Finite Group Databasebeta

← Group #13138057

Character table — Group #13138057

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444466666666881212121212121212121212121818181818181818242424242424242436363636363636363636363636363636363636363636363672727272
order12223446664412123366666612123666121212121212121222446666121212121212121222444488881212121212122424242424242424661212
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
χ51111111111-1-11111111111-1-11111111-1-1-1-1111111111-1-111-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111-1-11111111111-1-11111111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1
χ71111111111-1-11111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1111111-1-1
χ81111111111-1-11111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-111
χ91-1-1111-1-11-1i−i1-111-1-1-111-1i−i1-11-11-11ii−i−i-11-11-111-1-1i−i1-1ii−i−i1-1i−i1-1i−ii−i1-1ii−i−iii−i−iii−i−i1-11-1
χ101-1-1111-1-11-1i−i1-111-1-1-111-1i−i1-11-11-11ii−i−i-11-11-111-1-1i−i1-1ii−i−i-11i−i-11−ii−ii1-1ii−i−i−i−iii−i−iii-11-11
χ111-1-1111-1-11-1i−i1-111-1-1-111-1i−i1-11-11-11ii−i−i-1-11-11-1-111i−i1-1ii−i−i1-1−ii-11i−i−ii-11−i−iiiii−i−i−i−iii1-1-11
χ121-1-1111-1-11-1i−i1-111-1-1-111-1i−i1-11-11-11ii−i−i-1-11-11-1-111i−i1-1ii−i−i-11−ii1-1−iii−i-11−i−iii−i−iiiii−i−i-111-1
χ131-1-1111-1-11-1−ii1-111-1-1-111-1−ii1-11-11-11−i−iii-11-11-111-1-1−ii1-1−i−iii1-1−ii1-1−ii−ii1-1−i−iii−i−iii−i−iii1-11-1
χ141-1-1111-1-11-1−ii1-111-1-1-111-1−ii1-11-11-11−i−iii-11-11-111-1-1−ii1-1−i−iii-11−ii-11i−ii−i1-1−i−iiiii−i−iii−i−i-11-11
χ151-1-1111-1-11-1−ii1-111-1-1-111-1−ii1-11-11-11−i−iii-1-11-11-1-111−ii1-1−i−iii1-1i−i-11−iii−i-11ii−i−i−i−iiiii−i−i1-1-11
χ161-1-1111-1-11-1−ii1-111-1-1-111-1−ii1-11-11-11−i−iii-1-11-11-1-111−ii1-1−i−iii-11i−i1-1i−i−ii-11ii−i−iii−i−i−i−iii-111-1
χ17222222222222222-12-12-12-122-1-1-1-1-1-12-1-1-1-122222-1-1-1-122-1-1-1-1-1-10022000000-1-1-1-1-1-1000000000000
χ18222222222222222-12-12-12-122-1-1-1-1-1-12-1-1-1-12-2-2-2-2111122-1-1-1-1-1-100-2-2000000111111000000000000
χ1922222222222222-12-12-12-1222-1-1-1-122-12222-100000000-1-1-1-1-1-1-1-100002200220000000000-1-1-1-100-1-1
χ2022222222222222-12-12-12-1222-1-1-1-122-12222-100000000-1-1-1-1-1-1-1-10000-2-200-2-2000000000011110011
χ212222222222-2-2222-12-12-12-1-2-2-1-1-1-1-1-12111122222-1-1-1-1-2-2-1-1111100-2-2000000-1-11111000000000000
χ222222222222-2-2222-12-12-12-1-2-2-1-1-1-1-1-1211112-2-2-2-21111-2-2-1-11111002200000011-1-1-1-1000000000000
χ232222222222-2-222-12-12-12-12-2-2-1-1-1-122-1-2-2-2-2-10000000011-1-1111100002200-2-20000000000111100-1-1
χ242222222222-2-222-12-12-12-12-2-2-1-1-1-122-1-2-2-2-2-10000000011-1-111110000-2-200220000000000-1-1-1-10011
χ2522222-2-222200-2-222222222002222-2-2-20000-222-2-2222200-2-200000000000000-2-20000000000000000
χ2622222-2-222200-2-222222222002222-2-2-20000-2-2-222-2-2-2-200-2-200000000000000220000000000000000
χ2722222-2-222200-2-22-12-12-12-100-1-1-1-111-2−i3i3−i3i3-222-2-2-1-1-1-10011−i3i3−i3i3000000000011−i3i3−i3i3000000000000
χ2822222-2-222200-2-22-12-12-12-100-1-1-1-111-2−i3i3−i3i3-2-2-22211110011−i3i3−i3i30000000000-1-1i3−i3i3−i3000000000000
χ2922222-2-222200-2-22-12-12-12-100-1-1-1-111-2i3−i3i3−i3-222-2-2-1-1-1-10011i3−i3i3−i3000000000011i3−i3i3−i3000000000000
χ3022222-2-222200-2-22-12-12-12-100-1-1-1-111-2i3−i3i3−i3-2-2-22211110011i3−i3i3−i30000000000-1-1−i3i3−i3i3000000000000
χ312-2-2222-2-22-22i−2i2-22-1-21-2-1212i−2i-11-11-112−i−iii-22-22-2-1-1112i−2i-11−i−iii002i−2i000000-11−i−iii000000000000
χ322-2-2222-2-22-22i−2i2-22-1-21-2-1212i−2i-11-11-112−i−iii-2-22-2211-1-12i−2i-11−i−iii00−2i2i0000001-1ii−i−i000000000000
χ332-2-2222-2-22-22i−2i2-2-121-212-1-22i−2i-11-112-2-12i2i−2i−2i100000000−ii-11−i−iii00002-2002i−2i0000000000−i−iii00-11
χ342-2-2222-2-22-22i−2i2-2-121-212-1-22i−2i-11-112-2-12i2i−2i−2i100000000−ii-11−i−iii0000-2200−2i2i0000000000ii−i−i001-1
χ352-2-2222-2-22-2−2i2i2-22-1-21-2-121−2i2i-11-11-112ii−i−i-22-22-2-1-111−2i2i-11ii−i−i00−2i2i000000-11ii−i−i000000000000
χ362-2-2222-2-22-2−2i2i2-22-1-21-2-121−2i2i-11-11-112ii−i−i-2-22-2211-1-1−2i2i-11ii−i−i002i−2i0000001-1−i−iii000000000000
χ372-2-2222-2-22-2−2i2i2-2-121-212-1-2−2i2i-11-112-2-1−2i−2i2i2i100000000i−i-11ii−i−i00002-200−2i2i0000000000ii−i−i00-11
χ382-2-2222-2-22-2−2i2i2-2-121-212-1-2−2i2i-11-112-2-1−2i−2i2i2i100000000i−i-11ii−i−i0000-22002i−2i0000000000−i−iii001-1
χ392-2-222-22-22-200-2222-2-2-222-2002-22-2-22-2000022-2-2222-2-200-2200000000000000-220000000000000000
χ402-2-222-22-22-200-2222-2-2-222-2002-22-2-22-200002-222-2-2-22200-22000000000000002-20000000000000000
χ412-2-222-22-22-200-222-1-21-2-12100-11-111-1-23−3−3322-2-22-1-111001-13−3−3300000000001-13−3−33000000000000
χ422-2-222-22-22-200-222-1-21-2-12100-11-111-1-23−3−332-222-211-1-1001-13−3−330000000000-11−333−3000000000000
χ432-2-222-22-22-200-222-1-21-2-12100-11-111-1-2−333−322-2-22-1-111001-1−333−300000000001-1−333−3000000000000
χ442-2-222-22-22-200-222-1-21-2-12100-11-111-1-2−333−32-222-211-1-1001-1−333−30000000000-113−3−33000000000000
χ4544444444444444-2-2-2-2-2-2-2-2441111-2-2-2-2-2-2-2-200000000-2-21111110000000000000000000000000000
χ464444444444-4-444-2-2-2-2-2-2-2-2-4-41111-2-2-22222-2000000002211-1-1-1-10000000000000000000000000000
χ4744444-4-444400-4-4-24-24-24-2400-2-2-2-2-4-420000200000000002200000000000000000000000000000000
χ4844444-4-444400-4-4-2-2-2-2-2-2-2-2001111222−2i32i3−2i32i320000000000-1-1i3−i3i3−i30000000000000000000000000000
χ4944444-4-444400-4-4-2-2-2-2-2-2-2-20011112222i3−2i32i3−2i320000000000-1-1−i3i3−i3i30000000000000000000000000000
χ5044-4-44004-4-400004444-4-4-4-40044-4-40000000000000000000000000000000000000000000000000000
χ5144-4-44004-4-400004-24-2-42-4200-2-222000000000000−2i32i3−2i32i3000000000000000000000000000000000000
χ5244-4-44004-4-400004-24-2-42-4200-2-2220000000000002i3−2i32i3−2i3000000000000000000000000000000000000
χ5344-4-44004-4-40000-24-242-42-400-2-22200000000000000000000000000000000000000000000i6−i6i6−i60000
χ5444-4-44004-4-40000-24-242-42-400-2-22200000000000000000000000000000000000000000000−i6i6−i6i60000
χ554-44-4400-4-44000044-4-44-4-44004-4-440000000000000000000000000000000000000000000000000000
χ564-44-4400-4-4400004-2-4242-4-200-222-2000000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ574-44-4400-4-4400004-2-4242-4-200-222-20000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ584-44-4400-4-440000-242-4-2-42400-222-2000000000000000000000000000000000000000000006−6−660000
χ594-44-4400-4-440000-242-4-2-42400-222-200000000000000000000000000000000000000000000−666−60000
χ604-4-4444-4-44-44i−4i4-4-2-2222-2-224i−4i1-11-1-22-2−2i−2i2i2i200000000−2i2i1-1ii−i−i0000000000000000000000000000
χ614-4-4444-4-44-4−4i4i4-4-2-2222-2-22−4i4i1-11-1-22-22i2i−2i−2i2000000002i−2i1-1−i−iii0000000000000000000000000000
χ624-4-444-44-44-400-44-242-424-2-400-22-22-4420000-200000000002-200000000000000000000000000000000
χ634-4-444-44-44-400-44-2-2222-2-22001-11-12-2223−23−2323-20000000000-11−333−30000000000000000000000000000
χ644-4-444-44-44-400-44-2-2222-2-22001-11-12-22−232323−23-20000000000-113−3−330000000000000000000000000000
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
χ696-6-66-36-63-336i−6i-3300000000−3i3i00000000000000000000000000002-200002i−2i00000000−i−iii0000-1100
χ706-6-66-36-63-336i−6i-3300000000−3i3i0000000000000000000000000000-220000−2i2i00000000ii−i−i00001-100
χ716-6-66-36-63-33−6i6i-33000000003i−3i00000000000000000000000000002-20000−2i2i00000000ii−i−i0000-1100
χ726-6-66-36-63-33−6i6i-33000000003i−3i0000000000000000000000000000-2200002i−2i00000000−i−iii00001-100
χ7388-8-88008-8-80000-4-4-4-444440022-2-20000000000000000000000000000000000000000000000000000
χ748-88-8800-8-880000-4-444-444-4002-2-220000000000000000000000000000000000000000000000000000
χ7512121212-6-12-12-6-6-60066000000000000000000000000000000000000000000000000000000000000000000
χ761212-12-12-600-66600000000000000000000000000000000000000000000000000000000006−66−600000000
χ771212-12-12-600-6660000000000000000000000000000000000000000000000000000000000−66−6600000000
χ7812-1212-12-60066-60000000000000000000000000000000000000000000000000000000000i6−i6−i6i600000000
χ7912-1212-12-60066-60000000000000000000000000000000000000000000000000000000000−i6i6i6−i600000000
χ8012-12-1212-6-12126-66006-6000000000000000000000000000000000000000000000000000000000000000000

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