Finite Group Databasebeta

← Group #13137952

Character table — Group #13137952

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222244446666666688999912121212121212121212121218181818181818181818181818182424242424242424363636363636363636363636363636363636363672727272
order122234466644121233666666121244443666121212121212121244888888881212121212121212121212122244441212121212122424242424242424661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
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
χ51111111111-1-11111111111-1-1111111111-1-1-1-111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ61111111111-1-11111111111-1-1111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111-1-11111111111-1-1-1-1-1-111111-1-1-1-1111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-111
χ81111111111-1-11111111111-1-1-1-1-1-111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1
χ91-11-111-11-1-1i−i-1111-11-1-1-11i−iii−i−i1-11-11ii−i−i1-1-1i−iii−i−i11-1-1ii−i−ii−i1-1ii−i−i1-11-1i−ii−i11-1-111-1-1ii−i−i1-1i−i
χ101-11-111-11-1-1i−i-1111-11-1-1-11i−iii−i−i1-11-11ii−i−i1-1-1i−i−i−iii-1-111ii−i−ii−i1-1ii−i−i-111-1−iii−i11-1-1-1-111−i−iii-11−ii
χ111-11-111-11-1-1i−i-1111-11-1-1-11i−i−i−iii1-11-11ii−i−i1-1-1−iiii−i−i-1-111−i−iiii−i1-1ii−i−i1-1-11−ii−ii-1-111-1-111ii−i−i1-1−ii
χ121-11-111-11-1-1i−i-1111-11-1-1-11i−i−i−iii1-11-11ii−i−i1-1-1−ii−i−iii11-1-1−i−iiii−i1-1ii−i−i-11-11i−i−ii-1-11111-1-1−i−iii-11i−i
χ131-11-111-11-1-1−ii-1111-11-1-1-11−iiii−i−i1-11-11−i−iii1-1-1i−iii−i−i11-1-1ii−i−i−ii1-1−i−iii-11-11−iii−i-1-11111-1-1ii−i−i-11−ii
χ141-11-111-11-1-1−ii-1111-11-1-1-11−iiii−i−i1-11-11−i−iii1-1-1i−i−i−iii-1-111ii−i−i−ii1-1−i−iii1-1-11i−ii−i-1-111-1-111−i−iii1-1i−i
χ151-11-111-11-1-1−ii-1111-11-1-1-11−ii−i−iii1-11-11−i−iii1-1-1−iiii−i−i-1-111−i−iii−ii1-1−i−iii-111-1i−i−ii11-1-1-1-111ii−i−i-11i−i
χ161-11-111-11-1-1−ii-1111-11-1-1-11−ii−i−iii1-11-11−i−iii1-1-1−ii−i−iii11-1-1−i−iii−ii1-1−i−iii1-11-1−ii−ii11-1-111-1-1−i−iii1-1−ii
χ17222222222222222-1-1-1-1222220000-1-1-1-1-1222222-100222200000000-1-1-1-1-1-1-1-12200000000000000-1-1-1-1-1-100
χ18222222222222222-1-1-1-1222220000-1-1-1-1-1222222-100-2-2-2-200000000-1-1-1-1-1-1-1-1-2-20000000000000011111100
χ1922222222222222-12222-1-1-1222222-1-1-1-12-1-1-1-1-1-122200000000-1-1-1-122-1-1-1-1-1-1002200-1-1-1-1-1-1000000000000
χ2022222222222222-12222-1-1-122-2-2-2-2-1-1-1-12-1-1-1-1-1-12-2-200000000111122-1-1-1-1-1-100-2-200111111000000000000
χ212222222222-2-2222-1-1-1-1222-2-20000-1-1-1-1-1-2-2-2-222-10022220000000011-1-11111-2-200000000000000-1-1-1-11100
χ222222222222-2-2222-1-1-1-1222-2-20000-1-1-1-1-1-2-2-2-222-100-2-2-2-20000000011-1-1111122000000000000001111-1-100
χ232222222222-2-222-12222-1-1-1-2-22222-1-1-1-121111-1-122200000000-1-1-1-1-2-2-1-1111100-2-200-1-11111000000000000
χ242222222222-2-222-12222-1-1-1-2-2-2-2-2-2-1-1-1-121111-1-12-2-2000000001111-2-2-1-1111100220011-1-1-1-1000000000000
χ2522222-2-222200-2-2222222220022222222-20000-2-2-2-2-200000000222200-2-20000000000-2-20000000000000000
χ2622222-2-222200-2-22222222200-2-2-2-22222-20000-2-2-22200000000-2-2-2-200-2-20000000000220000000000000000
χ2722222-2-222200-2-2-12222-1-1-1002222-1-1-1-1-2−i3i3−i3i311-2-2-200000000-1-1-1-10011−i3i3−i3i300000011−i3i3−i3i3000000000000
χ2822222-2-222200-2-2-12222-1-1-1002222-1-1-1-1-2i3−i3i3−i311-2-2-200000000-1-1-1-10011i3−i3i3−i300000011i3−i3i3−i3000000000000
χ2922222-2-222200-2-2-12222-1-1-100-2-2-2-2-1-1-1-1-2−i3i3−i3i311-2220000000011110011−i3i3−i3i3000000-1-1i3−i3i3−i3000000000000
χ3022222-2-222200-2-2-12222-1-1-100-2-2-2-2-1-1-1-1-2i3−i3i3−i311-2220000000011110011i3−i3i3−i3000000-1-1−i3i3−i3i3000000000000
χ3122-2-2200-22-2000022-2-22-22-2002i−2i2i−2i2-2-2200000000002−22−2−i2i2−i2i22i−2i2i−2i00000000000000000000−i2i2−i2i22−22−20000
χ3222-2-2200-22-2000022-2-22-22-2002i−2i2i−2i2-2-220000000000−22−22i2−i2i2−i22i−2i2i−2i00000000000000000000i2−i2i2−i2−22−220000
χ3322-2-2200-22-2000022-2-22-22-200−2i2i−2i2i2-2-2200000000002−22−2i2−i2i2−i2−2i2i−2i2i00000000000000000000i2−i2i2−i22−22−20000
χ3422-2-2200-22-2000022-2-22-22-200−2i2i−2i2i2-2-220000000000−22−22−i2i2−i2i2−2i2i−2i2i00000000000000000000−i2i2−i2i2−22−220000
χ352-22-222-22-2-22i−2i-222-11-11-2-222i−2i0000-11-11-12i2i−2i−2i2-21002i2i−2i−2i00000000−ii-11−i−iii2-200000000000000−i−iii-1100
χ362-22-222-22-2-22i−2i-222-11-11-2-222i−2i0000-11-11-12i2i−2i−2i2-2100−2i−2i2i2i00000000−ii-11−i−iii-2200000000000000ii−i−i1-100
χ372-22-222-22-2-22i−2i-22-12-22-211-12i−2i2i2i−2i−2i-11-112−i−iii-11-22i−2i00000000−i−iii2i−2i-11−i−iii002-200−ii-1-111000000000000
χ382-22-222-22-2-22i−2i-22-12-22-211-12i−2i−2i−2i2i2i-11-112−i−iii-11-2−2i2i00000000ii−i−i2i−2i-11−i−iii00-2200i−i11-1-1000000000000
χ392-22-222-22-2-2−2i2i-222-11-11-2-22−2i2i0000-11-11-1−2i−2i2i2i2-21002i2i−2i−2i00000000i−i-11ii−i−i-2200000000000000−i−iii1-100
χ402-22-222-22-2-2−2i2i-222-11-11-2-22−2i2i0000-11-11-1−2i−2i2i2i2-2100−2i−2i2i2i00000000i−i-11ii−i−i2-200000000000000ii−i−i-1100
χ412-22-222-22-2-2−2i2i-22-12-22-211-1−2i2i2i2i−2i−2i-11-112ii−i−i-11-22i−2i00000000−i−iii−2i2i-11ii−i−i00-2200−ii11-1-1000000000000
χ422-22-222-22-2-2−2i2i-22-12-22-211-1−2i2i−2i−2i2i2i-11-112ii−i−i-11-2−2i2i00000000ii−i−i−2i2i-11ii−i−i002-200i−i-1-111000000000000
χ432-22-22-222-2-2002-222-22-2-2-22002i2i−2i−2i2-22-2-20000-222−2i2i000000002i2i−2i−2i00-220000000000−2i2i0000000000000000
χ442-22-22-222-2-2002-222-22-2-2-2200−2i−2i2i2i2-22-2-20000-2222i−2i00000000−2i−2i2i2i00-2200000000002i−2i0000000000000000
χ452-22-22-222-2-2002-2-12-22-211-1002i2i−2i−2i-11-11-23−3−331-12−2i2i00000000−i−iii001-13−3−33000000i−i−i3i3i3−i3000000000000
χ462-22-22-222-2-2002-2-12-22-211-1002i2i−2i−2i-11-11-2−333−31-12−2i2i00000000−i−iii001-1−333−3000000i−ii3−i3−i3i3000000000000
χ472-22-22-222-2-2002-2-12-22-211-100−2i−2i2i2i-11-11-23−3−331-122i−2i00000000ii−i−i001-13−3−33000000−iii3−i3−i3i3000000000000
χ482-22-22-222-2-2002-2-12-22-211-100−2i−2i2i2i-11-11-2−333−31-122i−2i00000000ii−i−i001-1−333−3000000−ii−i3i3i3−i3000000000000
χ492-2-22200-2-220000222-2-22-2-2002-2-2222-2-20000000000−i2i2i2−i2−i2i2i2−i22-2-2200000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ502-2-22200-2-220000222-2-22-2-2002-2-2222-2-20000000000i2−i2−i2i2i2−i2−i2i22-2-2200000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ512-2-22200-2-220000222-2-22-2-200-222-222-2-20000000000−i2i2i2−i2i2−i2−i2i2-222-200000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ522-2-22200-2-220000222-2-22-2-200-222-222-2-20000000000i2−i2−i2i2−i2i2i2−i2-222-200000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ5344444444444444-2-2-2-2-2-2-2-24400001111-2-2-2-2-2-2-2-200000000000000-2-2111111000000000000000000000000
χ544444444444-4-444-2-2-2-2-2-2-2-2-4-400001111-22222-2-2-2000000000000002211-1-1-1-1000000000000000000000000
χ5544444-4-444400-4-44-2-2-2-2444000000-2-2-2-220000-4-420000000000000000220000000000000000000000000000
χ5644444-4-444400-4-4-2-2-2-2-2-2-2-200000011112−2i32i3−2i32i32220000000000000000-1-1i3−i3i3−i3000000000000000000000000
χ5744444-4-444400-4-4-2-2-2-2-2-2-2-2000000111122i3−2i32i3−2i32220000000000000000-1-1−i3i3−i3i3000000000000000000000000
χ5844-4-4400-44-400004-222-2-44-4000000-222-2000000000022−2222−2200000000000000000000000000000000−22−220000
χ5944-4-4400-44-400004-222-2-44-4000000-222-20000000000−2222−2222000000000000000000000000000000002−22−20000
χ6044-4-4400-44-40000-24-4-442-22004i−4i4i−4i-222-2000000000000000000−2i2i−2i2i00000000000000000000000000000000
χ6144-4-4400-44-40000-24-4-442-2200−4i4i−4i4i-222-20000000000000000002i−2i2i−2i00000000000000000000000000000000
χ624-44-444-44-4-44i−4i-44-2-22-2222-24i−4i00001-11-1-2−2i−2i2i2i-22200000000000000−2i2i1-1ii−i−i000000000000000000000000
χ634-44-444-44-4-4−4i4i-44-2-22-2222-2−4i4i00001-11-1-22i2i−2i−2i-222000000000000002i−2i1-1−i−iii000000000000000000000000
χ644-44-44-444-4-4004-44-22-22-4-44000000-22-2220000-44-200000000000000002-20000000000000000000000000000
χ654-44-44-444-4-4004-4-2-22-2222-20000001-11-1223−23−23232-2-20000000000000000-11−333−3000000000000000000000000
χ664-44-44-444-4-4004-4-2-22-2222-20000001-11-12−232323−232-2-20000000000000000-113−3−33000000000000000000000000
χ674-4-44400-4-4400004-2-2224-4-4000000-2-2220000000000−2i22i22i2−2i200000000000000000000000000000000i2−i2−i2i20000
χ684-4-44400-4-4400004-2-2224-4-4000000-2-22200000000002i2−2i2−2i22i200000000000000000000000000000000−i2i2i2−i20000
χ694-4-44400-4-440000-244-4-4-222004-4-44-2-222000000000000000000-222-200000000000000000000000000000000
χ704-4-44400-4-440000-244-4-4-22200-444-4-2-2220000000000000000002-2-2200000000000000000000000000000000
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
χ756-66-6-36-6-3336i−6i3-300000000−3i3i000000000000000000000022-2-200000000000000002i−2i000000-1-111000000−ii
χ766-66-6-36-6-3336i−6i3-300000000−3i3i0000000000000000000000-2-2220000000000000000−2i2i00000011-1-1000000i−i
χ776-66-6-36-6-333−6i6i3-3000000003i−3i000000000000000000000022-2-20000000000000000−2i2i000000-1-111000000i−i
χ786-66-6-36-6-333−6i6i3-3000000003i−3i0000000000000000000000-2-22200000000000000002i−2i00000011-1-1000000−ii
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).