Finite Group Databasebeta

← Group #13165406

Character table — Group #13165406

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122224444444466888888889999121212121212121212121212181818181818181824242424242424242424242424242424363636363636363654545454545472727272
order122236663366666644336666662222444412121212121212124444666612121212121212121212121212121212224412121212444444661212
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
χ3111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-111
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ51111111111111111-1-111111111111111111111111111111111-1-111-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111-1-111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111
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
χ91-11-111-1-111-11-1-1-11i−i1111-1-1-1-11-11-1i−ii−iii−i−iii−i−i11-1-11-1-11i−ii−ii−ii−iii−i−iii−i−i1-11-111-1-1i−iii−i−i1-11-1
χ101-11-111-1-111-11-1-1-11i−i1111-1-1-1-11-11-1i−i−iiii−i−i−i−iii-1-1111-1-11i−ii−ii−i−iiii−i−i−i−iii1-1-11-1-111i−i−i−iii1-1-11
χ111-11-111-1-111-11-1-1-11i−i1111-1-1-1-11-11-1−iii−i−i−iiiii−i−i-1-1111-1-11i−i−iii−ii−i−i−iiiii−i−i-111-1-1-111i−i−i−iii-111-1
χ121-11-111-1-111-11-1-1-11i−i1111-1-1-1-11-11-1−ii−ii−i−iii−i−iii11-1-11-1-11i−i−iii−i−ii−i−iii−i−iii-11-1111-1-1i−iii−i−i-11-11
χ131-11-111-1-111-11-1-1-11−ii1111-1-1-1-11-11-1i−ii−iii−i−iii−i−i11-1-11-1-11−iii−i−iii−iii−i−iii−i−i-11-1111-1-1−ii−i−iii-11-11
χ141-11-111-1-111-11-1-1-11−ii1111-1-1-1-11-11-1i−i−iiii−i−i−i−iii-1-1111-1-11−iii−i−ii−iiii−i−i−i−iii-111-1-1-111−iiii−i−i-111-1
χ151-11-111-1-111-11-1-1-11−ii1111-1-1-1-11-11-1−iii−i−i−iiiii−i−i-1-1111-1-11−ii−ii−iii−i−i−iiiii−i−i1-1-11-1-111−iiii−i−i1-1-11
χ161-11-111-1-111-11-1-1-11−ii1111-1-1-1-11-11-1−ii−ii−i−iii−i−iii11-1-11-1-11−ii−ii−ii−ii−i−iii−i−iii1-11-111-1-1−ii−i−iii1-11-1
χ1722222222222222222222222222-2-2-2-20000000000000000-2-2-2-2220022000000000000000000-2-200000000
χ182222222222222222-2-222222222-2-2-2-20000000000000000-2-2-2-2-2-200-2-20000000000000000002200000000
χ192222-1-1-1-12222222200-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-100220022-1-1-1-1-1-1-1-10000-1-1-1-10000000000
χ202222-1-1-1-12222222200-1-1-1-1-1-1-1-1222222-2-2-1-1-1-11111-2-2-2-2-1-1-1-1002200-2-2-1-1-1-11111000011110000000000
χ212222-1-1-1-12222222200-1-1-1-1-1-1-1-12222-2-2221111-1-1-1-1-2-2-2-2-1-1-1-100-2-200221111-1-1-1-1000011110000000000
χ222222-1-1-1-12222222200-1-1-1-1-1-1-1-12222-2-2-2-2111111112222-1-1-1-100-2-200-2-2111111110000-1-1-1-10000000000
χ2322-2-22-22-2222-22-2-2-20022-2-22-22-22-2-220000000000002i−2i2i−2i22-2-2000000000000000000002i−2i2i−2i0000000000
χ2422-2-22-22-2222-22-2-2-20022-2-22-22-22-2-22000000000000−2i2i−2i2i22-2-200000000000000000000−2i2i−2i2i0000000000
χ2522-2-22-22-2222-22-2-2-20022-2-22-22-2-222-20000000000000000-2-222000000000000000000000000002i−2i2i−2i0000
χ2622-2-22-22-2222-22-2-2-20022-2-22-22-2-222-20000000000000000-2-22200000000000000000000000000−2i2i−2i2i0000
χ2722-2-2-11-11222-22-2-2-200-1-111-11-112-2-220000−i3i3−i3i33−33−32i−2i2i−2i-1-11100000000−i3i3−i3i33−33−30000−ii−ii0000000000
χ2822-2-2-11-11222-22-2-2-200-1-111-11-112-2-220000−i3i3−i3i3−33−33−2i2i−2i2i-1-11100000000−i3i3−i3i3−33−330000i−ii−i0000000000
χ2922-2-2-11-11222-22-2-2-200-1-111-11-112-2-220000i3−i3i3−i33−33−3−2i2i−2i2i-1-11100000000i3−i3i3−i33−33−30000i−ii−i0000000000
χ3022-2-2-11-11222-22-2-2-200-1-111-11-112-2-220000i3−i3i3−i3−33−332i−2i2i−2i-1-11100000000i3−i3i3−i3−33−330000−ii−ii0000000000
χ312-22-222-2-222-22-2-2-222i−2i2222-2-2-2-2-22-220000000000000000-222-22i−2i002i−2i000000000000000000−2i2i00000000
χ322-22-222-2-222-22-2-2-22−2i2i2222-2-2-2-2-22-220000000000000000-222-2−2i2i00−2i2i0000000000000000002i−2i00000000
χ332-22-2-1-11122-22-2-2-2200-1-1-1-111112-22-22i−2i2i−2i−i−iii−i−iii22-2-2-111-1002i−2i002i−2i−i−iii−i−iii0000-1-1110000000000
χ342-22-2-1-11122-22-2-2-2200-1-1-1-111112-22-22i−2i−2i2i−i−iiiii−i−i-2-222-111-1002i−2i00−2i2i−i−iiiii−i−i000011-1-10000000000
χ352-22-2-1-11122-22-2-2-2200-1-1-1-111112-22-2−2i2i2i−2iii−i−i−i−iii-2-222-111-100−2i2i002i−2iii−i−i−i−iii000011-1-10000000000
χ362-22-2-1-11122-22-2-2-2200-1-1-1-111112-22-2−2i2i−2i2iii−i−iii−i−i22-2-2-111-100−2i2i00−2i2iii−i−iii−i−i0000-1-1110000000000
χ372-2-222-2-2222-2-2-222-20022-2-2-22-2222-2-20000000000002i−2i−2i2i2-22-2000000000000000000002i−2i−2i2i0000000000
χ382-2-222-2-2222-2-2-222-20022-2-2-22-2222-2-2000000000000−2i2i2i−2i2-22-200000000000000000000−2i2i2i−2i0000000000
χ392-2-222-2-2222-2-2-222-20022-2-2-22-22-2-2220000000000000000-22-22000000000000000000000000002-2-220000
χ402-2-222-2-2222-2-2-222-20022-2-2-22-22-2-2220000000000000000-22-2200000000000000000000000000-222-20000
χ412-2-22-111-122-2-2-222-200-1-1111-11-122-2-200003−3−33−i3i3i3−i3−2i2i2i−2i-11-11000000003−3−33−i3i3i3−i30000i−i−ii0000000000
χ422-2-22-111-122-2-2-222-200-1-1111-11-122-2-200003−3−33i3−i3−i3i32i−2i−2i2i-11-11000000003−3−33i3−i3−i3i30000−iii−i0000000000
χ432-2-22-111-122-2-2-222-200-1-1111-11-122-2-20000−333−3−i3i3i3−i32i−2i−2i2i-11-1100000000−333−3−i3i3i3−i30000−iii−i0000000000
χ442-2-22-111-122-2-2-222-200-1-1111-11-122-2-20000−333−3i3−i3−i3i3−2i2i2i−2i-11-1100000000−333−3i3−i3−i3i30000i−i−ii0000000000
χ45444444441-21-2-2-211441-21-21-2-21000000220000222200000000-2-20011-1-10000-1-1-1-10022000000000000-1-1
χ46444444441-21-2-2-211441-21-21-2-21000000-2-20000-2-2-2-200000000-2-20011110000111100-2-200000000000011
χ47444444441-21-2-2-211-4-41-21-21-2-210000002200002222000000002200-1-1-1-10000-1-1-1-100-2-200000000000011
χ48444444441-21-2-2-211-4-41-21-21-2-21000000-2-20000-2-2-2-2000000002200-1-111000011110022000000000000-1-1
χ4944444444-21-2111-2-244-21-21-211-200002200222200000000000011-1-1-2-200-1-1-1-1000022000000000000-1-100
χ5044444444-21-2111-2-244-21-21-211-20000-2-200-2-2-2-20000000000001111-2-20011110000-2-20000000000001100
χ5144444444-21-2111-2-2-4-4-21-21-211-2000022002222000000000000-1-1-1-12200-1-1-1-10000-2-20000000000001100
χ5244444444-21-2111-2-2-4-4-21-21-211-20000-2-200-2-2-2-2000000000000-1-11122001111000022000000000000-1-100
χ534444-2-2-2-24444444400-2-2-2-2-2-2-2-2-4-4-4-4000000000000000022220000000000000000000000000000000000
χ5444-4-4-22-22444-44-4-4-400-2-222-22-22-444-4000000000000000022-2-20000000000000000000000000000000000
χ554-44-444-4-41-2-1-222-114i−4i1-21-2-122-10000002i−2i00002i2i−2i−2i00000000−2i2i00i−i−ii0000−i−iii002-2000000000000-11
χ564-44-444-4-41-2-1-222-114i−4i1-21-2-122-1000000−2i2i0000−2i−2i2i2i00000000−2i2i00i−ii−i0000ii−i−i00-220000000000001-1
χ574-44-444-4-41-2-1-222-11−4i4i1-21-2-122-10000002i−2i00002i2i−2i−2i000000002i−2i00−ii−ii0000−i−iii00-220000000000001-1
χ584-44-444-4-41-2-1-222-11−4i4i1-21-2-122-1000000−2i2i0000−2i−2i2i2i000000002i−2i00−iii−i0000ii−i−i002-2000000000000-11
χ594-44-444-4-4-2121-1-12-24i−4i-21-212-1-1200002i−2i002i2i−2i−2i000000000000i−i−ii−2i2i00−i−iii00002-2000000000000-1100
χ604-44-444-4-4-2121-1-12-24i−4i-21-212-1-120000−2i2i00−2i−2i2i2i000000000000i−ii−i−2i2i00ii−i−i0000-220000000000001-100
χ614-44-444-4-4-2121-1-12-2−4i4i-21-212-1-1200002i−2i002i2i−2i−2i000000000000−ii−ii2i−2i00−i−iii0000-220000000000001-100
χ624-44-444-4-4-2121-1-12-2−4i4i-21-212-1-120000−2i2i00−2i−2i2i2i000000000000−iii−i2i−2i00ii−i−i00002-2000000000000-1100
χ634-44-4-2-22244-44-4-4-4400-2-2-2-22222-44-4400000000000000002-2-220000000000000000000000000000000000
χ644-4-44-222-244-4-4-444-400-2-2222-22-2-4-44400000000000000002-22-20000000000000000000000000000000000
χ658888-4-4-4-42-42-4-4-42200-12-12-122-1000000440000-2-2-2-200000000000000-2-200001111000000000000000000
χ668888-4-4-4-42-42-4-4-42200-12-12-122-1000000-4-40000222200000000000000220000-1-1-1-1000000000000000000
χ678888-4-4-4-4-42-4222-4-4002-12-12-1-1200004400-2-2-2-200000000000000-2-2000011110000000000000000000000
χ688888-4-4-4-4-42-4222-4-4002-12-12-1-120000-4-400222200000000000000220000-1-1-1-10000000000000000000000
χ6988-8-88-88-82-424-44-2-2002-4-2424-4-20000000000000000000000000000000000000000000000000000000000
χ7088-8-88-88-8-42-4-22-24400-424-2-4-2240000000000000000000000000000000000000000000000000000000000
χ7188-8-8-44-442-424-44-2-200-121-2-1-22100000000000023−2323−2300000000000000000000−33−33000000000000000000
χ7288-8-8-44-442-424-44-2-200-121-2-1-221000000000000−2323−2323000000000000000000003−33−3000000000000000000
χ7388-8-8-44-44-42-4-22-244002-1-2121-1-200000000−2i32i3−2i32i300000000000000000000i3−i3i3−i30000000000000000000000
χ7488-8-8-44-44-42-4-22-244002-1-2121-1-2000000002i3−2i32i3−2i300000000000000000000−i3i3−i3i30000000000000000000000
χ758-88-8-4-4442-4-2-444-2200-12-121-2-210000004i−4i0000−2i−2i2i2i00000000000000−2i2i0000ii−i−i000000000000000000
χ768-88-8-4-4442-4-2-444-2200-12-121-2-21000000−4i4i00002i2i−2i−2i000000000000002i−2i0000−i−iii000000000000000000
χ778-88-8-4-444-4242-2-24-4002-12-1-211-200004i−4i00−2i−2i2i2i00000000000000−2i2i0000ii−i−i0000000000000000000000
χ788-88-8-4-444-4242-2-24-4002-12-1-211-20000−4i4i002i2i−2i−2i000000000000002i−2i0000−i−iii0000000000000000000000
χ798-8-888-8-882-4-244-42-2002-4-24-2-4420000000000000000000000000000000000000000000000000000000000
χ808-8-888-8-88-424-2-22-4400-424-242-2-40000000000000000000000000000000000000000000000000000000000
χ818-8-88-444-42-4-244-42-200-121-212-2-1000000000000−2i32i32i3−2i300000000000000000000i3−i3−i3i3000000000000000000
χ828-8-88-444-42-4-244-42-200-121-212-2-10000000000002i3−2i3−2i32i300000000000000000000−i3i3i3−i3000000000000000000
χ838-8-88-444-4-424-2-22-44002-1-21-2-1120000000023−23−232300000000000000000000−333−30000000000000000000000
χ848-8-88-444-4-424-2-22-44002-1-21-2-11200000000−232323−23000000000000000000003−3−330000000000000000000000

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