Finite Group Databasebeta

← Group #13140624

Character table — Group #13140624

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444466666666881212121212121212121212121818181818181818242424242424242436363636363636363636363636363636363636363636363672727272
order12223446662212123366666666366666661212121244441212121266666612124444448888121212121212242424242424242412121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111-1-11111111111-1-11-1-1-1-1111111111111111-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111-1-11111111111-1-11-1-1-1-1111111111111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1
χ71111111111-1-11111111111-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-1111111-1-1
χ81111111111-1-11111111111-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111111111-1-1-1-1-1-111
χ91-11-111-1-1-111-1-1111-111-1-1-11-1111-1-1-1-1111-1-1i−ii−iii−i−i1-111-1-11-11-1i−ii−i1-1i−ii−iii−i−i11-1-1ii−i−i1-1i−i
χ101-11-111-1-1-111-1-1111-111-1-1-11-1111-1-1-1-1111-1-1i−ii−iii−i−i1-111-1-11-1-11i−i−ii-11−iii−iii−i−i-1-111−i−iii-11−ii
χ111-11-111-1-1-111-1-1111-111-1-1-11-1111-1-1-1-1111-1-1−ii−ii−i−iii1-111-1-11-11-1−ii−ii1-1−ii−ii−i−iii11-1-1−i−iii1-1−ii
χ121-11-111-1-1-111-1-1111-111-1-1-11-1111-1-1-1-1111-1-1−ii−ii−i−iii1-111-1-11-1-11−iii−i-11i−i−ii−i−iii-1-111ii−i−i-11i−i
χ131-11-111-1-1-11-11-1111-111-1-1-1-111-1-111-1-1111-1-1i−ii−iii−i−i-11-1-1111-11-1−iii−i-11−iii−i−i−iii-1-111−i−iii1-1i−i
χ141-11-111-1-1-11-11-1111-111-1-1-1-111-1-111-1-1111-1-1i−ii−iii−i−i-11-1-1111-1-11−ii−ii1-1i−ii−i−i−iii11-1-1ii−i−i-11−ii
χ151-11-111-1-1-11-11-1111-111-1-1-1-111-1-111-1-1111-1-1−ii−ii−i−iii-11-1-1111-11-1i−i−ii-11i−i−iiii−i−i-1-111ii−i−i1-1−ii
χ161-11-111-1-1-11-11-1111-111-1-1-1-111-1-111-1-1111-1-1−ii−ii−i−iii-11-1-1111-1-11i−ii−i1-1−ii−iiii−i−i11-1-1−i−iii-11i−i
χ17222222222222222-122-1-12-122-1-1-1-1-1-1-1-12-1-122222-1-1-1-122-1-1-1-1-1-10022000000-1-1-1-1-1-1000000000000
χ18222222222222222-122-1-12-122-1-1-1-1-1-1-1-12-1-12-2-2-2-2111122-1-1-1-1-1-100-2-2000000111111000000000000
χ1922222222222222-12-1-122-1222-12222-1-1-1-122-100000000-1-1-1-1-1-1-1-100002200220000000000-1-1-1-100-1-1
χ2022222222222222-12-1-122-1222-12222-1-1-1-122-100000000-1-1-1-1-1-1-1-10000-2-200-2-2000000000011110011
χ212222222222-2-2222-122-1-12-1-2-2-11111-1-1-12-1-122222-1-1-1-1-2-21111-1-100-2-2000000-1-11111000000000000
χ222222222222-2-2222-122-1-12-1-2-2-11111-1-1-12-1-12-2-2-2-21111-2-21111-1-1002200000011-1-1-1-1000000000000
χ232222222222-2-222-12-1-122-12-2-2-1-2-2-2-2-1-1-1-122-100000000111111-1-100002200-2-20000000000111100-1-1
χ242222222222-2-222-12-1-122-12-2-2-1-2-2-2-2-1-1-1-122-100000000111111-1-10000-2-200220000000000-1-1-1-10011
χ2522222-2-222200-2-2222222220020000222-2-2-2-222-2-2-2-2-2-2000000-2-20000000000220000000000000000
χ2622222-2-222200-2-2222222220020000222-2-2-2-2-2-2222222000000-2-20000000000-2-20000000000000000
χ2722222-2-222200-2-22-122-1-12-100-1−i3i3−i3i3-1-1-1-211-222-2-2111100−i3i3−i3i3110000000000-1-1−i3i3−i3i3000000000000
χ2822222-2-222200-2-22-122-1-12-100-1−i3i3−i3i3-1-1-1-211-2-2-222-1-1-1-100−i3i3−i3i311000000000011i3−i3i3−i3000000000000
χ2922222-2-222200-2-22-122-1-12-100-1i3−i3i3−i3-1-1-1-211-222-2-2111100i3−i3i3−i3110000000000-1-1i3−i3i3−i3000000000000
χ3022222-2-222200-2-22-122-1-12-100-1i3−i3i3−i3-1-1-1-211-2-2-222-1-1-1-100i3−i3i3−i311000000000011−i3i3−i3i3000000000000
χ312-22-222-2-2-222-2-222-1-22-11-212-2-1-1-11111-12-11-22i−2i2i−2i−i−iii2-2-1-111-11002i−2i000000−ii−i−iii000000000000
χ322-22-222-2-2-222-2-222-1-22-11-212-2-1-1-11111-12-11-2−2i2i−2i2iii−i−i2-2-1-111-1100−2i2i000000i−iii−i−i000000000000
χ332-22-222-2-2-222-2-22-121-12-21-22-2-122-2-211-1-12-2100000000-11-1-111-1100002i−2i002i−2i0000000000−i−iii00−ii
χ342-22-222-2-2-222-2-22-121-12-21-22-2-122-2-211-1-12-2100000000-11-1-111-110000−2i2i00−2i2i0000000000ii−i−i00i−i
χ352-22-222-2-2-22-22-222-1-22-11-21-22-111-1-111-12-11-22i−2i2i−2i−i−iii-2211-1-1-1100−2i2i000000−iiii−i−i000000000000
χ362-22-222-2-2-22-22-222-1-22-11-21-22-111-1-111-12-11-2−2i2i−2i2iii−i−i-2211-1-1-11002i−2i000000i−i−i−iii000000000000
χ372-22-222-2-2-22-22-22-121-12-21-2-22-1-2-22211-1-12-21000000001-111-1-1-1100002i−2i00−2i2i0000000000ii−i−i00−ii
χ382-22-222-2-2-22-22-22-121-12-21-2-22-1-2-22211-1-12-21000000001-111-1-1-110000−2i2i002i−2i0000000000−i−iii00i−i
χ392-22-22-22-2-22002-222-222-2-2-20020000-2-22-2-2222i−2i−2i2i−2i−2i2i2i000000-2200000000002i−2i0000000000000000
χ402-22-22-22-2-22002-222-222-2-2-20020000-2-22-2-222−2i2i2i−2i2i2i−2i−2i000000-220000000000−2i2i0000000000000000
χ412-22-22-22-2-22002-22-1-22-11-2100-1−i3i3i3−i311-1-21-122i−2i−2i2iii−i−i00−i3i3i3−i31-10000000000−ii3−3−33000000000000
χ422-22-22-22-2-22002-22-1-22-11-2100-1−i3i3i3−i311-1-21-12−2i2i2i−2i−i−iii00−i3i3i3−i31-10000000000i−i−333−3000000000000
χ432-22-22-22-2-22002-22-1-22-11-2100-1i3−i3−i3i311-1-21-122i−2i−2i2iii−i−i00i3−i3−i3i31-10000000000−ii−333−3000000000000
χ442-22-22-22-2-22002-22-1-22-11-2100-1i3−i3−i3i311-1-21-12−2i2i2i−2i−i−iii00i3−i3−i3i31-10000000000i−i3−3−33000000000000
χ4544444444444444-2-2-2-2-2-2-2-2441-2-2-2-2111-2-2-2-200000000-2-21111110000000000000000000000000000
χ464444444444-4-444-2-2-2-2-2-2-2-2-4-412222111-2-2-2-20000000022-1-1-1-1110000000000000000000000000000
χ4744444-4-444400-4-4-24-2-244-2400-20000-2-2-22-4-4200000000000000220000000000000000000000000000
χ4844444-4-444400-4-4-2-2-2-2-2-2-2-2001−2i32i3−2i32i311122220000000000i3−i3i3−i3-1-10000000000000000000000000000
χ4944444-4-444400-4-4-2-2-2-2-2-2-2-20012i3−2i32i3−2i311122220000000000−i3i3−i3i3-1-10000000000000000000000000000
χ5044-4-44004-4-40000444-4-44-4-400400004-4-4000000000000000000000000000000000000000000000000
χ5144-4-44004-4-400004-24-42-2-4200-20000-2220000000023−2323−23000000000000000000000000000000000000
χ5244-4-44004-4-400004-24-42-2-4200-20000-22200000000−2323−2323000000000000000000000000000000000000
χ5344-4-44004-4-40000-24-22-442-400-20000-22200000000000000000000000000000000000000006−66−60000
χ5444-4-44004-4-40000-24-22-442-400-20000-2220000000000000000000000000000000000000000−66−660000
χ554-44-444-4-4-444-4-44-2-22-2-22224-41-2-222-1-11-2-22200000000-2211-1-11-10000000000000000000000000000
χ564-44-444-4-4-44-44-44-2-22-2-2222-44122-2-2-1-11-2-222000000002-2-1-1111-10000000000000000000000000000
χ574-44-44-44-4-44004-4-242-24-42-400-2000022-22-44-2000000000000002-20000000000000000000000000000
χ584-44-44-44-4-44004-4-2-22-2-2222001−2i32i32i3−2i3-1-1122-2-20000000000i3−i3−i3i3-110000000000000000000000000000
χ594-44-44-44-4-44004-4-2-22-2-22220012i3−2i3−2i32i3-1-1122-2-20000000000−i3i3i3−i3-110000000000000000000000000000
χ604-4-44400-44-4000044-4-4-4-4440040000-44-4000000000000000000000000000000000000000000000000
χ614-4-44400-44-400004-2-4-4224-200-200002-2200000000−2i32i32i3−2i3000000000000000000000000000000000000
χ624-4-44400-44-400004-2-4-4224-200-200002-22000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ634-4-44400-44-40000-2422-4-4-2400-200002-220000000000000000000000000000000000000000i6−i6−i6i60000
χ644-4-44400-44-40000-2422-4-4-2400-200002-220000000000000000000000000000000000000000−i6i6i6−i60000
χ656666-366-3-3-366-3-300000000-3-300000000000000000000000000002200002200000000-1-1-1-10000-1-100
χ666666-366-3-3-366-3-300000000-3-30000000000000000000000000000-2-20000-2-200000000111100001100
χ676666-366-3-3-3-6-6-3-300000000330000000000000000000000000000220000-2-20000000011110000-1-100
χ686666-366-3-3-3-6-6-3-300000000330000000000000000000000000000-2-200002200000000-1-1-1-100001100
χ696-66-6-36-633-36-63-300000000-3300000000000000000000000000002-200002-200000000-1-1110000-1100
χ706-66-6-36-633-36-63-300000000-330000000000000000000000000000-220000-220000000011-1-100001-100
χ716-66-6-36-633-3-663-3000000003-300000000000000000000000000002-20000-220000000011-1-10000-1100
χ726-66-6-36-633-3-663-3000000003-30000000000000000000000000000-2200002-200000000-1-11100001-100
χ7388-8-88008-8-80000-4-4-444-44400200002-2-2000000000000000000000000000000000000000000000000
χ748-8-88800-88-80000-4-44444-4-40020000-22-2000000000000000000000000000000000000000000000000
χ7512121212-6-12-12-6-6-60066000000000000000000000000000000000000000000000000000000000000000000
χ761212-12-12-600-66600000000000000000000000000000000000000000000000000000000006−66−600000000
χ771212-12-12-600-6660000000000000000000000000000000000000000000000000000000000−66−6600000000
χ7812-1212-12-6-121266-600-66000000000000000000000000000000000000000000000000000000000000000000
χ7912-12-1212-6006-6600000000000000000000000000000000000000000000000000000000006−6−6600000000
χ8012-12-1212-6006-660000000000000000000000000000000000000000000000000000000000−666−600000000

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