Finite Group Databasebeta

← Group #13137949

Character table — Group #13137949

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444466666666881212121212121212121212121818181818181818242424242424242436363636363636363636363636363636363636363636363672727272
order1222344666441212336666661212366612121212121212124444121212121212121212121212224444666688881212242424242424242412121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ51111111111-1-11111111111-1-1111111-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ61111111111-1-11111111111-1-1111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ71111111111-1-11111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-111-1-11111-1-1-1-1-1-111
χ81111111111-1-11111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ91-11-111-1-11-1i−i-1111-11-1-1-11i−i1-11-11-1ii−i−i1-1i−ii−iii−i−ii−i1-1ii−i−i1-11-1i−i11-1-1i−i1-1i−i11-1-1ii−i−ii−i1-1
χ101-11-111-1-11-1i−i-1111-11-1-1-11i−i1-11-11-1ii−i−i1-1i−ii−iii−i−ii−i1-1ii−i−i1-1-11−ii11-1-1−ii-11i−i-1-111−i−iii−ii-11
χ111-11-111-1-11-1i−i-1111-11-1-1-11i−i1-11-11-1ii−i−i1-1−ii−ii−i−iiii−i1-1ii−i−i-111-1−ii-1-111i−i-11−ii-1-111ii−i−i−ii1-1
χ121-11-111-1-11-1i−i-1111-11-1-1-11i−i1-11-11-1ii−i−i1-1−ii−ii−i−iiii−i1-1ii−i−i-11-11i−i-1-111−ii1-1−ii11-1-1−i−iiii−i-11
χ131-11-111-1-11-1−ii-1111-11-1-1-11−ii1-11-11-1−i−iii1-1i−ii−iii−i−i−ii1-1−i−iii-111-1i−i-1-111−ii-11i−i-1-111−i−iiii−i1-1
χ141-11-111-1-11-1−ii-1111-11-1-1-11−ii1-11-11-1−i−iii1-1i−ii−iii−i−i−ii1-1−i−iii-11-11−ii-1-111i−i1-1i−i11-1-1ii−i−i−ii-11
χ151-11-111-1-11-1−ii-1111-11-1-1-11−ii1-11-11-1−i−iii1-1−ii−ii−i−iii−ii1-1−i−iii1-11-1−ii11-1-1−ii1-1−ii11-1-1−i−iii−ii1-1
χ161-11-111-1-11-1−ii-1111-11-1-1-11−ii1-11-11-1−i−iii1-1−ii−ii−i−iii−ii1-1−i−iii1-1-11i−i11-1-1i−i-11−ii-1-111ii−i−ii−i-11
χ17222222222222222-12-12-1-1222-1-1-1-1-1-1-1-1-1-1222222-1-1-1-122-1-1-1-1-1-1220000-1-1-1-10000-1-1000000000000
χ18222222222222222-12-12-1-1222-1-1-1-1-1-1-1-1-1-122-2-2-2-2111122-1-1-1-1-1-1-2-200001111000011000000000000
χ1922222222222222-12-12-122-122-1-1-1-1222222-1-100000000-1-1-1-1-1-1-1-100220000002200000000-1-1-1-100-1-1
χ2022222222222222-12-12-122-122-1-1-1-1222222-1-100000000-1-1-1-1-1-1-1-100-2-2000000-2-20000000011110011
χ212222222222-2-2222-12-12-1-12-2-2-1-1-1-1-1-11111222222-1-1-1-1-2-2-1-11111-2-2000011110000-1-1000000000000
χ222222222222-2-2222-12-12-1-12-2-2-1-1-1-1-1-1111122-2-2-2-21111-2-2-1-11111220000-1-1-1-1000011000000000000
χ232222222222-2-222-12-12-122-1-2-2-1-1-1-122-2-2-2-2-1-10000000011-1-111110022000000-2-200000000111100-1-1
χ242222222222-2-222-12-12-122-1-2-2-1-1-1-122-2-2-2-2-1-10000000011-1-1111100-2-20000002200000000-1-1-1-10011
χ2522222-2-222200-2-222222222002222-2-20000-2-222-2-2-2-2-2-200-2-200000000000000000022000000000000
χ2622222-2-222200-2-222222222002222-2-20000-2-2-2-222222200-2-2000000000000000000-2-2000000000000
χ2722222-2-222200-2-22-12-12-1-1200-1-1-1-111−i3i3−i3i3-2-222-2-211110011−i3i3−i3i3000000−i3i3−i3i30000-1-1000000000000
χ2822222-2-222200-2-22-12-12-1-1200-1-1-1-111−i3i3−i3i3-2-2-2-222-1-1-1-10011−i3i3−i3i3000000i3−i3i3−i3000011000000000000
χ2922222-2-222200-2-22-12-12-1-1200-1-1-1-111i3−i3i3−i3-2-222-2-211110011i3−i3i3−i3000000i3−i3i3−i30000-1-1000000000000
χ3022222-2-222200-2-22-12-12-1-1200-1-1-1-111i3−i3i3−i3-2-2-2-222-1-1-1-10011i3−i3i3−i3000000−i3i3−i3i3000011000000000000
χ312-22-222-2-22-22i−2i-222-1-2-1-21122i−2i-11-11-11−i−iii2-22i−2i2i−2i−i−iii2i−2i-11−i−iii2-20000-1-1110000−ii000000000000
χ322-22-222-2-22-22i−2i-222-1-2-1-21122i−2i-11-11-11−i−iii2-2−2i2i−2i2iii−i−i2i−2i-11−i−iii-22000011-1-10000i−i000000000000
χ332-22-222-2-22-22i−2i-22-12121-2-2-12i−2i-11-112-22i2i−2i−2i-1100000000−ii-11−i−iii002-20000002i−2i00000000−i−iii00-11
χ342-22-222-2-22-22i−2i-22-12121-2-2-12i−2i-11-112-22i2i−2i−2i-1100000000−ii-11−i−iii00-22000000−2i2i00000000ii−i−i001-1
χ352-22-222-2-22-2−2i2i-222-1-2-1-2112−2i2i-11-11-11ii−i−i2-22i−2i2i−2i−i−iii−2i2i-11ii−i−i-22000011-1-10000−ii000000000000
χ362-22-222-2-22-2−2i2i-222-1-2-1-2112−2i2i-11-11-11ii−i−i2-2−2i2i−2i2iii−i−i−2i2i-11ii−i−i2-20000-1-1110000i−i000000000000
χ372-22-222-2-22-2−2i2i-22-12121-2-2-1−2i2i-11-112-2−2i−2i2i2i-1100000000i−i-11ii−i−i002-2000000−2i2i00000000ii−i−i00-11
χ382-22-222-2-22-2−2i2i-22-12121-2-2-1−2i2i-11-112-2−2i−2i2i2i-1100000000i−i-11ii−i−i00-220000002i−2i00000000−i−iii001-1
χ392-22-22-22-22-2002-222-22-2-2-22002-22-2-220000-222i−2i−2i2i−2i−2i2i2i00-220000000000000000002i−2i000000000000
χ402-22-22-22-22-2002-222-22-2-2-22002-22-2-220000-22−2i2i2i−2i2i2i−2i−2i00-22000000000000000000−2i2i000000000000
χ412-22-22-22-22-2002-22-1-2-1-211200-11-111-13−3−33-222i−2i−2i2iii−i−i001-13−3−33000000−i3i3i3−i30000−ii000000000000
χ422-22-22-22-22-2002-22-1-2-1-211200-11-111-13−3−33-22−2i2i2i−2i−i−iii001-13−3−33000000i3−i3−i3i30000i−i000000000000
χ432-22-22-22-22-2002-22-1-2-1-211200-11-111-1−333−3-222i−2i−2i2iii−i−i001-1−333−3000000i3−i3−i3i30000−ii000000000000
χ442-22-22-22-22-2002-22-1-2-1-211200-11-111-1−333−3-22−2i2i2i−2i−i−iii001-1−333−3000000−i3i3i3−i30000i−i000000000000
χ4544444444444444-2-2-2-2-2-2-2-2441111-2-2-2-2-2-2-2-200000000-2-21111110000000000000000000000000000
χ464444444444-4-444-2-2-2-2-2-2-2-2-4-41111-2-22222-2-2000000002211-1-1-1-10000000000000000000000000000
χ4744444-4-444400-4-4-24-24-244-200-2-2-2-2-4-400002200000000002200000000000000000000000000000000
χ4844444-4-444400-4-4-2-2-2-2-2-2-2-200111122−2i32i3−2i32i3220000000000-1-1i3−i3i3−i30000000000000000000000000000
χ4944444-4-444400-4-4-2-2-2-2-2-2-2-2001111222i3−2i32i3−2i3220000000000-1-1−i3i3−i3i30000000000000000000000000000
χ5044-4-44004-4-40000444-4-44-4-40044-4-40000000000000000000000000000000000000000000000000000
χ5144-4-44004-4-400004-242-4-22-400-2-22200000000000023−2323−23000000000000000000000000000000000000
χ5244-4-44004-4-400004-242-4-22-400-2-222000000000000−2323−2323000000000000000000000000000000000000
χ5344-4-44004-4-40000-24-2-424-4200-2-22200000000000000000000000000000000000000000000i6−i6i6−i60000
χ5444-4-44004-4-40000-24-2-424-4200-2-22200000000000000000000000000000000000000000000−i6i6−i6i60000
χ554-44-444-4-44-44i−4i-44-2-22-2222-24i−4i1-11-1-22−2i−2i2i2i-2200000000−2i2i1-1ii−i−i0000000000000000000000000000
χ564-44-444-4-44-4−4i4i-44-2-22-2222-2−4i4i1-11-1-222i2i−2i−2i-22000000002i−2i1-1−i−iii0000000000000000000000000000
χ574-44-44-44-44-4004-4-24242-4-4-200-22-22-4400002-200000000002-200000000000000000000000000000000
χ584-44-44-44-44-4004-4-2-22-2222-2001-11-12-223−23−23232-20000000000-11−333−30000000000000000000000000000
χ594-44-44-44-44-4004-4-2-22-2222-2001-11-12-2−232323−232-20000000000-113−3−330000000000000000000000000000
χ604-4-44400-4-44000044-4-44-44-4004-4-440000000000000000000000000000000000000000000000000000
χ614-4-44400-4-4400004-2-4242-2-400-222-2000000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ624-4-44400-4-4400004-2-4242-2-400-222-20000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ634-4-44400-4-440000-242-4-2-44200-222-2000000000000000000000000000000000000000000006−6−660000
χ644-4-44400-4-440000-242-4-2-44200-222-200000000000000000000000000000000000000000000−666−60000
χ656666-366-3-3-366-3-300000000-3-300000000000000000000000000000000220000002200-1-1-1-10000-1-100
χ666666-366-3-3-366-3-300000000-3-300000000000000000000000000000000-2-2000000-2-200111100001100
χ676666-366-3-3-3-6-6-3-300000000330000000000000000000000000000000022000000-2-20011110000-1-100
χ686666-366-3-3-3-6-6-3-3000000003300000000000000000000000000000000-2-20000002200-1-1-1-100001100
χ696-66-6-36-63-336i−6i3-300000000−3i3i000000000000000000000000000000002i−2i0000002-200-1-1110000−ii00
χ706-66-6-36-63-336i−6i3-300000000−3i3i00000000000000000000000000000000−2i2i000000-220011-1-10000i−i00
χ716-66-6-36-63-33−6i6i3-3000000003i−3i000000000000000000000000000000002i−2i000000-220011-1-10000−ii00
χ726-66-6-36-63-33−6i6i3-3000000003i−3i00000000000000000000000000000000−2i2i0000002-200-1-1110000i−i00
χ7388-8-88008-8-80000-4-4-444-4440022-2-20000000000000000000000000000000000000000000000000000
χ748-8-88800-8-880000-4-444-44-44002-2-220000000000000000000000000000000000000000000000000000
χ7512121212-6-12-12-6-6-60066000000000000000000000000000000000000000000000000000000000000000000
χ761212-12-12-600-6660000000000000000000000000000000000000000000000000000000000i6−i6i6−i600000000
χ771212-12-12-600-6660000000000000000000000000000000000000000000000000000000000−i6i6−i6i600000000
χ7812-1212-12-6-12126-6600-66000000000000000000000000000000000000000000000000000000000000000000
χ7912-12-1212-60066-60000000000000000000000000000000000000000000000000000000000i6−i6−i6i600000000
χ8012-12-1212-60066-60000000000000000000000000000000000000000000000000000000000−i6i6i6−i600000000

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