Finite Group Databasebeta

← Group #13137956

Character table — Group #13137956

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222244446666666688999912121212121212121212121218181818181818181818181818182424242424242424363636363636363636363636363636363636363672727272
order12223446664412123366666612124444366612121212121212124488888888121212121212121212121212444444121212121212242424242424242412121212
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
χ3111111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111-1-11111111111-1-111111111-1-1-1-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ61111111111-1-11111111111-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-111
χ81111111111-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1
χ91-1-1111-1-11-1i−i-1111-1-1-1-111i−iii−i−i1-11-1ii−i−i11-1-1i−i11-1-1ii−i−iii−i−ii−i1-1ii−i−ii−i1-11-1i−i11-1-111-1-1ii−i−ii−i1-1
χ101-1-1111-1-11-1i−i-1111-1-1-1-111i−iii−i−i1-11-1ii−i−i11-1-1i−i-1-111−i−iiiii−i−ii−i1-1ii−i−i−ii1-1-11i−i11-1-1-1-111−i−iii−ii-11
χ111-1-1111-1-11-1i−i-1111-1-1-1-111i−i−i−iii1-11-1ii−i−i11-1-1−ii11-1-1−i−iii−i−iiii−i1-1ii−i−ii−i-11-11−ii-1-11111-1-1−i−iiii−i-11
χ121-1-1111-1-11-1i−i-1111-1-1-1-111i−i−i−iii1-11-1ii−i−i11-1-1−ii-1-111ii−i−i−i−iiii−i1-1ii−i−i−ii-111-1−ii-1-111-1-111ii−i−i−ii1-1
χ131-1-1111-1-11-1−ii-1111-1-1-1-111−iiii−i−i1-11-1−i−iii11-1-1i−i11-1-1ii−i−iii−i−i−ii1-1−i−iii−ii-11-11i−i-1-11111-1-1ii−i−i−ii-11
χ141-1-1111-1-11-1−ii-1111-1-1-1-111−iiii−i−i1-11-1−i−iii11-1-1i−i-1-111−i−iiiii−i−i−ii1-1−i−iiii−i-111-1i−i-1-111-1-111−i−iiii−i1-1
χ151-1-1111-1-11-1−ii-1111-1-1-1-111−ii−i−iii1-11-1−i−iii11-1-1−ii11-1-1−i−iii−i−iii−ii1-1−i−iii−ii1-11-1−ii11-1-111-1-1−i−iii−ii1-1
χ161-1-1111-1-11-1−ii-1111-1-1-1-111−ii−i−iii1-11-1−i−iii11-1-1−ii-1-111ii−i−i−i−iii−ii1-1−i−iiii−i1-1-11−ii11-1-1-1-111ii−i−ii−i-11
χ17222222222222222-122-1-12-1222222-1-1-1-1-1-1-1-12-1-122200000000-1-1-1-122-1-1-1-1-1-1002200-1-1-1-1-1-1000000000000
χ18222222222222222-122-1-12-122-2-2-2-2-1-1-1-1-1-1-1-12-1-12-2-200000000111122-1-1-1-1-1-100-2-200111111000000000000
χ1922222222222222-12-1-122-12220000-1-1-1-12222-122-100000022220000-1-1-1-1-1-1-1-10000220000000000-1-1-1-100-1-1
χ2022222222222222-12-1-122-12220000-1-1-1-12222-122-1000000-2-2-2-20000-1-1-1-1-1-1-1-10000-2-2000000000011110011
χ212222222222-2-2222-122-1-12-1-2-22222-1-1-1-111112-1-122200000000-1-1-1-1-2-2-1-1111100-2-200-1-11111000000000000
χ222222222222-2-2222-122-1-12-1-2-2-2-2-2-2-1-1-1-111112-1-12-2-2000000001111-2-2-1-1111100220011-1-1-1-1000000000000
χ232222222222-2-222-12-1-122-12-2-20000-1-1-1-1-2-2-2-2-122-10000002222000011-1-111110000-2-20000000000-1-1-1-10011
χ242222222222-2-222-12-1-122-12-2-20000-1-1-1-1-2-2-2-2-122-1000000-2-2-2-2000011-1-111110000220000000000111100-1-1
χ2522222-2-222200-2-22222222200222222220000-2-2-2-2-2-200000000222200-2-20000000000-2-20000000000000000
χ2622222-2-222200-2-22222222200-2-2-2-222220000-2-2-2-22200000000-2-2-2-200-2-20000000000220000000000000000
χ2722222-2-222200-2-22-122-1-12-1002222-1-1-1-1−i3i3−i3i3-211-2-2-200000000-1-1-1-10011−i3i3−i3i300000011−i3i3−i3i3000000000000
χ2822222-2-222200-2-22-122-1-12-1002222-1-1-1-1i3−i3i3−i3-211-2-2-200000000-1-1-1-10011i3−i3i3−i300000011i3−i3i3−i3000000000000
χ2922222-2-222200-2-22-122-1-12-100-2-2-2-2-1-1-1-1−i3i3−i3i3-211-2220000000011110011−i3i3−i3i3000000-1-1i3−i3i3−i3000000000000
χ3022222-2-222200-2-22-122-1-12-100-2-2-2-2-1-1-1-1i3−i3i3−i3-211-2220000000011110011i3−i3i3−i3000000-1-1−i3i3−i3i3000000000000
χ3122-2-22002-2-20000222-22-2-2-2002-22-222-2-200000000002−22−22−22−22-22-2000000000000000000002−22−22−22−20000
χ3222-2-22002-2-20000222-22-2-2-2002-22-222-2-20000000000−22−22−22−222-22-200000000000000000000−22−22−22−220000
χ3322-2-22002-2-20000222-22-2-2-200-22-2222-2-200000000002−22−2−22−22-22-22000000000000000000002−22−2−22−220000
χ3422-2-22002-2-20000222-22-2-2-200-22-2222-2-20000000000−22−222−22−2-22-2200000000000000000000−22−222−22−20000
χ352-22-2200-2-22000022-22-22-2-2002i−2i−2i2i2-2-2200000000002−2−22i2−i2−i2i22i−2i−2i2i000000000000000000002−2−22i2−i2−i2i20000
χ362-22-2200-2-22000022-22-22-2-2002i−2i−2i2i2-2-220000000000−222−2−i2i2i2−i22i−2i−2i2i00000000000000000000−222−2−i2i2i2−i20000
χ372-22-2200-2-22000022-22-22-2-200−2i2i2i−2i2-2-2200000000002−2−22−i2i2i2−i2−2i2i2i−2i000000000000000000002−2−22−i2i2i2−i20000
χ382-22-2200-2-22000022-22-22-2-200−2i2i2i−2i2-2-220000000000−222−2i2−i2−i2i2−2i2i2i−2i00000000000000000000−222−2i2−i2−i2i20000
χ392-2-2222-2-22-22i−2i-222-1-2-2112-12i−2i2i2i−2i−2i-11-11−i−iii2-11-22i−2i00000000−i−iii2i−2i-11−i−iii002-200−ii-1-111000000000000
χ402-2-2222-2-22-22i−2i-222-1-2-2112-12i−2i−2i−2i2i2i-11-11−i−iii2-11-2−2i2i00000000ii−i−i2i−2i-11−i−iii00-2200i−i11-1-1000000000000
χ412-2-2222-2-22-22i−2i-22-1211-2-2-122i−2i0000-11-112i2i−2i−2i-12-210000002i2i−2i−2i0000−ii-11−i−iii00002-20000000000−i−iii00-11
χ422-2-2222-2-22-22i−2i-22-1211-2-2-122i−2i0000-11-112i2i−2i−2i-12-21000000−2i−2i2i2i0000−ii-11−i−iii0000-220000000000ii−i−i001-1
χ432-2-2222-2-22-2−2i2i-222-1-2-2112-1−2i2i2i2i−2i−2i-11-11ii−i−i2-11-22i−2i00000000−i−iii−2i2i-11ii−i−i00-2200−ii11-1-1000000000000
χ442-2-2222-2-22-2−2i2i-222-1-2-2112-1−2i2i−2i−2i2i2i-11-11ii−i−i2-11-2−2i2i00000000ii−i−i−2i2i-11ii−i−i002-200i−i-1-111000000000000
χ452-2-2222-2-22-2−2i2i-22-1211-2-2-12−2i2i0000-11-11−2i−2i2i2i-12-210000002i2i−2i−2i0000i−i-11ii−i−i0000-220000000000−i−iii001-1
χ462-2-2222-2-22-2−2i2i-22-1211-2-2-12−2i2i0000-11-11−2i−2i2i2i-12-21000000−2i−2i2i2i0000i−i-11ii−i−i00002-20000000000ii−i−i00-11
χ472-2-222-22-22-2002-222-2-2-2-222002i2i−2i−2i2-22-20000-2-222−2i2i000000002i2i−2i−2i00-220000000000−2i2i0000000000000000
χ482-2-222-22-22-2002-222-2-2-2-22200−2i−2i2i2i2-22-20000-2-2222i−2i00000000−2i−2i2i2i00-2200000000002i−2i0000000000000000
χ492-2-222-22-22-2002-22-1-2-2112-1002i2i−2i−2i-11-113−3−33-21-12−2i2i00000000−i−iii001-13−3−33000000i−i−i3i3i3−i3000000000000
χ502-2-222-22-22-2002-22-1-2-2112-1002i2i−2i−2i-11-11−333−3-21-12−2i2i00000000−i−iii001-1−333−3000000i−ii3−i3−i3i3000000000000
χ512-2-222-22-22-2002-22-1-2-2112-100−2i−2i2i2i-11-113−3−33-21-122i−2i00000000ii−i−i001-13−3−33000000−iii3−i3−i3i3000000000000
χ522-2-222-22-22-2002-22-1-2-2112-100−2i−2i2i2i-11-11−333−3-21-122i−2i00000000ii−i−i001-1−333−3000000−ii−i3i3i3−i3000000000000
χ5344444444444444-2-2-2-2-2-2-2-24400001111-2-2-2-2-2-2-2-200000000000000-2-2111111000000000000000000000000
χ544444444444-4-444-2-2-2-2-2-2-2-2-4-4000011112222-2-2-2-2000000000000002211-1-1-1-1000000000000000000000000
χ5544444-4-444400-4-4-24-2-244-24000000-2-2-2-200002-4-420000000000000000220000000000000000000000000000
χ5644444-4-444400-4-4-2-2-2-2-2-2-2-20000001111−2i32i3−2i32i322220000000000000000-1-1i3−i3i3−i3000000000000000000000000
χ5744444-4-444400-4-4-2-2-2-2-2-2-2-200000011112i3−2i32i3−2i322220000000000000000-1-1−i3i3−i3i3000000000000000000000000
χ5844-4-44004-4-400004-24-4-22-42004-44-4-2-222000000000000000000-22-2200000000000000000000000000000000
χ5944-4-44004-4-400004-24-4-22-4200-44-44-2-2220000000000000000002-22-200000000000000000000000000000000
χ6044-4-44004-4-40000-24-224-42-4000000-2-2220000000000000022−2222−220000000000000000000000000000−22−220000
χ6144-4-44004-4-40000-24-224-42-4000000-2-22200000000000000−2222−222200000000000000000000000000002−22−20000
χ624-44-4400-4-4400004-2-442-2-42004i−4i−4i4i-222-2000000000000000000−2i2i2i−2i00000000000000000000000000000000
χ634-44-4400-4-4400004-2-442-2-4200−4i4i4i−4i-222-20000000000000000002i−2i−2i2i00000000000000000000000000000000
χ644-44-4400-4-440000-242-2-442-4000000-222-200000000000000−2i22i22i2−2i20000000000000000000000000000i2−i2−i2i20000
χ654-44-4400-4-440000-242-2-442-4000000-222-2000000000000002i2−2i2−2i22i20000000000000000000000000000−i2i2i2−i20000
χ664-4-4444-4-44-44i−4i-44-2-22222-2-24i−4i00001-11-1−2i−2i2i2i-2-22200000000000000−2i2i1-1ii−i−i000000000000000000000000
χ674-4-4444-4-44-4−4i4i-44-2-22222-2-2−4i4i00001-11-12i2i−2i−2i-2-222000000000000002i−2i1-1−i−iii000000000000000000000000
χ684-4-444-44-44-4004-4-2422-4-4-24000000-22-2200002-44-200000000000000002-20000000000000000000000000000
χ694-4-444-44-44-4004-4-2-22222-2-20000001-11-123−23−232322-2-20000000000000000-11−333−3000000000000000000000000
χ704-4-444-44-44-4004-4-2-22222-2-20000001-11-1−232323−2322-2-20000000000000000-113−3−33000000000000000000000000
χ716666-366-3-3-366-3-300000000-3-300000000000000000022220000000000000000220000000000-1-1-1-10000-1-100
χ726666-366-3-3-366-3-300000000-3-3000000000000000000-2-2-2-20000000000000000-2-20000000000111100001100
χ736666-366-3-3-3-6-6-3-3000000003300000000000000000022220000000000000000-2-20000000000-1-1-1-100001100
χ746666-366-3-3-3-6-6-3-30000000033000000000000000000-2-2-2-2000000000000000022000000000011110000-1-100
χ756-6-66-36-63-336i−6i3-300000000−3i3i00000000000000000022-2-200000000000000002i−2i0000000000-1-1110000−ii00
χ766-6-66-36-63-336i−6i3-300000000−3i3i000000000000000000-2-2220000000000000000−2i2i000000000011-1-10000i−i00
χ776-6-66-36-63-33−6i6i3-3000000003i−3i00000000000000000022-2-20000000000000000−2i2i0000000000-1-1110000i−i00
χ786-6-66-36-63-33−6i6i3-3000000003i−3i000000000000000000-2-22200000000000000002i−2i000000000011-1-10000−ii00
χ7988-8-88008-8-80000-4-4-44-444400000022-2-2000000000000000000000000000000000000000000000000000000
χ808-88-8800-8-880000-4-44-44-4440000002-2-22000000000000000000000000000000000000000000000000000000
χ8112121212-6-12-12-6-6-60066000000000000000000000000000000000000000000000000000000000000000000000000
χ821212-12-12-600-6660000000000000000000000000000000022−2222−220000000000000000000000000000−22−2200000000
χ831212-12-12-600-66600000000000000000000000000000000−2222−222200000000000000000000000000002−22−200000000
χ8412-1212-12-60066-60000000000000000000000000000000022−22−22220000000000000000000000000000−222−200000000
χ8512-1212-12-60066-600000000000000000000000000000000−222222−2200000000000000000000000000002−2−2200000000
χ8612-12-1212-6-12126-6600-66000000000000000000000000000000000000000000000000000000000000000000000000

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