Finite Group Databasebeta

← Group #13165380

Character table — Group #13165380

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122224444444466888888889999121212121212121212121212181818181818181824242424242424242424242424242424363636363636363654545454545472727272
order12223666336666664433666666222244441212121212121212444466661212121212121212121212121212121244441212121244444412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-1-111-1-1
χ3111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-111
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ51111111111111111-1-111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111-1-111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111
χ71111111111111111-1-1111111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1
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
χ91-11-111-1-111-1-111-1-11-11111-1-1-1-1-1-111i−ii−iii−i−iii−i−i11-1-11-1-1111-1-1i−ii−iii−i−iii−i−ii−ii−i11-1-11-111-1-1i−ii−i
χ101-11-111-1-111-1-111-1-11-11111-1-1-1-1-1-111i−i−iiii−i−i−i−iii-1-1111-1-1111-1-1i−i−iiii−i−i−i−iiii−i−ii-1-1111-1-1-111i−i−ii
χ111-11-111-1-111-1-111-1-11-11111-1-1-1-1-1-111−iii−i−i−iiiii−i−i-1-1111-1-1111-1-1−iii−i−i−iiiii−i−i−iii−i-1-1111-1-1-111−iii−i
χ121-11-111-1-111-1-111-1-11-11111-1-1-1-1-1-111−ii−ii−i−iii−i−iii11-1-11-1-1111-1-1−ii−ii−i−iii−i−iii−ii−ii11-1-11-111-1-1−ii−ii
χ131-11-111-1-111-1-111-1-1-111111-1-1-1-1-1-111i−ii−iii−i−iii−i−i11-1-11-1-11-1-111i−ii−iii−i−iii−i−i−ii−ii11-1-1-11-1-111−ii−ii
χ141-11-111-1-111-1-111-1-1-111111-1-1-1-1-1-111i−i−iiii−i−i−i−iii-1-1111-1-11-1-111i−i−iiii−i−i−i−iii−iii−i-1-111-1111-1-1−iii−i
χ151-11-111-1-111-1-111-1-1-111111-1-1-1-1-1-111−iii−i−i−iiiii−i−i-1-1111-1-11-1-111−iii−i−i−iiiii−i−ii−i−ii-1-111-1111-1-1i−i−ii
χ161-11-111-1-111-1-111-1-1-111111-1-1-1-1-1-111−ii−ii−i−iii−i−iii11-1-11-1-11-1-111−ii−ii−i−iii−i−iiii−ii−i11-1-1-11-1-111i−ii−i
χ1722222222222222222222222222-2-2-2-20000000000000000-2-2-2-2222200000000000000000000-2-200000000
χ182222222222222222-2-222222222-2-2-2-20000000000000000-2-2-2-2-2-2-2-2000000000000000000002200000000
χ192222-1-1-1-12222222200-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-100002222-1-1-1-1-1-1-1-10000-1-1-1-10000000000
χ202222-1-1-1-12222222200-1-1-1-1-1-1-1-1222222-2-2-1-1-1-11111-2-2-2-2-1-1-1-1000022-2-2-1-1-1-11111000011110000000000
χ212222-1-1-1-12222222200-1-1-1-1-1-1-1-12222-2-2221111-1-1-1-1-2-2-2-2-1-1-1-10000-2-2221111-1-1-1-1000011110000000000
χ222222-1-1-1-12222222200-1-1-1-1-1-1-1-12222-2-2-2-2111111112222-1-1-1-10000-2-2-2-2111111110000-1-1-1-10000000000
χ2322-2-22-22-22222-2-2-2-20022-2-222-2-22-22-20000000000002-22-2-22-22000000000000000000002-22-20000000000
χ2422-2-22-22-22222-2-2-2-20022-2-222-2-22-22-2000000000000-22-22-22-2200000000000000000000-22-220000000000
χ2522-2-22-22-22222-2-2-2-20022-2-222-2-2-22-2200000000000000002-22-2000000000000000000000000002-22-20000
χ2622-2-22-22-22222-2-2-2-20022-2-222-2-2-22-2200000000000000002-22-200000000000000000000000000-22-220000
χ2722-2-2-11-112222-2-2-2-200-1-111-1-1112-22-200003−33−33−33−32-22-21-11-1000000003−33−33−33−30000-11-110000000000
χ2822-2-2-11-112222-2-2-2-200-1-111-1-1112-22-200003−33−3−33−33-22-221-11-1000000003−33−3−33−3300001-11-10000000000
χ2922-2-2-11-112222-2-2-2-200-1-111-1-1112-22-20000−33−333−33−3-22-221-11-100000000−33−333−33−300001-11-10000000000
χ3022-2-2-11-112222-2-2-2-200-1-111-1-1112-22-20000−33−33−33−332-22-21-11-100000000−33−33−33−330000-11-110000000000
χ312-22-222-2-222-2-222-2-22-22222-2-2-2-222-2-20000000000000000-222-222-2-200000000000000000000-2200000000
χ322-22-222-2-222-2-222-2-2-222222-2-2-2-222-2-20000000000000000-222-2-2-222000000000000000000002-200000000
χ332-22-2-1-11122-2-222-2-200-1-1-1-11111-2-2222i−2i2i−2i−i−iii−i−iii22-2-2-111-100002i−2i2i−2i−i−iii−i−iii0000-1-1110000000000
χ342-22-2-1-11122-2-222-2-200-1-1-1-11111-2-2222i−2i−2i2i−i−iiiii−i−i-2-222-111-100002i−2i−2i2i−i−iiiii−i−i000011-1-10000000000
χ352-22-2-1-11122-2-222-2-200-1-1-1-11111-2-222−2i2i2i−2iii−i−i−i−iii-2-222-111-10000−2i2i2i−2iii−i−i−i−iii000011-1-10000000000
χ362-22-2-1-11122-2-222-2-200-1-1-1-11111-2-222−2i2i−2i2iii−i−iii−i−i22-2-2-111-10000−2i2i−2i2iii−i−iii−i−i0000-1-1110000000000
χ372-2-222-2-2222-2-2-2-2220022-2-2-2-2222-2-22000000000000000022-2-2000000000000000000000000002-2-220000
χ382-2-222-2-2222-2-2-2-2220022-2-2-2-2222-2-22000000000000000022-2-200000000000000000000000000-222-20000
χ392-2-222-2-2222-2-2-2-2220022-2-2-2-222-222-20000000000002-2-22-2-222000000000000000000002-2-220000000000
χ402-2-222-2-2222-2-2-2-2220022-2-2-2-222-222-2000000000000-222-2-2-22200000000000000000000-222-20000000000
χ412-2-22-111-122-2-2-2-22200-1-11111-1-1-222-20000−i3i3i3−i3−i3i3i3−i32-2-2211-1-100000000−i3i3i3−i3−i3i3i3−i30000-111-10000000000
χ422-2-22-111-122-2-2-2-22200-1-11111-1-1-222-20000−i3i3i3−i3i3−i3−i3i3-222-211-1-100000000−i3i3i3−i3i3−i3−i3i300001-1-110000000000
χ432-2-22-111-122-2-2-2-22200-1-11111-1-1-222-20000i3−i3−i3i3−i3i3i3−i3-222-211-1-100000000i3−i3−i3i3−i3i3i3−i300001-1-110000000000
χ442-2-22-111-122-2-2-2-22200-1-11111-1-1-222-20000i3−i3−i3i3i3−i3−i3i32-2-2211-1-100000000i3−i3−i3i3i3−i3−i3i30000-111-10000000000
χ45444444441-21-21-21-2441-21-21-21-20000002200002222000000001-21-200-1-10000-1-1-1-10022000000000000-1-1
χ46444444441-21-21-21-2441-21-21-21-2000000-2-20000-2-2-2-2000000001-21-200110000111100-2-200000000000011
χ47444444441-21-21-21-2-4-41-21-21-21-2000000220000222200000000-12-1200-1-10000-1-1-1-100-2-200000000000011
χ48444444441-21-21-21-2-4-41-21-21-21-2000000-2-20000-2-2-2-200000000-12-120011000011110022000000000000-1-1
χ4944444444-21-21-21-2144-21-21-21-21000022002222000000000000-21-21-1-100-1-1-1-1000022000000000000-1-100
χ5044444444-21-21-21-2144-21-21-21-210000-2-200-2-2-2-2000000000000-21-21110011110000-2-20000000000001100
χ5144444444-21-21-21-21-4-4-21-21-21-210000220022220000000000002-12-1-1-100-1-1-1-10000-2-20000000000001100
χ5244444444-21-21-21-21-4-4-21-21-21-210000-2-200-2-2-2-20000000000002-12-111001111000022000000000000-1-100
χ534444-2-2-2-24444444400-2-2-2-2-2-2-2-2-4-4-4-4000000000000000022220000000000000000000000000000000000
χ5444-4-4-22-224444-4-4-4-400-2-222-2-222-44-440000000000000000-22-220000000000000000000000000000000000
χ554-44-444-4-41-2-121-2-124-41-21-2-12-120000002i−2i00002i2i−2i−2i000000001-2-1200−ii0000−i−iii002i−2i000000000000−ii
χ564-44-444-4-41-2-121-2-124-41-21-2-12-12000000−2i2i0000−2i−2i2i2i000000001-2-1200i−i0000ii−i−i00−2i2i000000000000i−i
χ574-44-444-4-41-2-121-2-12-441-21-2-12-120000002i−2i00002i2i−2i−2i00000000-121-200−ii0000−i−iii00−2i2i000000000000i−i
χ584-44-444-4-41-2-121-2-12-441-21-2-12-12000000−2i2i0000−2i−2i2i2i00000000-121-200i−i0000ii−i−i002i−2i000000000000−ii
χ594-44-444-4-4-212-1-212-14-4-21-212-12-100002i−2i002i2i−2i−2i000000000000-212-1−ii00−i−iii00002i−2i000000000000−ii00
χ604-44-444-4-4-212-1-212-14-4-21-212-12-10000−2i2i00−2i−2i2i2i000000000000-212-1i−i00ii−i−i0000−2i2i000000000000i−i00
χ614-44-444-4-4-212-1-212-1-44-21-212-12-100002i−2i002i2i−2i−2i0000000000002-1-21−ii00−i−iii0000−2i2i000000000000i−i00
χ624-44-444-4-4-212-1-212-1-44-21-212-12-10000−2i2i00−2i−2i2i2i0000000000002-1-21i−i00ii−i−i00002i−2i000000000000−ii00
χ634-44-4-2-22244-4-444-4-400-2-2-2-2222244-4-400000000000000002-2-220000000000000000000000000000000000
χ644-4-44-222-244-4-4-4-44400-2-22222-2-24-4-440000000000000000-2-2220000000000000000000000000000000000
χ658888-4-4-4-42-42-42-42-400-12-12-12-12000000440000-2-2-2-200000000000000-2-200001111000000000000000000
χ668888-4-4-4-42-42-42-42-400-12-12-12-12000000-4-40000222200000000000000220000-1-1-1-1000000000000000000
χ678888-4-4-4-4-42-42-42-42002-12-12-12-100004400-2-2-2-20000000000000000-2-20011110000000000000000000000
χ688888-4-4-4-4-42-42-42-42002-12-12-12-10000-4-400222200000000000000002200-1-1-1-10000000000000000000000
χ6988-8-88-88-82-42-4-24-24002-4-242-4-240000000000000000000000000000000000000000000000000000000000
χ7088-8-88-88-8-42-424-24-200-424-2-424-20000000000000000000000000000000000000000000000000000000000
χ7188-8-8-44-442-42-4-24-2400-121-2-121-200000000000023−2323−2300000000000000000000−33−33000000000000000000
χ7288-8-8-44-442-42-4-24-2400-121-2-121-2000000000000−2323−2323000000000000000000003−33−3000000000000000000
χ7388-8-8-44-44-42-424-24-2002-1-212-1-210000000023−2323−2300000000000000000000−33−330000000000000000000000
χ7488-8-8-44-44-42-424-24-2002-1-212-1-2100000000−2323−2323000000000000000000003−33−30000000000000000000000
χ758-88-8-4-4442-4-242-4-2400-12-121-21-20000004i−4i0000−2i−2i2i2i00000000000000−2i2i0000ii−i−i000000000000000000
χ768-88-8-4-4442-4-242-4-2400-12-121-21-2000000−4i4i00002i2i−2i−2i000000000000002i−2i0000−i−iii000000000000000000
χ778-88-8-4-444-424-2-424-2002-12-1-21-2100004i−4i00−2i−2i2i2i0000000000000000−2i2i00ii−i−i0000000000000000000000
χ788-88-8-4-444-424-2-424-2002-12-1-21-210000−4i4i002i2i−2i−2i00000000000000002i−2i00−i−iii0000000000000000000000
χ798-8-888-8-882-4-24-242-4002-4-24-242-40000000000000000000000000000000000000000000000000000000000
χ808-8-888-8-88-424-24-2-4200-424-24-2-420000000000000000000000000000000000000000000000000000000000
χ818-8-88-444-42-4-24-242-400-121-21-2-12000000000000−2i32i32i3−2i300000000000000000000i3−i3−i3i3000000000000000000
χ828-8-88-444-42-4-24-242-400-121-21-2-120000000000002i3−2i3−2i32i300000000000000000000−i3i3i3−i3000000000000000000
χ838-8-88-444-4-424-24-2-42002-1-21-212-100000000−2i32i32i3−2i300000000000000000000i3−i3−i3i30000000000000000000000
χ848-8-88-444-4-424-24-2-42002-1-21-212-1000000002i3−2i3−2i32i300000000000000000000−i3i3i3−i30000000000000000000000

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