Finite Group Databasebeta

← Group #13137954

Character table — Group #13137954

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222244446666666688999912121212121212121212121218181818181818181818181818182424242424242424363636363636363636363636363636363636363672727272
order12223446664412123366666612124444366612121212121212124488888888121212121212121212121212222244666612122424242424242424661212
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
χ3111111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ4111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111
χ51111111111-1-11111111111-1-111111111111-1-1-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ61111111111-1-11111111111-1-111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111
χ71111111111-1-11111111111-1-1-1-1-1-11111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-111
χ81111111111-1-11111111111-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-11111-1-11111-1-1-1-111-1-1
χ911-1-111-1-11-1i−i-1111-111-1-1-1i−iii−i−i1-11-111-1ii−i−i-1i−iii−i−i11-1-1ii−i−ii−i1-1ii−i−i1-11-1i−i11-1-1i−i11-1-1ii−i−i1-1i−i
χ1011-1-111-1-11-1i−i-1111-111-1-1-1i−iii−i−i1-11-111-1ii−i−i-1i−i−i−iii-1-111ii−i−ii−i1-1ii−i−i1-1-11−ii11-1-1i−i-1-111−i−iii-11−ii
χ1111-1-111-1-11-1i−i-1111-111-1-1-1i−i−i−iii1-11-111-1ii−i−i-1−iiii−i−i-1-111−i−iiii−i1-1ii−i−i-111-1−ii-1-111−ii-1-111ii−i−i1-1−ii
χ1211-1-111-1-11-1i−i-1111-111-1-1-1i−i−i−iii1-11-111-1ii−i−i-1−ii−i−iii11-1-1−i−iiii−i1-1ii−i−i-11-11i−i-1-111−ii11-1-1−i−iii-11i−i
χ1311-1-111-1-11-1−ii-1111-111-1-1-1−iiii−i−i1-11-111-1−i−iii-1i−iii−i−i11-1-1ii−i−i−ii1-1−i−iii-11-11−ii-1-111i−i11-1-1ii−i−i-11−ii
χ1411-1-111-1-11-1−ii-1111-111-1-1-1−iiii−i−i1-11-111-1−i−iii-1i−i−i−iii-1-111ii−i−i−ii1-1−i−iii-111-1i−i-1-111i−i-1-111−i−iii1-1i−i
χ1511-1-111-1-11-1−ii-1111-111-1-1-1−ii−i−iii1-11-111-1−i−iii-1−iiii−i−i-1-111−i−iii−ii1-1−i−iii1-1-11i−i11-1-1−ii-1-111ii−i−i-11i−i
χ1611-1-111-1-11-1−ii-1111-111-1-1-1−ii−i−iii1-11-111-1−i−iii-1−ii−i−iii11-1-1−i−iii−ii1-1−i−iii1-11-1−ii11-1-1−ii11-1-1−i−iii1-1−ii
χ17222222222222222-122-12-1-1222222-1-1-1-12-1-1-1-1-1-122200000000-1-1-1-122-1-1-1-1-1-1220000-1-1-1-1-1-1000000000000
χ18222222222222222-122-12-1-122-2-2-2-2-1-1-1-12-1-1-1-1-1-12-2-200000000111122-1-1-1-1-1-1-2-20000111111000000000000
χ1922222222222222-12-1-12-122220000-1-1-1-1-1222222-100222200000000-1-1-1-1-1-1-1-10022000000000000-1-1-1-1-1-100
χ2022222222222222-12-1-12-122220000-1-1-1-1-1222222-100-2-2-2-200000000-1-1-1-1-1-1-1-100-2-200000000000011111100
χ212222222222-2-2222-122-12-1-1-2-22222-1-1-1-12-1-1111122200000000-1-1-1-1-2-2-1-11111-2-200001111-1-1000000000000
χ222222222222-2-2222-122-12-1-1-2-2-2-2-2-2-1-1-1-12-1-111112-2-2000000001111-2-2-1-11111220000-1-1-1-111000000000000
χ232222222222-2-222-12-1-12-122-2-20000-1-1-1-1-122-2-2-2-2-10022220000000011-1-1111100-2-2000000000000-1-1-1-11100
χ242222222222-2-222-12-1-12-122-2-20000-1-1-1-1-122-2-2-2-2-100-2-2-2-20000000011-1-1111100220000000000001111-1-100
χ2522222-2-222200-2-2222222220022222222-2-2-20000-2-2-200000000222200-2-200000000000000-2-2000000000000
χ2622222-2-222200-2-22222222200-2-2-2-22222-2-2-20000-22200000000-2-2-2-200-2-20000000000000022000000000000
χ2722222-2-222200-2-22-122-12-1-1002222-1-1-1-1-211−i3i3−i3i3-2-2-200000000-1-1-1-10011−i3i3−i3i3000000−i3i3−i3i311000000000000
χ2822222-2-222200-2-22-122-12-1-1002222-1-1-1-1-211i3−i3i3−i3-2-2-200000000-1-1-1-10011i3−i3i3−i3000000i3−i3i3−i311000000000000
χ2922222-2-222200-2-22-122-12-1-100-2-2-2-2-1-1-1-1-211−i3i3−i3i3-2220000000011110011−i3i3−i3i3000000i3−i3i3−i3-1-1000000000000
χ3022222-2-222200-2-22-122-12-1-100-2-2-2-2-1-1-1-1-211i3−i3i3−i3-2220000000011110011i3−i3i3−i3000000−i3i3−i3i3-1-1000000000000
χ3122-2-222-2-22-22i−2i-222-1-22-1-2112i−2i2i2i−2i−2i-11-112-11−i−iii-22i−2i00000000−i−iii2i−2i-11−i−iii2-20000-1-111−ii000000000000
χ3222-2-222-2-22-22i−2i-222-1-22-1-2112i−2i−2i−2i2i2i-11-112-11−i−iii-2−2i2i00000000ii−i−i2i−2i-11−i−iii-22000011-1-1i−i000000000000
χ3322-2-222-2-22-22i−2i-22-121-121-2-22i−2i0000-11-11-12-22i2i−2i−2i1002i2i−2i−2i00000000−ii-11−i−iii002-2000000000000−i−iii-1100
χ3422-2-222-2-22-22i−2i-22-121-121-2-22i−2i0000-11-11-12-22i2i−2i−2i100−2i−2i2i2i00000000−ii-11−i−iii00-22000000000000ii−i−i1-100
χ3522-2-222-2-22-2−2i2i-222-1-22-1-211−2i2i2i2i−2i−2i-11-112-11ii−i−i-22i−2i00000000−i−iii−2i2i-11ii−i−i-22000011-1-1−ii000000000000
χ3622-2-222-2-22-2−2i2i-222-1-22-1-211−2i2i−2i−2i2i2i-11-112-11ii−i−i-2−2i2i00000000ii−i−i−2i2i-11ii−i−i2-20000-1-111i−i000000000000
χ3722-2-222-2-22-2−2i2i-22-121-121-2-2−2i2i0000-11-11-12-2−2i−2i2i2i1002i2i−2i−2i00000000i−i-11ii−i−i00-22000000000000−i−iii1-100
χ3822-2-222-2-22-2−2i2i-22-121-121-2-2−2i2i0000-11-11-12-2−2i−2i2i2i100−2i−2i2i2i00000000i−i-11ii−i−i002-2000000000000ii−i−i-1100
χ3922-2-22-22-22-2002-222-222-2-2-2002i2i−2i−2i2-22-2-2-2200002−2i2i000000002i2i−2i−2i00-2200000000000000−2i2i000000000000
χ4022-2-22-22-22-2002-222-222-2-2-200−2i−2i2i2i2-22-2-2-22000022i−2i00000000−2i−2i2i2i00-22000000000000002i−2i000000000000
χ4122-2-22-22-22-2002-22-1-22-1-211002i2i−2i−2i-11-11-21-13−3−332−2i2i00000000−i−iii001-13−3−33000000−i3i3i3−i3i−i000000000000
χ4222-2-22-22-22-2002-22-1-22-1-211002i2i−2i−2i-11-11-21-1−333−32−2i2i00000000−i−iii001-1−333−3000000i3−i3−i3i3i−i000000000000
χ4322-2-22-22-22-2002-22-1-22-1-21100−2i−2i2i2i-11-11-21-13−3−3322i−2i00000000ii−i−i001-13−3−33000000i3−i3−i3i3−ii000000000000
χ4422-2-22-22-22-2002-22-1-22-1-21100−2i−2i2i2i-11-11-21-1−333−322i−2i00000000ii−i−i001-1−333−3000000−i3i3i3−i3−ii000000000000
χ452-22-22002-2-20000222-2-2-22-2002i−2i2i−2i22-2-20000000000−i2i2−i2i22−22−22i−2i2i−2i000000000000000000002−22−2−i2i2−i2i20000
χ462-22-22002-2-20000222-2-2-22-2002i−2i2i−2i22-2-20000000000i2−i2i2−i2−22−222i−2i2i−2i00000000000000000000−22−22i2−i2i2−i20000
χ472-22-22002-2-20000222-2-2-22-200−2i2i−2i2i22-2-20000000000−i2i2−i2i2−22−22−2i2i−2i2i00000000000000000000−22−22−i2i2−i2i20000
χ482-22-22002-2-20000222-2-2-22-200−2i2i−2i2i22-2-20000000000i2−i2i2−i22−22−2−2i2i−2i2i000000000000000000002−22−2i2−i2i2−i20000
χ492-2-22200-2-22000022-2-2-22-22002-2-222-2-2200000000002−2−22−222−22-2-2200000000000000000000−222−22−2−220000
χ502-2-22200-2-22000022-2-2-22-22002-2-222-2-220000000000−222−22−2−222-2-22000000000000000000002−2−22−222−20000
χ512-2-22200-2-22000022-2-2-22-2200-222-22-2-2200000000002−2−222−2−22-222-2000000000000000000002−2−222−2−220000
χ522-2-22200-2-22000022-2-2-22-2200-222-22-2-220000000000−222−2−222−2-222-200000000000000000000−222−2−222−20000
χ5344444444444444-2-2-2-2-2-2-2-24400001111-2-2-2-2-2-2-2-200000000000000-2-2111111000000000000000000000000
χ544444444444-4-444-2-2-2-2-2-2-2-2-4-400001111-2-2-22222-2000000000000002211-1-1-1-1000000000000000000000000
χ5544444-4-444400-4-4-24-2-24-244000000-2-2-2-22-4-4000020000000000000000220000000000000000000000000000
χ5644444-4-444400-4-4-2-2-2-2-2-2-2-20000001111222−2i32i3−2i32i320000000000000000-1-1i3−i3i3−i3000000000000000000000000
χ5744444-4-444400-4-4-2-2-2-2-2-2-2-200000011112222i3−2i32i3−2i320000000000000000-1-1−i3i3−i3i3000000000000000000000000
χ5844-4-444-4-44-44i−4i-44-2-22-2-22224i−4i00001-11-1-2-22−2i−2i2i2i200000000000000−2i2i1-1ii−i−i000000000000000000000000
χ5944-4-444-4-44-4−4i4i-44-2-22-2-2222−4i4i00001-11-1-2-222i2i−2i−2i2000000000000002i−2i1-1−i−iii000000000000000000000000
χ6044-4-44-44-44-4004-4-242-242-4-4000000-22-222-440000-200000000000000002-20000000000000000000000000000
χ6144-4-44-44-44-4004-4-2-22-2-22220000001-11-122-223−23−2323-20000000000000000-11−333−3000000000000000000000000
χ6244-4-44-44-44-4004-4-2-22-2-22220000001-11-122-2−232323−23-20000000000000000-113−3−33000000000000000000000000
χ634-44-44004-4-400004-24-42-4-22004i−4i4i−4i-2-222000000000000000000−2i2i−2i2i00000000000000000000000000000000
χ644-44-44004-4-400004-24-42-4-2200−4i4i−4i4i-2-2220000000000000000002i−2i2i−2i00000000000000000000000000000000
χ654-44-44004-4-40000-24-22-424-4000000-2-2220000000000−2i22i2−2i22i200000000000000000000000000000000i2−i2i2−i20000
χ664-44-44004-4-40000-24-22-424-4000000-2-22200000000002i2−2i22i2−2i200000000000000000000000000000000−i2i2−i2i20000
χ674-4-44400-4-4400004-2-4-4242-2004-4-44-222-2000000000000000000-222-200000000000000000000000000000000
χ684-4-44400-4-4400004-2-4-4242-200-444-4-222-20000000000000000002-2-2200000000000000000000000000000000
χ694-4-44400-4-440000-2422-4-2-44000000-222-2000000000022−22−222200000000000000000000000000000000−222−20000
χ704-4-44400-4-440000-2422-4-2-44000000-222-20000000000−222222−22000000000000000000000000000000002−2−220000
χ716666-366-3-3-366-3-300000000-3-300000000000000000000002222000000000000000022000000-1-1-1-1000000-1-1
χ726666-366-3-3-366-3-300000000-3-30000000000000000000000-2-2-2-20000000000000000-2-2000000111100000011
χ736666-366-3-3-3-6-6-3-30000000033000000000000000000000022220000000000000000-2-2000000-1-1-1-100000011
χ746666-366-3-3-3-6-6-3-300000000330000000000000000000000-2-2-2-20000000000000000220000001111000000-1-1
χ7566-6-6-36-63-336i−6i3-300000000−3i3i000000000000000000000022-2-200000000000000002i−2i000000-1-111000000−ii
χ7666-6-6-36-63-336i−6i3-300000000−3i3i0000000000000000000000-2-2220000000000000000−2i2i00000011-1-1000000i−i
χ7766-6-6-36-63-33−6i6i3-3000000003i−3i000000000000000000000022-2-20000000000000000−2i2i000000-1-111000000i−i
χ7866-6-6-36-63-33−6i6i3-3000000003i−3i0000000000000000000000-2-22200000000000000002i−2i00000011-1-1000000−ii
χ798-88-88008-8-80000-4-4-4444-4400000022-2-2000000000000000000000000000000000000000000000000000000
χ808-8-88800-8-880000-4-4444-44-40000002-2-22000000000000000000000000000000000000000000000000000000
χ8112121212-6-12-12-6-6-60066000000000000000000000000000000000000000000000000000000000000000000000000
χ821212-12-12-6-12126-6600-66000000000000000000000000000000000000000000000000000000000000000000000000
χ8312-1212-12-600-66600000000000000000000000000000000000022−2222−22000000000000000000000000−22−2200000000
χ8412-1212-12-600-666000000000000000000000000000000000000−2222−22220000000000000000000000002−22−200000000
χ8512-12-1212-60066-600000000000000000000000000000000000022−22−2222000000000000000000000000−222−200000000
χ8612-12-1212-60066-6000000000000000000000000000000000000−222222−220000000000000000000000002−2−2200000000

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