Finite Group Databasebeta

← Group #13137953

Character table — Group #13137953

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444466666666881212121212121212121212121818181818181818242424242424242436363636363636363636363636363636363636363636363672727272
order12223446664412123366666612123666121212121212121244441212121212121212121212122222446666888812122424242424242424661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-111
χ51111111111-1-11111111111-1-11111111-1-1-1-1111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ61111111111-1-11111111111-1-11111111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ71111111111-1-11111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-111-1-11111-1-1-1-111-1-1
χ81111111111-1-11111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-111
χ911-1-111-11-1-1i−i-1111-111-1-1-1i−i1-11-111-1ii−i−i-1i−ii−iii−i−ii−i1-1ii−i−i1-11-1i−i11-1-1i−i1-1i−i11-1-1ii−i−i1-1i−i
χ1011-1-111-11-1-1i−i-1111-111-1-1-1i−i1-11-111-1ii−i−i-1i−ii−iii−i−ii−i1-1ii−i−i1-1-11−ii11-1-1−ii-11i−i-1-111−i−iii-11−ii
χ1111-1-111-11-1-1i−i-1111-111-1-1-1i−i1-11-111-1ii−i−i-1−ii−ii−i−iiii−i1-1ii−i−i-111-1−ii-1-111i−i-11−ii-1-111ii−i−i1-1−ii
χ1211-1-111-11-1-1i−i-1111-111-1-1-1i−i1-11-111-1ii−i−i-1−ii−ii−i−iiii−i1-1ii−i−i-11-11i−i-1-111−ii1-1−ii11-1-1−i−iii-11i−i
χ1311-1-111-11-1-1−ii-1111-111-1-1-1−ii1-11-111-1−i−iii-1i−ii−iii−i−i−ii1-1−i−iii-111-1i−i-1-111−ii-11i−i-1-111−i−iii1-1i−i
χ1411-1-111-11-1-1−ii-1111-111-1-1-1−ii1-11-111-1−i−iii-1i−ii−iii−i−i−ii1-1−i−iii-11-11−ii-1-111i−i1-1i−i11-1-1ii−i−i-11−ii
χ1511-1-111-11-1-1−ii-1111-111-1-1-1−ii1-11-111-1−i−iii-1−ii−ii−i−iii−ii1-1−i−iii1-11-1−ii11-1-1−ii1-1−ii11-1-1−i−iii1-1−ii
χ1611-1-111-11-1-1−ii-1111-111-1-1-1−ii1-11-111-1−i−iii-1−ii−ii−i−iii−ii1-1−i−iii1-1-11i−i11-1-1i−i-11−ii-1-111ii−i−i-11i−i
χ17222222222222222-122-12-1-122-1-1-1-12-1-1-1-1-1-122222-1-1-1-122-1-1-1-1-1-1220000-1-1-1-10000-1-1000000000000
χ18222222222222222-122-12-1-122-1-1-1-12-1-1-1-1-1-12-2-2-2-2111122-1-1-1-1-1-1-2-200001111000011000000000000
χ1922222222222222-12-1-12-12222-1-1-1-1-1222222-100000000-1-1-1-1-1-1-1-100220000002200000000-1-1-1-1-1-100
χ2022222222222222-12-1-12-12222-1-1-1-1-1222222-100000000-1-1-1-1-1-1-1-100-2-2000000-2-20000000011111100
χ212222222222-2-2222-122-12-1-1-2-2-1-1-1-12-1-1111122222-1-1-1-1-2-2-1-11111-2-2000011110000-1-1000000000000
χ222222222222-2-2222-122-12-1-1-2-2-1-1-1-12-1-111112-2-2-2-21111-2-2-1-11111220000-1-1-1-1000011000000000000
χ232222222222-2-222-12-1-12-122-2-2-1-1-1-1-122-2-2-2-2-10000000011-1-111110022000000-2-2000000001111-1-100
χ242222222222-2-222-12-1-12-122-2-2-1-1-1-1-122-2-2-2-2-10000000011-1-1111100-2-20000002200000000-1-1-1-11100
χ2522222-2-222200-2-222222222002222-2-2-20000-222-2-2222200-2-2000000000000000000-2-2000000000000
χ2622222-2-222200-2-222222222002222-2-2-20000-2-2-222-2-2-2-200-2-200000000000000000022000000000000
χ2722222-2-222200-2-22-122-12-1-100-1-1-1-1-211−i3i3−i3i3-222-2-2-1-1-1-10011−i3i3−i3i3000000−i3i3−i3i3000011000000000000
χ2822222-2-222200-2-22-122-12-1-100-1-1-1-1-211−i3i3−i3i3-2-2-22211110011−i3i3−i3i3000000i3−i3i3−i30000-1-1000000000000
χ2922222-2-222200-2-22-122-12-1-100-1-1-1-1-211i3−i3i3−i3-222-2-2-1-1-1-10011i3−i3i3−i3000000i3−i3i3−i3000011000000000000
χ3022222-2-222200-2-22-122-12-1-100-1-1-1-1-211i3−i3i3−i3-2-2-22211110011i3−i3i3−i3000000−i3i3−i3i30000-1-1000000000000
χ3122-2-222-22-2-22i−2i-222-1-22-1-2112i−2i-11-112-11−i−iii-22i−2i2i−2i−i−iii2i−2i-11−i−iii2-20000-1-1110000−ii000000000000
χ3222-2-222-22-2-22i−2i-222-1-22-1-2112i−2i-11-112-11−i−iii-2−2i2i−2i2iii−i−i2i−2i-11−i−iii-22000011-1-10000i−i000000000000
χ3322-2-222-22-2-22i−2i-22-121-121-2-22i−2i-11-11-12-22i2i−2i−2i100000000−ii-11−i−iii002-20000002i−2i00000000−i−iii-1100
χ3422-2-222-22-2-22i−2i-22-121-121-2-22i−2i-11-11-12-22i2i−2i−2i100000000−ii-11−i−iii00-22000000−2i2i00000000ii−i−i1-100
χ3522-2-222-22-2-2−2i2i-222-1-22-1-211−2i2i-11-112-11ii−i−i-22i−2i2i−2i−i−iii−2i2i-11ii−i−i-22000011-1-10000−ii000000000000
χ3622-2-222-22-2-2−2i2i-222-1-22-1-211−2i2i-11-112-11ii−i−i-2−2i2i−2i2iii−i−i−2i2i-11ii−i−i2-20000-1-1110000i−i000000000000
χ3722-2-222-22-2-2−2i2i-22-121-121-2-2−2i2i-11-11-12-2−2i−2i2i2i100000000i−i-11ii−i−i002-2000000−2i2i00000000ii−i−i-1100
χ3822-2-222-22-2-2−2i2i-22-121-121-2-2−2i2i-11-11-12-2−2i−2i2i2i100000000i−i-11ii−i−i00-220000002i−2i00000000−i−iii1-100
χ3922-2-22-222-2-2002-222-222-2-2-2002-22-2-2-22000022i−2i−2i2i2i2i−2i−2i00-22000000000000000000−2i2i000000000000
χ4022-2-22-222-2-2002-222-222-2-2-2002-22-2-2-2200002−2i2i2i−2i−2i−2i2i2i00-220000000000000000002i−2i000000000000
χ4122-2-22-222-2-2002-22-1-22-1-21100-11-11-21-13−3−3322i−2i−2i2i−i−iii001-13−3−33000000−i3i3i3−i30000i−i000000000000
χ4222-2-22-222-2-2002-22-1-22-1-21100-11-11-21-13−3−332−2i2i2i−2iii−i−i001-13−3−33000000i3−i3−i3i30000−ii000000000000
χ4322-2-22-222-2-2002-22-1-22-1-21100-11-11-21-1−333−322i−2i−2i2i−i−iii001-1−333−3000000i3−i3−i3i30000i−i000000000000
χ4422-2-22-222-2-2002-22-1-22-1-21100-11-11-21-1−333−32−2i2i2i−2iii−i−i001-1−333−3000000−i3i3i3−i30000−ii000000000000
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
χ4744444-4-444400-4-4-24-2-24-24400-2-2-2-22-4-40000200000000002200000000000000000000000000000000
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
χ5044-4-444-44-4-44i−4i-44-2-22-2-22224i−4i1-11-1-2-22−2i−2i2i2i200000000−2i2i1-1ii−i−i0000000000000000000000000000
χ5144-4-444-44-4-4−4i4i-44-2-22-2-2222−4i4i1-11-1-2-222i2i−2i−2i2000000002i−2i1-1−i−iii0000000000000000000000000000
χ5244-4-44-444-4-4004-4-242-242-4-400-22-222-440000-200000000002-200000000000000000000000000000000
χ5344-4-44-444-4-4004-4-2-22-2-2222001-11-122-223−23−2323-20000000000-11−333−30000000000000000000000000000
χ5444-4-44-444-4-4004-4-2-22-2-2222001-11-122-2−232323−23-20000000000-113−3−330000000000000000000000000000
χ554-44-4400-44-4000044-4-4-44-44004-4-440000000000000000000000000000000000000000000000000000
χ564-44-4400-44-400004-2-4-4242-200-222-2000000000000−2i32i3−2i32i3000000000000000000000000000000000000
χ574-44-4400-44-400004-2-4-4242-200-222-20000000000002i3−2i32i3−2i3000000000000000000000000000000000000
χ584-44-4400-44-40000-2422-4-2-4400-222-200000000000000000000000000000000000000000000i6−i6i6−i60000
χ594-44-4400-44-40000-2422-4-2-4400-222-200000000000000000000000000000000000000000000−i6i6−i6i60000
χ604-4-44400-4-440000444-4-4-44-40044-4-40000000000000000000000000000000000000000000000000000
χ614-4-44400-4-4400004-24-42-4-2200-2-22200000000000023−23−2323000000000000000000000000000000000000
χ624-4-44400-4-4400004-24-42-4-2200-2-222000000000000−232323−23000000000000000000000000000000000000
χ634-4-44400-4-440000-24-22-424-400-2-222000000000000000000000000000000000000000000006−6−660000
χ644-4-44400-4-440000-24-22-424-400-2-22200000000000000000000000000000000000000000000−666−60000
χ656666-366-3-3-366-3-300000000-3-300000000000000000000000000000000220000002200-1-1-1-1000000-1-1
χ666666-366-3-3-366-3-300000000-3-300000000000000000000000000000000-2-2000000-2-200111100000011
χ676666-366-3-3-3-6-6-3-300000000330000000000000000000000000000000022000000-2-2001111000000-1-1
χ686666-366-3-3-3-6-6-3-3000000003300000000000000000000000000000000-2-20000002200-1-1-1-100000011
χ6966-6-6-36-6-3336i−6i3-300000000−3i3i000000000000000000000000000000002i−2i0000002-200-1-111000000−ii
χ7066-6-6-36-6-3336i−6i3-300000000−3i3i00000000000000000000000000000000−2i2i000000-220011-1-1000000i−i
χ7166-6-6-36-6-333−6i6i3-3000000003i−3i000000000000000000000000000000002i−2i000000-220011-1-1000000−ii
χ7266-6-6-36-6-333−6i6i3-3000000003i−3i00000000000000000000000000000000−2i2i0000002-200-1-111000000i−i
χ738-88-8800-88-80000-4-4444-44-4002-2-220000000000000000000000000000000000000000000000000000
χ748-8-88800-8-880000-4-4-4444-440022-2-20000000000000000000000000000000000000000000000000000
χ7512121212-6-12-12-6-6-60066000000000000000000000000000000000000000000000000000000000000000000
χ761212-12-12-6-1212-66600-66000000000000000000000000000000000000000000000000000000000000000000
χ7712-1212-12-6006-6600000000000000000000000000000000000000000000000000000000006−66−600000000
χ7812-1212-12-6006-660000000000000000000000000000000000000000000000000000000000−66−6600000000
χ7912-12-1212-60066-600000000000000000000000000000000000000000000000000000000006−6−6600000000
χ8012-12-1212-60066-60000000000000000000000000000000000000000000000000000000000−666−600000000

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