Finite Group Databasebeta

← Group #13137955

Character table — Group #13137955

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444466666666881212121212121212121212121818181818181818242424242424242436363636363636363636363636363636363636363636363672727272
order12223446664412123366666612123666121212121212121244441212121212121212121212124444448888121212121212242424242424242412121212
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
χ51111111111-1-11111111111-1-11111-1-1-1-1111111111111-1-111-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111-1-11111111111-1-11111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1
χ71111111111-1-11111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1111111-1-1
χ81111111111-1-11111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-111
χ91-1-1111-11-1-1i−i-1111-1-1-1-111i−i1-11-1ii−i−i11-1-1i−ii−iii−i−ii−i1-1ii−i−ii−i1-11-11-1i−ii−i11-1-111-1-1ii−i−ii−i1-1
χ101-1-1111-11-1-1i−i-1111-1-1-1-111i−i1-11-1ii−i−i11-1-1i−ii−iii−i−ii−i1-1ii−i−i−ii1-1-11-11−iii−i11-1-1-1-111−i−iii−ii-11
χ111-1-1111-11-1-1i−i-1111-1-1-1-111i−i1-11-1ii−i−i11-1-1−ii−ii−i−iiii−i1-1ii−i−ii−i-11-111-1−ii−ii-1-11111-1-1−i−iiii−i-11
χ121-1-1111-11-1-1i−i-1111-1-1-1-111i−i1-11-1ii−i−i11-1-1−ii−ii−i−iiii−i1-1ii−i−i−ii-111-1-11i−i−ii-1-111-1-111ii−i−i−ii1-1
χ131-1-1111-11-1-1−ii-1111-1-1-1-111−ii1-11-1−i−iii11-1-1i−ii−iii−i−i−ii1-1−i−iiii−i-111-1-11−iii−i-1-111-1-111−i−iiii−i1-1
χ141-1-1111-11-1-1−ii-1111-1-1-1-111−ii1-11-1−i−iii11-1-1i−ii−iii−i−i−ii1-1−i−iii−ii-11-111-1i−ii−i-1-11111-1-1ii−i−i−ii-11
χ151-1-1111-11-1-1−ii-1111-1-1-1-111−ii1-11-1−i−iii11-1-1−ii−ii−i−iii−ii1-1−i−iiii−i1-1-11-11i−i−ii11-1-1-1-111ii−i−ii−i-11
χ161-1-1111-11-1-1−ii-1111-1-1-1-111−ii1-11-1−i−iii11-1-1−ii−ii−i−iii−ii1-1−i−iii−ii1-11-11-1−ii−ii11-1-111-1-1−i−iii−ii1-1
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
χ1922222222222222-12-1-122-1222-1-1-1-12222-122-100000000-1-1-1-1-1-1-1-100002200220000000000-1-1-1-100-1-1
χ2022222222222222-12-1-122-1222-1-1-1-12222-122-100000000-1-1-1-1-1-1-1-10000-2-200-2-2000000000011110011
χ212222222222-2-2222-122-1-12-1-2-2-1-1-1-111112-1-122222-1-1-1-1-2-2-1-1111100-2-2000000-1-11111000000000000
χ222222222222-2-2222-122-1-12-1-2-2-1-1-1-111112-1-12-2-2-2-21111-2-2-1-11111002200000011-1-1-1-1000000000000
χ232222222222-2-222-12-1-122-12-2-2-1-1-1-1-2-2-2-2-122-10000000011-1-1111100002200-2-20000000000111100-1-1
χ242222222222-2-222-12-1-122-12-2-2-1-1-1-1-2-2-2-2-122-10000000011-1-111110000-2-200220000000000-1-1-1-10011
χ2522222-2-222200-2-2222222220022220000-2-2-2-222-2-2-2-2-2-200-2-200000000000000220000000000000000
χ2622222-2-222200-2-2222222220022220000-2-2-2-2-2-222222200-2-200000000000000-2-20000000000000000
χ2722222-2-222200-2-22-122-1-12-100-1-1-1-1−i3i3−i3i3-211-222-2-211110011−i3i3−i3i30000000000-1-1−i3i3−i3i3000000000000
χ2822222-2-222200-2-22-122-1-12-100-1-1-1-1−i3i3−i3i3-211-2-2-222-1-1-1-10011−i3i3−i3i3000000000011i3−i3i3−i3000000000000
χ2922222-2-222200-2-22-122-1-12-100-1-1-1-1i3−i3i3−i3-211-222-2-211110011i3−i3i3−i30000000000-1-1i3−i3i3−i3000000000000
χ3022222-2-222200-2-22-122-1-12-100-1-1-1-1i3−i3i3−i3-211-2-2-222-1-1-1-10011i3−i3i3−i3000000000011−i3i3−i3i3000000000000
χ312-2-2222-22-2-22i−2i-222-1-2-2112-12i−2i-11-11−i−iii2-11-22i−2i2i−2i−i−iii2i−2i-11−i−iii002-2000000−ii-1-111000000000000
χ322-2-2222-22-2-22i−2i-222-1-2-2112-12i−2i-11-11−i−iii2-11-2−2i2i−2i2iii−i−i2i−2i-11−i−iii00-22000000i−i11-1-1000000000000
χ332-2-2222-22-2-22i−2i-22-1211-2-2-122i−2i-11-112i2i−2i−2i-12-2100000000−ii-11−i−iii00002-2002i−2i0000000000−i−iii00-11
χ342-2-2222-22-2-22i−2i-22-1211-2-2-122i−2i-11-112i2i−2i−2i-12-2100000000−ii-11−i−iii0000-2200−2i2i0000000000ii−i−i001-1
χ352-2-2222-22-2-2−2i2i-222-1-2-2112-1−2i2i-11-11ii−i−i2-11-22i−2i2i−2i−i−iii−2i2i-11ii−i−i00-22000000−ii11-1-1000000000000
χ362-2-2222-22-2-2−2i2i-222-1-2-2112-1−2i2i-11-11ii−i−i2-11-2−2i2i−2i2iii−i−i−2i2i-11ii−i−i002-2000000i−i-1-111000000000000
χ372-2-2222-22-2-2−2i2i-22-1211-2-2-12−2i2i-11-11−2i−2i2i2i-12-2100000000i−i-11ii−i−i00002-200−2i2i0000000000ii−i−i00-11
χ382-2-2222-22-2-2−2i2i-22-1211-2-2-12−2i2i-11-11−2i−2i2i2i-12-2100000000i−i-11ii−i−i0000-22002i−2i0000000000−i−iii001-1
χ392-2-222-222-2-2002-222-2-2-2-222002-22-20000-2-2222i−2i−2i2i−2i−2i2i2i00-22000000000000002i−2i0000000000000000
χ402-2-222-222-2-2002-222-2-2-2-222002-22-20000-2-222−2i2i2i−2i2i2i−2i−2i00-2200000000000000−2i2i0000000000000000
χ412-2-222-222-2-2002-22-1-2-2112-100-11-113−3−33-21-122i−2i−2i2iii−i−i001-13−3−330000000000−ii−i3i3i3−i3000000000000
χ422-2-222-222-2-2002-22-1-2-2112-100-11-113−3−33-21-12−2i2i2i−2i−i−iii001-13−3−330000000000i−ii3−i3−i3i3000000000000
χ432-2-222-222-2-2002-22-1-2-2112-100-11-11−333−3-21-122i−2i−2i2iii−i−i001-1−333−30000000000−iii3−i3−i3i3000000000000
χ442-2-222-222-2-2002-22-1-2-2112-100-11-11−333−3-21-12−2i2i2i−2i−i−iii001-1−333−30000000000i−i−i3i3i3−i3000000000000
χ4544444444444444-2-2-2-2-2-2-2-2441111-2-2-2-2-2-2-2-200000000-2-21111110000000000000000000000000000
χ464444444444-4-444-2-2-2-2-2-2-2-2-4-411112222-2-2-2-2000000002211-1-1-1-10000000000000000000000000000
χ4744444-4-444400-4-4-24-2-244-2400-2-2-2-200002-4-4200000000002200000000000000000000000000000000
χ4844444-4-444400-4-4-2-2-2-2-2-2-2-2001111−2i32i3−2i32i322220000000000-1-1i3−i3i3−i30000000000000000000000000000
χ4944444-4-444400-4-4-2-2-2-2-2-2-2-20011112i3−2i32i3−2i322220000000000-1-1−i3i3−i3i30000000000000000000000000000
χ5044-4-4400-44-4000044-44-44-4-4004-4-440000000000000000000000000000000000000000000000000000
χ5144-4-4400-44-400004-2-442-2-4200-222-200000000000023−2323−23000000000000000000000000000000000000
χ5244-4-4400-44-400004-2-442-2-4200-222-2000000000000−2323−2323000000000000000000000000000000000000
χ5344-4-4400-44-40000-242-2-442-400-222-2000000000000000000000000000000000000000000006−66−60000
χ5444-4-4400-44-40000-242-2-442-400-222-200000000000000000000000000000000000000000000−66−660000
χ554-44-4400-4-440000444-44-4-4-40044-4-40000000000000000000000000000000000000000000000000000
χ564-44-4400-4-4400004-24-4-22-4200-2-222000000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ574-44-4400-4-4400004-24-4-22-4200-2-2220000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ584-44-4400-4-440000-24-224-42-400-2-22200000000000000000000000000000000000000000000i6−i6−i6i60000
χ594-44-4400-4-440000-24-224-42-400-2-22200000000000000000000000000000000000000000000−i6i6i6−i60000
χ604-4-4444-44-4-44i−4i-44-2-22222-2-24i−4i1-11-1−2i−2i2i2i-2-22200000000−2i2i1-1ii−i−i0000000000000000000000000000
χ614-4-4444-44-4-4−4i4i-44-2-22222-2-2−4i4i1-11-12i2i−2i−2i-2-222000000002i−2i1-1−i−iii0000000000000000000000000000
χ624-4-444-444-4-4004-4-2422-4-4-2400-22-2200002-44-200000000002-200000000000000000000000000000000
χ634-4-444-444-4-4004-4-2-22222-2-2001-11-123−23−232322-2-20000000000-11−333−30000000000000000000000000000
χ644-4-444-444-4-4004-4-2-22222-2-2001-11-1−232323−2322-2-20000000000-113−3−330000000000000000000000000000
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
χ696-6-66-36-6-3336i−6i3-300000000−3i3i00000000000000000000000000002i−2i00002-200000000-1-1110000−ii00
χ706-6-66-36-6-3336i−6i3-300000000−3i3i0000000000000000000000000000−2i2i0000-220000000011-1-10000i−i00
χ716-6-66-36-6-333−6i6i3-3000000003i−3i00000000000000000000000000002i−2i0000-220000000011-1-10000−ii00
χ726-6-66-36-6-333−6i6i3-3000000003i−3i0000000000000000000000000000−2i2i00002-200000000-1-1110000i−i00
χ7388-8-8800-88-80000-4-44-44-444002-2-220000000000000000000000000000000000000000000000000000
χ748-88-8800-8-880000-4-4-44-44440022-2-20000000000000000000000000000000000000000000000000000
χ7512121212-6-12-12-6-6-60066000000000000000000000000000000000000000000000000000000000000000000
χ761212-12-12-6006-6600000000000000000000000000000000000000000000000000000000006−66−600000000
χ771212-12-12-6006-660000000000000000000000000000000000000000000000000000000000−66−6600000000
χ7812-1212-12-60066-600000000000000000000000000000000000000000000000000000000006−6−6600000000
χ7912-1212-12-60066-60000000000000000000000000000000000000000000000000000000000−666−600000000
χ8012-12-1212-6-1212-66600-66000000000000000000000000000000000000000000000000000000000000000000

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