Finite Group Databasebeta

← Group #13138054

Character table — Group #13138054

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444466666666881212121212121212121212121818181818181818242424242424242436363636363636363636363636363636363636363636363672727272
order12223446664412123366666612123666121212121212121222441212121212121212121212122222446688881212121224242424242424246666
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111
χ51111111111-1-11111111111-1-111111-1-1-1-111111111111-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111-1-11111111111-1-111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1
χ71111111111-1-11111111111-1-111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1111111-1-1
χ81111111111-1-11111111111-1-111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-111111111-1-1-1-1-1-111
χ91-11-111-1-11-1i−i1-111-11-1-11-1i−i1-11-11ii−i−i1-1-11-11-111-1-1i−i1-1ii−i−i1-11-1i−i1-1i−ii−iii−i−iii−i−iii−i−i1-11-1
χ101-11-111-1-11-1i−i1-111-11-1-11-1i−i1-11-11ii−i−i1-1-11-11-111-1-1i−i1-1ii−i−i-11-11i−i1-1−ii−iiii−i−i−i−iii−i−iii-11-11
χ111-11-111-1-11-1i−i1-111-11-1-11-1i−i1-11-11ii−i−i1-1-1-11-11-1-111i−i1-1ii−i−i1-1-11−ii-11i−i−ii−i−iiiii−i−i−i−iii1-1-11
χ121-11-111-1-11-1i−i1-111-11-1-11-1i−i1-11-11ii−i−i1-1-1-11-11-1-111i−i1-1ii−i−i-111-1−ii-11−iii−i−i−iii−i−iiiii−i−i-111-1
χ131-11-111-1-11-1−ii1-111-11-1-11-1−ii1-11-11−i−iii1-1-11-11-111-1-1−ii1-1−i−iii1-11-1−ii1-1−ii−ii−i−iii−i−iii−i−iii1-11-1
χ141-11-111-1-11-1−ii1-111-11-1-11-1−ii1-11-11−i−iii1-1-11-11-111-1-1−ii1-1−i−iii-11-11−ii1-1i−ii−i−i−iiiii−i−iii−i−i-11-11
χ151-11-111-1-11-1−ii1-111-11-1-11-1−ii1-11-11−i−iii1-1-1-11-11-1-111−ii1-1−i−iii1-1-11i−i-11−iii−iii−i−i−i−iiiii−i−i1-1-11
χ161-11-111-1-11-1−ii1-111-11-1-11-1−ii1-11-11−i−iii1-1-1-11-11-1-111−ii1-1−i−iii-111-1i−i-11i−i−iiii−i−iii−i−i−i−iii-111-1
χ17222222222222222-1-1-12-12222-1-1-1-1-1222222-100000000-1-1-1-1-1-1-1-100220000002200000000-1-1-1-100-1-1
χ18222222222222222-1-1-12-12222-1-1-1-1-1222222-100000000-1-1-1-1-1-1-1-100-2-2000000-2-20000000011110011
χ1922222222222222-1222-12-1-122-1-1-1-12-1-1-1-1-1-122222-1-1-1-122-1-1-1-1-1-1000022-1-10000-1-1-1-1000000000000
χ2022222222222222-1222-12-1-122-1-1-1-12-1-1-1-1-1-12-2-2-2-2111122-1-1-1-1-1-10000-2-21100001111000000000000
χ212222222222-2-2222-1-1-12-122-2-2-1-1-1-1-1-2-2-2-222-10000000011-1-111110022000000-2-200000000111100-1-1
χ222222222222-2-2222-1-1-12-122-2-2-1-1-1-1-1-2-2-2-222-10000000011-1-1111100-2-20000002200000000-1-1-1-10011
χ232222222222-2-222-1222-12-1-1-2-2-1-1-1-121111-1-122222-1-1-1-1-2-2-1-111110000-2-2-1-100001111000000000000
χ242222222222-2-222-1222-12-1-1-2-2-1-1-1-121111-1-12-2-2-2-21111-2-2-1-11111000022110000-1-1-1-1000000000000
χ2522222-2-222200-2-222222222002222-20000-2-2-222-2-2-2-2-2-200-2-200000000002200000000000000000000
χ2622222-2-222200-2-222222222002222-20000-2-2-2-2-222222200-2-20000000000-2-200000000000000000000
χ2722222-2-222200-2-2-1222-12-1-100-1-1-1-1-2−i3i3−i3i311-222-2-211110011−i3i3−i3i3000000-1-10000−i3i3−i3i3000000000000
χ2822222-2-222200-2-2-1222-12-1-100-1-1-1-1-2−i3i3−i3i311-2-2-222-1-1-1-10011−i3i3−i3i3000000110000i3−i3i3−i3000000000000
χ2922222-2-222200-2-2-1222-12-1-100-1-1-1-1-2i3−i3i3−i311-222-2-211110011i3−i3i3−i3000000-1-10000i3−i3i3−i3000000000000
χ3022222-2-222200-2-2-1222-12-1-100-1-1-1-1-2i3−i3i3−i311-2-2-222-1-1-1-10011i3−i3i3−i3000000110000−i3i3−i3i3000000000000
χ312-22-222-2-22-22i−2i2-22-11-1-212-22i−2i-11-11-12i2i−2i−2i2-2100000000−ii-11−i−iii002-20000002i−2i00000000−i−iii00-11
χ322-22-222-2-22-22i−2i2-22-11-1-212-22i−2i-11-11-12i2i−2i−2i2-2100000000−ii-11−i−iii00-22000000−2i2i00000000ii−i−i001-1
χ332-22-222-2-22-22i−2i2-2-12-221-2-112i−2i-11-112−i−iii-11-22-22-2-1-1112i−2i-11−i−iii00002i−2i-110000−i−iii000000000000
χ342-22-222-2-22-22i−2i2-2-12-221-2-112i−2i-11-112−i−iii-11-2-22-2211-1-12i−2i-11−i−iii0000−2i2i1-10000ii−i−i000000000000
χ352-22-222-2-22-2−2i2i2-22-11-1-212-2−2i2i-11-11-1−2i−2i2i2i2-2100000000i−i-11ii−i−i002-2000000−2i2i00000000ii−i−i00-11
χ362-22-222-2-22-2−2i2i2-22-11-1-212-2−2i2i-11-11-1−2i−2i2i2i2-2100000000i−i-11ii−i−i00-220000002i−2i00000000−i−iii001-1
χ372-22-222-2-22-2−2i2i2-2-12-221-2-11−2i2i-11-112ii−i−i-11-22-22-2-1-111−2i2i-11ii−i−i0000−2i2i-110000ii−i−i000000000000
χ382-22-222-2-22-2−2i2i2-2-12-221-2-11−2i2i-11-112ii−i−i-11-2-22-2211-1-1−2i2i-11ii−i−i00002i−2i1-10000−i−iii000000000000
χ392-22-22-22-22-200-2222-22-2-22-2002-22-2-20000-2222-2-22-2-22200-2200000000002-200000000000000000000
χ402-22-22-22-22-200-2222-22-2-22-2002-22-2-20000-222-222-222-2-200-220000000000-2200000000000000000000
χ412-22-22-22-22-200-22-12-221-2-1100-11-11-23−3−331-122-2-2211-1-1001-13−3−33000000-1100003−3−33000000000000
χ422-22-22-22-22-200-22-12-221-2-1100-11-11-23−3−331-12-222-2-1-111001-13−3−330000001-10000−333−3000000000000
χ432-22-22-22-22-200-22-12-221-2-1100-11-11-2−333−31-122-2-2211-1-1001-1−333−3000000-110000−333−3000000000000
χ442-22-22-22-22-200-22-12-221-2-1100-11-11-2−333−31-12-222-2-1-111001-1−333−30000001-100003−3−33000000000000
χ4544444444444444-2-2-2-2-2-2-2-2441111-2-2-2-2-2-2-2-200000000-2-21111110000000000000000000000000000
χ464444444444-4-444-2-2-2-2-2-2-2-2-4-41111-22222-2-2-2000000002211-1-1-1-10000000000000000000000000000
χ4744444-4-444400-4-44-2-2-24-24400-2-2-2-220000-4-4200000000002200000000000000000000000000000000
χ4844444-4-444400-4-4-2-2-2-2-2-2-2-20011112−2i32i3−2i32i32220000000000-1-1i3−i3i3−i30000000000000000000000000000
χ4944444-4-444400-4-4-2-2-2-2-2-2-2-200111122i3−2i32i3−2i32220000000000-1-1−i3i3−i3i30000000000000000000000000000
χ5044-4-4400-4-44000044-4-444-4-4004-4-440000000000000000000000000000000000000000000000000000
χ5144-4-4400-4-4400004-2224-2-4-400-222-200000000000000000000000000000000000000000000i6−i6i6−i60000
χ5244-4-4400-4-4400004-2224-2-4-400-222-200000000000000000000000000000000000000000000−i6i6−i6i60000
χ5344-4-4400-4-440000-24-4-4-242200-222-200000000000023−2323−23000000000000000000000000000000000000
χ5444-4-4400-4-440000-24-4-4-242200-222-2000000000000−2323−2323000000000000000000000000000000000000
χ554-44-444-4-44-44i−4i4-4-2-22-222-224i−4i1-11-1-2−2i−2i2i2i-22200000000−2i2i1-1ii−i−i0000000000000000000000000000
χ564-44-444-4-44-4−4i4i4-4-2-22-222-22−4i4i1-11-1-22i2i−2i−2i-222000000002i−2i1-1−i−iii0000000000000000000000000000
χ574-44-44-44-44-400-444-22-2-424-400-22-2220000-44-200000000002-200000000000000000000000000000000
χ584-44-44-44-44-400-44-2-22-222-22001-11-1223−23−23232-2-20000000000-11−333−30000000000000000000000000000
χ594-44-44-44-44-400-44-2-22-222-22001-11-12−232323−232-2-20000000000-113−3−330000000000000000000000000000
χ604-4-444004-4-40000444-4-4-4-440044-4-40000000000000000000000000000000000000000000000000000
χ614-4-444004-4-400004-2-22-42-4400-2-222000000000000000000000000000000000000000000006−6−660000
χ624-4-444004-4-400004-2-22-42-4400-2-22200000000000000000000000000000000000000000000−666−60000
χ634-4-444004-4-40000-244-42-42-200-2-22200000000000023−23−2323000000000000000000000000000000000000
χ644-4-444004-4-40000-244-42-42-200-2-222000000000000−232323−23000000000000000000000000000000000000
χ656666-366-3-3-366-3-300000000-3-300000000000000000000000000002200000022000000-1-1-1-10000-1-100
χ666666-366-3-3-366-3-300000000-3-30000000000000000000000000000-2-2000000-2-2000000111100001100
χ676666-366-3-3-3-6-6-3-30000000033000000000000000000000000000022000000-2-200000011110000-1-100
χ686666-366-3-3-3-6-6-3-300000000330000000000000000000000000000-2-200000022000000-1-1-1-100001100
χ696-66-6-36-63-336i−6i-3300000000−3i3i00000000000000000000000000002-20000002i−2i000000−i−iii0000-1100
χ706-66-6-36-63-336i−6i-3300000000−3i3i0000000000000000000000000000-22000000−2i2i000000ii−i−i00001-100
χ716-66-6-36-63-33−6i6i-33000000003i−3i00000000000000000000000000002-2000000−2i2i000000ii−i−i0000-1100
χ726-66-6-36-63-33−6i6i-33000000003i−3i0000000000000000000000000000-220000002i−2i000000−i−iii00001-100
χ7388-8-8800-8-880000-4-444-4-444002-2-220000000000000000000000000000000000000000000000000000
χ748-8-888008-8-80000-4-4-44444-40022-2-20000000000000000000000000000000000000000000000000000
χ7512121212-6-12-12-6-6-60066000000000000000000000000000000000000000000000000000000000000000000
χ761212-12-12-60066-60000000000000000000000000000000000000000000000000000000000i6−i6i6−i600000000
χ771212-12-12-60066-60000000000000000000000000000000000000000000000000000000000−i6i6−i6i600000000
χ7812-1212-12-6-12126-66006-6000000000000000000000000000000000000000000000000000000000000000000
χ7912-12-1212-600-66600000000000000000000000000000000000000000000000000000000006−6−6600000000
χ8012-12-1212-600-6660000000000000000000000000000000000000000000000000000000000−666−600000000

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