ii−i−i1-1i−iii−i−ii−i11-1-11-1i−i
χ101-11-11-11-111-1-11-11-1i−i111-1-1-11-11-1-111-1−ii11-1-1−i−iii−i−iii11-1-11-1i−i−iii−i11-1-1−i−iii-11i−i−i−iiii−i-1-111-11i−i
χ111-11-11-11-111-1-11-11-1i−i111-1-1-11-11-1-11-11i−i-1-111ii−i−i−i−iii11-1-1-11i−ii−ii−i-1-111ii−i−i1-1−ii−i−iiii−i-1-1111-1−ii
χ121-11-11-11-111-1-11-11-1i−i111-1-1-11-11-1-11-11−ii-1-111−i−iiiii−i−i11-1-1-11i−i−iii−i-1-111−i−iii-11−iiii−i−ii−i11-1-1-11−ii
χ131-11-11-11-111-1-11-11-1−ii111-1-1-11-11-1-111-1i−i11-1-1ii−i−iii−i−i11-1-11-1−iii−i−ii11-1-1ii−i−i-11−iiii−i−i−ii-1-111-11−ii
χ141-11-11-11-111-1-11-11-1−ii111-1-1-11-11-1-111-1−ii11-1-1−i−iii−i−iii11-1-11-1−ii−ii−ii11-1-1−i−iii1-1−ii−i−iii−ii11-1-11-1−ii
χ151-11-11-11-111-1-11-11-1−ii111-1-1-11-11-1-11-11i−i-1-111ii−i−i−i−iii11-1-1-11−iii−i−ii-1-111ii−i−i-11i−i−i−iii−ii11-1-1-11i−i
χ161-11-11-11-111-1-11-11-1−ii111-1-1-11-11-1-11-11−ii-1-111−i−iiiii−i−i11-1-1-11−ii−ii−ii-1-111−i−iii1-1i−iii−i−i−ii-1-1111-1i−i
χ1722222222222222222222222222-2-2-2-20000000000000000-2-2-2-2002200220000000000000000-2-200000000
χ182222222222222222-2-222222222-2-2-2-20000000000000000-2-2-2-200-2-200-2-200000000000000002200000000
χ192222-1-1-1-12222222200-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-122002200-1-1-1-1-1-1-1-10000-1-1-1-10000000000
χ202222-1-1-1-12222222200-1-1-1-1-1-1-1-1222222-2-2-1-1-1-11111-2-2-2-2-1-1-1-12200-2-200-1-1-1-11111000011110000000000
χ212222-1-1-1-12222222200-1-1-1-1-1-1-1-12222-2-2221111-1-1-1-1-2-2-2-2-1-1-1-1-2-20022001111-1-1-1-1000011110000000000
χ222222-1-1-1-12222222200-1-1-1-1-1-1-1-12222-2-2-2-2111111112222-1-1-1-1-2-200-2-200111111110000-1-1-1-10000000000
χ2322-2-222-2-22222-2-2-2-20022-222-2-2-22-22-20000000000002-22-22-2-22000000000000000000002-22-20000000000
χ2422-2-222-2-22222-2-2-2-20022-222-2-2-22-22-2000000000000-22-222-2-2200000000000000000000-22-220000000000
χ2522-2-222-2-22222-2-2-2-20022-222-2-2-2-22-220000000000000000-222-2000000000000000000000000002-22-20000
χ2622-2-222-2-22222-2-2-2-20022-222-2-2-2-22-220000000000000000-222-200000000000000000000000000-22-220000
χ2722-2-2-1-1112222-2-2-2-200-1-11-1-11112-22-200003−33−33−33−32-22-2-111-1000000003−33−33−33−30000-11-110000000000
χ2822-2-2-1-1112222-2-2-2-200-1-11-1-11112-22-200003−33−3−33−33-22-22-111-1000000003−33−3−33−3300001-11-10000000000
χ2922-2-2-1-1112222-2-2-2-200-1-11-1-11112-22-20000−33−333−33−3-22-22-111-100000000−33−333−33−300001-11-10000000000
χ3022-2-2-1-1112222-2-2-2-200-1-11-1-11112-22-20000−33−33−33−332-22-2-111-100000000−33−33−33−330000-11-110000000000
χ312-22-22-22-222-2-22-22-22i−2i222-2-2-22-2-222-20000000000000000-2-222002i−2i002i−2i0000000000000000−2i2i00000000
χ322-22-22-22-222-2-22-22-2−2i2i222-2-2-22-2-222-20000000000000000-2-22200−2i2i00−2i2i00000000000000002i−2i00000000
χ332-22-2-11-1122-2-22-22-200-1-1-1111-112-2-222-22i−2i-1-111−i−iii2i2i−2i−2i-1-1112-2002i−2i00-1-111−i−iii0000−i−iii0000000000
χ342-22-2-11-1122-2-22-22-200-1-1-1111-112-2-222-2−2i2i-1-111ii−i−i−2i−2i2i2i-1-1112-200−2i2i00-1-111ii−i−i0000ii−i−i0000000000
χ352-22-2-11-1122-2-22-22-200-1-1-1111-112-2-22-222i−2i11-1-1−i−iii−2i−2i2i2i-1-111-22002i−2i0011-1-1−i−iii0000ii−i−i0000000000
χ362-22-2-11-1122-2-22-22-200-1-1-1111-112-2-22-22−2i2i11-1-1ii−i−i2i2i−2i−2i-1-111-2200−2i2i0011-1-1ii−i−i0000−i−iii0000000000
χ372-2-222-2-2222-2-2-22-220022-2-2-22-2222-2-20000000000002i−2i−2i2i2-22-2000000000000000000002i−2i−2i2i0000000000
χ382-2-222-2-2222-2-2-22-220022-2-2-22-2222-2-2000000000000−2i2i2i−2i2-22-200000000000000000000−2i2i2i−2i0000000000
χ392-2-222-2-2222-2-2-22-220022-2-2-22-22-2-2220000000000000000-22-22000000000000000000000000002-2-220000
χ402-2-222-2-2222-2-2-22-220022-2-2-22-22-2-2220000000000000000-22-2200000000000000000000000000-222-20000
χ412-2-22-111-122-2-2-22-2200-1-1111-11-122-2-200003−3−33−i3i3i3−i3−2i2i2i−2i-11-11000000003−3−33−i3i3i3−i30000i−i−ii0000000000
χ422-2-22-111-122-2-2-22-2200-1-1111-11-122-2-200003−3−33i3−i3−i3i32i−2i−2i2i-11-11000000003−3−33i3−i3−i3i30000−iii−i0000000000
χ432-2-22-111-122-2-2-22-2200-1-1111-11-122-2-20000−333−3−i3i3i3−i32i−2i−2i2i-11-1100000000−333−3−i3i3i3−i30000−iii−i0000000000
χ442-2-22-111-122-2-2-22-2200-1-1111-11-122-2-20000−333−3i3−i3−i3i3−2i2i2i−2i-11-1100000000−333−3i3−i3−i3i30000i−i−ii0000000000
χ45444444441-21-21-2-21441-2-21-211-2000022002222000000000000-1-1-2-20011-1-1-1-100000022000000000000-1-1
χ46444444441-21-21-2-21441-2-21-211-20000-2-200-2-2-2-200000000000011-2-200111111000000-2-200000000000011
χ47444444441-21-21-2-21-4-41-2-21-211-2000022002222000000000000-1-12200-1-1-1-1-1-1000000-2-200000000000011
χ48444444441-21-21-2-21-4-41-2-21-211-20000-2-200-2-2-2-2000000000000112200-1-1111100000022000000000000-1-1
χ4944444444-21-21-211-244-211-21-2-210000002200002222000000000011-1-1-2-20000-1-1-1-122000000000000-1-100
χ5044444444-21-21-211-244-211-21-2-21000000-2-20000-2-2-2-200000000001111-2-200001111-2-20000000000001100
χ5144444444-21-21-211-2-4-4-211-21-2-2100000022000022220000000000-1-1-1-1220000-1-1-1-1-2-20000000000001100
χ5244444444-21-21-211-2-4-4-211-21-2-21000000-2-20000-2-2-2-20000000000-1-111220000111122000000000000-1-100
χ534444-2-2-2-24444444400-2-2-2-2-2-2-2-2-4-4-4-4000000000000000022220000000000000000000000000000000000
χ5444-4-4-2-2224444-4-4-4-400-2-22-2-2222-44-4400000000000000002-2-220000000000000000000000000000000000
χ554-44-44-44-41-2-1212-2-14i−4i1-2-2-12-11200002-20022-2-2000000000000-11−2i2i00i−i-1-1110000002i−2i000000000000−ii
χ564-44-44-44-41-2-1212-2-14i−4i1-2-2-12-1120000-2200-2-2220000000000001-1−2i2i00i−i11-1-1000000−2i2i000000000000i−i
χ574-44-44-44-41-2-1212-2-1−4i4i1-2-2-12-11200002-20022-2-2000000000000-112i−2i00−ii-1-111000000−2i2i000000000000i−i
χ584-44-44-44-41-2-1212-2-1−4i4i1-2-2-12-1120000-2200-2-2220000000000001-12i−2i00−ii11-1-10000002i−2i000000000000−ii
χ594-44-44-44-4-212-1-2-1124i−4i-2112-12-2-10000002i−2i00002i2i−2i−2i0000000000i−i−ii−2i2i0000−i−iii2-2000000000000-1100
χ604-44-44-44-4-212-1-2-1124i−4i-2112-12-2-1000000−2i2i0000−2i−2i2i2i0000000000i−ii−i−2i2i0000ii−i−i-220000000000001-100
χ614-44-44-44-4-212-1-2-112−4i4i-2112-12-2-10000002i−2i00002i2i−2i−2i0000000000−ii−ii2i−2i0000−i−iii-220000000000001-100
χ624-44-44-44-4-212-1-2-112−4i4i-2112-12-2-1000000−2i2i0000−2i−2i2i2i0000000000−iii−i2i−2i0000ii−i−i2-2000000000000-1100
χ634-44-4-22-2244-4-44-44-400-2-2-2222-22-444-4000000000000000022-2-20000000000000000000000000000000000
χ644-4-44-222-244-4-4-44-4400-2-2222-22-2-4-44400000000000000002-22-20000000000000000000000000000000000
χ658888-4-4-4-42-42-42-4-4200-122-12-1-1200004400-2-2-2-2000000000000-2-200000011110000000000000000000000
χ668888-4-4-4-42-42-42-4-4200-122-12-1-120000-4-400222200000000000022000000-1-1-1-10000000000000000000000
χ678888-4-4-4-4-42-42-422-4002-1-12-122-1000000440000-2-2-2-2000000000000-2-20000001111000000000000000000
χ688888-4-4-4-4-42-42-422-4002-1-12-122-1000000-4-40000222200000000000022000000-1-1-1-1000000000000000000
χ6988-8-888-8-82-42-4-244-2002-442-4-2-240000000000000000000000000000000000000000000000000000000000
χ7088-8-888-8-8-42-424-2-2400-42-2-4244-20000000000000000000000000000000000000000000000000000000000
χ7188-8-8-4-4442-42-4-244-200-12-2-1211-20000000023−2323−2300000000000000000000−33−330000000000000000000000
χ7288-8-8-4-4442-42-4-244-200-12-2-1211-200000000−2323−2323000000000000000000003−33−30000000000000000000000
χ7388-8-8-4-444-42-424-2-24002-112-1-2-2100000000000023−2323−2300000000000000000000−33−33000000000000000000
χ7488-8-8-4-444-42-424-2-24002-112-1-2-21000000000000−2323−2323000000000000000000003−33−3000000000000000000
χ758-88-8-44-442-4-2424-4-200-1221-21-1-200004-400-2-222000000000000-2200000011-1-10000000000000000000000
χ768-88-8-44-442-4-2424-4-200-1221-21-1-20000-440022-2-20000000000002-2000000-1-1110000000000000000000000
χ778-88-8-44-44-424-2-4-224002-1-1-21-2210000004i−4i0000−2i−2i2i2i000000000000−2i2i000000ii−i−i000000000000000000
χ788-88-8-44-44-424-2-4-224002-1-1-21-221000000−4i4i00002i2i−2i−2i0000000000002i−2i000000−i−iii000000000000000000
χ798-8-888-8-882-4-24-2-442002-44-242-2-40000000000000000000000000000000000000000000000000000000000
χ808-8-888-8-88-424-242-2-400-42-24-2-4420000000000000000000000000000000000000000000000000000000000
χ818-8-88-444-42-4-24-2-44200-12-21-2-1120000000023−23−232300000000000000000000−333−30000000000000000000000
χ828-8-88-444-42-4-24-2-44200-12-21-2-11200000000−232323−23000000000000000000003−3−330000000000000000000000
χ838-8-88-444-4-424-242-2-4002-11-212-2-1000000000000−2i32i32i3−2i300000000000000000000i3−i3−i3i3000000000000000000
χ848-8-88-444-4-424-242-2-4002-11-212-2-10000000000002i3−2i3−2i32i300000000000000000000−i3i3i3−i3000000000000000000

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