Finite Group Databasebeta

← Group #13137950

Character table — Group #13137950

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222244446666666688999912121212121212121212121218181818181818181818181818182424242424242424363636363636363636363636363636363636363672727272
order1222344666441212336666661212444436661212121212121212448888888812121212121212121212121222444466661212242424242424242412121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ4111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1
χ51111111111-1-11111111111-1-11111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ61111111111-1-11111111111-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111
χ71111111111-1-11111111111-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1111111-1-1
χ81111111111-1-11111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-111
χ91-11-111-11-1-1i−i-1111-11-1-1-11i−iii−i−i1-11-11-1ii−i−i1-1i−iii−i−i11-1-1ii−i−ii−i1-1ii−i−i1-11-1i−i11-1-1i−i11-1-1ii−i−ii−i1-1
χ101-11-111-11-1-1i−i-1111-11-1-1-11i−iii−i−i1-11-11-1ii−i−i1-1i−i−i−iii-1-111ii−i−ii−i1-1ii−i−i1-1-11−ii11-1-1i−i-1-111−i−iii−ii-11
χ111-11-111-11-1-1i−i-1111-11-1-1-11i−i−i−iii1-11-11-1ii−i−i1-1−iiii−i−i-1-111−i−iiii−i1-1ii−i−i-111-1−ii-1-111−ii-1-111ii−i−i−ii1-1
χ121-11-111-11-1-1i−i-1111-11-1-1-11i−i−i−iii1-11-11-1ii−i−i1-1−ii−i−iii11-1-1−i−iiii−i1-1ii−i−i-11-11i−i-1-111−ii11-1-1−i−iiii−i-11
χ131-11-111-11-1-1−ii-1111-11-1-1-11−iiii−i−i1-11-11-1−i−iii1-1i−iii−i−i11-1-1ii−i−i−ii1-1−i−iii-11-11−ii-1-111i−i11-1-1ii−i−i−ii-11
χ141-11-111-11-1-1−ii-1111-11-1-1-11−iiii−i−i1-11-11-1−i−iii1-1i−i−i−iii-1-111ii−i−i−ii1-1−i−iii-111-1i−i-1-111i−i-1-111−i−iiii−i1-1
χ151-11-111-11-1-1−ii-1111-11-1-1-11−ii−i−iii1-11-11-1−i−iii1-1−iiii−i−i-1-111−i−iii−ii1-1−i−iii1-1-11i−i11-1-1−ii-1-111ii−i−ii−i-11
χ161-11-111-11-1-1−ii-1111-11-1-1-11−ii−i−iii1-11-11-1−i−iii1-1−ii−i−iii11-1-1−i−iii−ii1-1−i−iii1-11-1−ii11-1-1−ii11-1-1−i−iii−ii1-1
χ17222222222222222-12-12-1-12222222-1-1-1-1-1-1-1-1-1-1222200000000-1-1-1-122-1-1-1-1-1-1220000-1-1-1-1-1-1000000000000
χ18222222222222222-12-12-1-1222-2-2-2-2-1-1-1-1-1-1-1-1-1-122-2-200000000111122-1-1-1-1-1-1-2-20000111111000000000000
χ1922222222222222-12-12-122-1220000-1-1-1-1222222-1-100222200000000-1-1-1-1-1-1-1-10022000000000000-1-1-1-100-1-1
χ2022222222222222-12-12-122-1220000-1-1-1-1222222-1-100-2-2-2-200000000-1-1-1-1-1-1-1-100-2-200000000000011110011
χ212222222222-2-2222-12-12-1-12-2-22222-1-1-1-1-1-11111222200000000-1-1-1-1-2-2-1-11111-2-200001111-1-1000000000000
χ222222222222-2-2222-12-12-1-12-2-2-2-2-2-2-1-1-1-1-1-1111122-2-2000000001111-2-2-1-11111220000-1-1-1-111000000000000
χ232222222222-2-222-12-12-122-1-2-20000-1-1-1-122-2-2-2-2-1-10022220000000011-1-1111100-2-2000000000000-1-1-1-10011
χ242222222222-2-222-12-12-122-1-2-20000-1-1-1-122-2-2-2-2-1-100-2-2-2-20000000011-1-111110022000000000000111100-1-1
χ2522222-2-222200-2-2222222220022222222-2-20000-2-2-2-200000000222200-2-200000000000000-2-2000000000000
χ2622222-2-222200-2-22222222200-2-2-2-22222-2-20000-2-22200000000-2-2-2-200-2-20000000000000022000000000000
χ2722222-2-222200-2-22-12-12-1-12002222-1-1-1-111−i3i3−i3i3-2-2-2-200000000-1-1-1-10011−i3i3−i3i3000000−i3i3−i3i311000000000000
χ2822222-2-222200-2-22-12-12-1-12002222-1-1-1-111i3−i3i3−i3-2-2-2-200000000-1-1-1-10011i3−i3i3−i3000000i3−i3i3−i311000000000000
χ2922222-2-222200-2-22-12-12-1-1200-2-2-2-2-1-1-1-111−i3i3−i3i3-2-2220000000011110011−i3i3−i3i3000000i3−i3i3−i3-1-1000000000000
χ3022222-2-222200-2-22-12-12-1-1200-2-2-2-2-1-1-1-111i3−i3i3−i3-2-2220000000011110011i3−i3i3−i3000000−i3i3−i3i3-1-1000000000000
χ3122-2-2200-22-2000022-2-22-22-2002-22-22-2-220000000000−i2i2−i2i2−i2i2−i2i22-22-200000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ3222-2-2200-22-2000022-2-22-22-2002-22-22-2-220000000000i2−i2i2−i2i2−i2i2−i22-22-200000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ3322-2-2200-22-2000022-2-22-22-200-22-222-2-220000000000−i2i2−i2i2i2−i2i2−i2-22-2200000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ3422-2-2200-22-2000022-2-22-22-200-22-222-2-220000000000i2−i2i2−i2−i2i2−i2i2-22-2200000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ352-22-222-22-2-22i−2i-222-1-2-1-21122i−2i2i2i−2i−2i-11-11-11−i−iii2-22i−2i00000000−i−iii2i−2i-11−i−iii2-20000-1-111−ii000000000000
χ362-22-222-22-2-22i−2i-222-1-2-1-21122i−2i−2i−2i2i2i-11-11-11−i−iii2-2−2i2i00000000ii−i−i2i−2i-11−i−iii-22000011-1-1i−i000000000000
χ372-22-222-22-2-22i−2i-22-12121-2-2-12i−2i0000-11-112-22i2i−2i−2i-11002i2i−2i−2i00000000−ii-11−i−iii002-2000000000000−i−iii00-11
χ382-22-222-22-2-22i−2i-22-12121-2-2-12i−2i0000-11-112-22i2i−2i−2i-1100−2i−2i2i2i00000000−ii-11−i−iii00-22000000000000ii−i−i001-1
χ392-22-222-22-2-2−2i2i-222-1-2-1-2112−2i2i2i2i−2i−2i-11-11-11ii−i−i2-22i−2i00000000−i−iii−2i2i-11ii−i−i-22000011-1-1−ii000000000000
χ402-22-222-22-2-2−2i2i-222-1-2-1-2112−2i2i−2i−2i2i2i-11-11-11ii−i−i2-2−2i2i00000000ii−i−i−2i2i-11ii−i−i2-20000-1-111i−i000000000000
χ412-22-222-22-2-2−2i2i-22-12121-2-2-1−2i2i0000-11-112-2−2i−2i2i2i-11002i2i−2i−2i00000000i−i-11ii−i−i00-22000000000000−i−iii001-1
χ422-22-222-22-2-2−2i2i-22-12121-2-2-1−2i2i0000-11-112-2−2i−2i2i2i-1100−2i−2i2i2i00000000i−i-11ii−i−i002-2000000000000ii−i−i00-11
χ432-22-22-222-2-2002-222-22-2-2-22002i2i−2i−2i2-22-2-220000-22−2i2i000000002i2i−2i−2i00-2200000000000000−2i2i000000000000
χ442-22-22-222-2-2002-222-22-2-2-2200−2i−2i2i2i2-22-2-220000-222i−2i00000000−2i−2i2i2i00-22000000000000002i−2i000000000000
χ452-22-22-222-2-2002-22-1-2-1-2112002i2i−2i−2i-11-111-13−3−33-22−2i2i00000000−i−iii001-13−3−33000000−i3i3i3−i3i−i000000000000
χ462-22-22-222-2-2002-22-1-2-1-2112002i2i−2i−2i-11-111-1−333−3-22−2i2i00000000−i−iii001-1−333−3000000i3−i3−i3i3i−i000000000000
χ472-22-22-222-2-2002-22-1-2-1-211200−2i−2i2i2i-11-111-13−3−33-222i−2i00000000ii−i−i001-13−3−33000000i3−i3−i3i3−ii000000000000
χ482-22-22-222-2-2002-22-1-2-1-211200−2i−2i2i2i-11-111-1−333−3-222i−2i00000000ii−i−i001-1−333−3000000−i3i3i3−i3−ii000000000000
χ492-2-22200-2-220000222-2-22-2-2002i−2i−2i2i22-2-200000000002−2−22−i2i2i2−i22i−2i−2i2i00000000000000000000−i2i2i2−i22−2−220000
χ502-2-22200-2-220000222-2-22-2-2002i−2i−2i2i22-2-20000000000−222−2i2−i2−i2i22i−2i−2i2i00000000000000000000i2−i2−i2i2−222−20000
χ512-2-22200-2-220000222-2-22-2-200−2i2i2i−2i22-2-200000000002−2−22i2−i2−i2i2−2i2i2i−2i00000000000000000000i2−i2−i2i22−2−220000
χ522-2-22200-2-220000222-2-22-2-200−2i2i2i−2i22-2-20000000000−222−2−i2i2i2−i2−2i2i2i−2i00000000000000000000−i2i2i2−i2−222−20000
χ5344444444444444-2-2-2-2-2-2-2-24400001111-2-2-2-2-2-2-2-200000000000000-2-2111111000000000000000000000000
χ544444444444-4-444-2-2-2-2-2-2-2-2-4-400001111-2-22222-2-2000000000000002211-1-1-1-1000000000000000000000000
χ5544444-4-444400-4-4-24-24-244-2000000-2-2-2-2-4-40000220000000000000000220000000000000000000000000000
χ5644444-4-444400-4-4-2-2-2-2-2-2-2-2000000111122−2i32i3−2i32i3220000000000000000-1-1i3−i3i3−i3000000000000000000000000
χ5744444-4-444400-4-4-2-2-2-2-2-2-2-20000001111222i3−2i32i3−2i3220000000000000000-1-1−i3i3−i3i3000000000000000000000000
χ5844-4-4400-44-400004-2-4242-2-4004-44-4-222-2000000000000000000-22-2200000000000000000000000000000000
χ5944-4-4400-44-400004-2-4242-2-400-44-44-222-20000000000000000002-22-200000000000000000000000000000000
χ6044-4-4400-44-40000-242-4-2-442000000-222-20000000000−2i22i2−2i22i200000000000000000000000000000000i2−i2i2−i20000
χ6144-4-4400-44-40000-242-4-2-442000000-222-200000000002i2−2i22i2−2i200000000000000000000000000000000−i2i2−i2i20000
χ624-44-444-44-4-44i−4i-44-2-22-2222-24i−4i00001-11-1-22−2i−2i2i2i-2200000000000000−2i2i1-1ii−i−i000000000000000000000000
χ634-44-444-44-4-4−4i4i-44-2-22-2222-2−4i4i00001-11-1-222i2i−2i−2i-22000000000000002i−2i1-1−i−iii000000000000000000000000
χ644-44-44-444-4-4004-4-24242-4-4-2000000-22-22-4400002-200000000000000002-20000000000000000000000000000
χ654-44-44-444-4-4004-4-2-22-2222-20000001-11-12-223−23−23232-20000000000000000-11−333−3000000000000000000000000
χ664-44-44-444-4-4004-4-2-22-2222-20000001-11-12-2−232323−232-20000000000000000-113−3−33000000000000000000000000
χ674-4-44400-4-4400004-242-4-22-4004i−4i−4i4i-2-222000000000000000000−2i2i2i−2i00000000000000000000000000000000
χ684-4-44400-4-4400004-242-4-22-400−4i4i4i−4i-2-2220000000000000000002i−2i−2i2i00000000000000000000000000000000
χ694-4-44400-4-440000-24-2-424-42000000-2-222000000000022−22−222200000000000000000000000000000000−222−20000
χ704-4-44400-4-440000-24-2-424-42000000-2-2220000000000−222222−22000000000000000000000000000000002−2−220000
χ716666-366-3-3-366-3-300000000-3-300000000000000000000002222000000000000000022000000-1-1-1-10000-1-100
χ726666-366-3-3-366-3-300000000-3-30000000000000000000000-2-2-2-20000000000000000-2-2000000111100001100
χ736666-366-3-3-3-6-6-3-30000000033000000000000000000000022220000000000000000-2-2000000-1-1-1-100001100
χ746666-366-3-3-3-6-6-3-300000000330000000000000000000000-2-2-2-200000000000000002200000011110000-1-100
χ756-66-6-36-6-3336i−6i3-300000000−3i3i000000000000000000000022-2-200000000000000002i−2i000000-1-1110000−ii00
χ766-66-6-36-6-3336i−6i3-300000000−3i3i0000000000000000000000-2-2220000000000000000−2i2i00000011-1-10000i−i00
χ776-66-6-36-6-333−6i6i3-3000000003i−3i000000000000000000000022-2-20000000000000000−2i2i000000-1-1110000i−i00
χ786-66-6-36-6-333−6i6i3-3000000003i−3i0000000000000000000000-2-22200000000000000002i−2i00000011-1-10000−ii00
χ7988-8-8800-88-80000-4-444-44-440000002-2-22000000000000000000000000000000000000000000000000000000
χ808-8-88800-8-880000-4-4-444-44400000022-2-2000000000000000000000000000000000000000000000000000000
χ8112121212-6-12-12-6-6-60066000000000000000000000000000000000000000000000000000000000000000000000000
χ821212-12-12-6006-66000000000000000000000000000000000000−2i22i2−2i22i2000000000000000000000000i2−i2i2−i200000000
χ831212-12-12-6006-660000000000000000000000000000000000002i2−2i22i2−2i2000000000000000000000000−i2i2−i2i200000000
χ8412-1212-12-6-1212-66600-66000000000000000000000000000000000000000000000000000000000000000000000000
χ8512-12-1212-60066-6000000000000000000000000000000000000−2i22i22i2−2i2000000000000000000000000i2−i2−i2i200000000
χ8612-12-1212-60066-60000000000000000000000000000000000002i2−2i2−2i22i2000000000000000000000000−i2i2i2−i200000000

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