Finite Group Databasebeta

← Group #13140623

Character table — Group #13140623

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222244446666666688999912121212121212121212121218181818181818181818181818182424242424242424363636363636363636363636363636363636363672727272
order12223446662212123366666666444436666666121212124488888888121212126666661212444444121212121212242424242424242412121212
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
χ51111111111-1-11111111111-1-111111-1-1-1-1111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ61111111111-1-11111111111-1-111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111-1-11111111111-1-1-1-1-1-11-1-1-1-11111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111111111-1-1-1-1-1-111
χ81111111111-1-11111111111-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-1-1
χ911-1-111-1-1-111-1-1111-111-1-1-11-1ii−i−i111-1-1-1-1111-1-1i−i11-1-1ii−i−iii−i−i1-111-1-11-11-1i−ii−ii−iii−i−i11-1-1ii−i−i1-1i−i
χ1011-1-111-1-1-111-1-1111-111-1-1-11-1ii−i−i111-1-1-1-1111-1-1i−i-1-111−i−iiiii−i−i1-111-1-11-1-11i−i−iii−iii−i−i-1-111−i−iii-11−ii
χ1111-1-111-1-1-111-1-1111-111-1-1-11-1−i−iii111-1-1-1-1111-1-1−ii11-1-1−i−iii−i−iii1-111-1-11-11-1−ii−ii−ii−i−iii11-1-1−i−iii1-1−ii
χ1211-1-111-1-1-111-1-1111-111-1-1-11-1−i−iii111-1-1-1-1111-1-1−ii-1-111ii−i−i−i−iii1-111-1-11-1-11−iii−i−ii−i−iii-1-111ii−i−i-11i−i
χ1311-1-111-1-1-11-11-1111-111-1-1-1-11ii−i−i1-1-111-1-1111-1-1i−i11-1-1ii−i−iii−i−i-11-1-1111-1-11−ii−iii−i−i−iii11-1-1ii−i−i-11−ii
χ1411-1-111-1-1-11-11-1111-111-1-1-1-11ii−i−i1-1-111-1-1111-1-1i−i-1-111−i−iiiii−i−i-11-1-1111-11-1−iii−ii−i−i−iii-1-111−i−iii1-1i−i
χ1511-1-111-1-1-11-11-1111-111-1-1-1-11−i−iii1-1-111-1-1111-1-1−ii11-1-1−i−iii−i−iii-11-1-1111-1-11i−ii−i−iiii−i−i11-1-1−i−iii-11i−i
χ1611-1-111-1-1-11-11-1111-111-1-1-1-11−i−iii1-1-111-1-1111-1-1−ii-1-111ii−i−i−i−iii-11-1-1111-11-1i−i−ii−iiii−i−i-1-111ii−i−i1-1−ii
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
χ1922222222222222-12-1-122-12220000-12222-1-1-1-122-100000022220000-1-1-1-1-1-1-1-10000220000000000-1-1-1-100-1-1
χ2022222222222222-12-1-122-12220000-12222-1-1-1-122-1000000-2-2-2-20000-1-1-1-1-1-1-1-10000-2-2000000000011110011
χ212222222222-2-2222-122-1-12-1-2-22222-11111-1-1-12-1-122200000000-1-1-1-1-2-21111-1-100-2-200-1-11111000000000000
χ222222222222-2-2222-122-1-12-1-2-2-2-2-2-2-11111-1-1-12-1-12-2-2000000001111-2-21111-1-100220011-1-1-1-1000000000000
χ232222222222-2-222-12-1-122-12-2-20000-1-2-2-2-2-1-1-1-122-100000022220000111111-1-10000-2-20000000000-1-1-1-10011
χ242222222222-2-222-12-1-122-12-2-20000-1-2-2-2-2-1-1-1-122-1000000-2-2-2-20000111111-1-10000220000000000111100-1-1
χ2522222-2-222200-2-22222222200222220000222-2-2-2-2-2-2000000002222000000-2-2000000-2-20000000000000000
χ2622222-2-222200-2-22222222200-2-2-2-220000222-2-2-2-22200000000-2-2-2-2000000-2-2000000220000000000000000
χ2722222-2-222200-2-22-122-1-12-1002222-1−i3i3−i3i3-1-1-1-211-2-2-200000000-1-1-1-100−i3i3−i3i31100000011−i3i3−i3i3000000000000
χ2822222-2-222200-2-22-122-1-12-1002222-1i3−i3i3−i3-1-1-1-211-2-2-200000000-1-1-1-100i3−i3i3−i31100000011i3−i3i3−i3000000000000
χ2922222-2-222200-2-22-122-1-12-100-2-2-2-2-1−i3i3−i3i3-1-1-1-211-22200000000111100−i3i3−i3i311000000-1-1i3−i3i3−i3000000000000
χ3022222-2-222200-2-22-122-1-12-100-2-2-2-2-1i3−i3i3−i3-1-1-1-211-22200000000111100i3−i3i3−i311000000-1-1−i3i3−i3i3000000000000
χ3122-2-222-2-2-222-2-222-1-22-11-212-22i2i−2i−2i-1-1-11111-12-11-22i−2i00000000−i−iii2-2-1-111-11002i−2i00−ii−i−iii000000000000
χ3222-2-222-2-2-222-2-222-1-22-11-212-2−2i−2i2i2i-1-1-11111-12-11-2−2i2i00000000ii−i−i2-2-1-111-1100−2i2i00i−iii−i−i000000000000
χ3322-2-222-2-2-222-2-22-121-12-21-22-20000-122-2-211-1-12-210000002i2i−2i−2i0000-11-1-111-1100002i−2i0000000000−i−iii00−ii
χ3422-2-222-2-2-222-2-22-121-12-21-22-20000-122-2-211-1-12-21000000−2i−2i2i2i0000-11-1-111-110000−2i2i0000000000ii−i−i00i−i
χ3522-2-222-2-2-22-22-222-1-22-11-21-222i2i−2i−2i-111-1-111-12-11-22i−2i00000000−i−iii-2211-1-1-1100−2i2i00−iiii−i−i000000000000
χ3622-2-222-2-2-22-22-222-1-22-11-21-22−2i−2i2i2i-111-1-111-12-11-2−2i2i00000000ii−i−i-2211-1-1-11002i−2i00i−i−i−iii000000000000
χ3722-2-222-2-2-22-22-22-121-12-21-2-220000-1-2-22211-1-12-210000002i2i−2i−2i00001-111-1-1-110000−2i2i0000000000−i−iii00i−i
χ3822-2-222-2-2-22-22-22-121-12-21-2-220000-1-2-22211-1-12-21000000−2i−2i2i2i00001-111-1-1-1100002i−2i0000000000ii−i−i00−ii
χ3922-2-22-22-2-22002-222-222-2-2-2002i2i−2i−2i20000-2-22-2-222−2i2i000000002i2i−2i−2i000000-22000000−2i2i0000000000000000
χ4022-2-22-22-2-22002-222-222-2-2-200−2i−2i2i2i20000-2-22-2-2222i−2i00000000−2i−2i2i2i000000-220000002i−2i0000000000000000
χ4122-2-22-22-2-22002-22-1-22-11-21002i2i−2i−2i-1−i3i3i3−i311-1-21-12−2i2i00000000−i−iii00−i3i3i3−i31-1000000i−i3−3−33000000000000
χ4222-2-22-22-2-22002-22-1-22-11-21002i2i−2i−2i-1i3−i3−i3i311-1-21-12−2i2i00000000−i−iii00i3−i3−i3i31-1000000i−i−333−3000000000000
χ4322-2-22-22-2-22002-22-1-22-11-2100−2i−2i2i2i-1−i3i3i3−i311-1-21-122i−2i00000000ii−i−i00−i3i3i3−i31-1000000−ii−333−3000000000000
χ4422-2-22-22-2-22002-22-1-22-11-2100−2i−2i2i2i-1i3−i3−i3i311-1-21-122i−2i00000000ii−i−i00i3−i3−i3i31-1000000−ii3−3−33000000000000
χ452-22-22002-2-20000222-2-2-2-22002-22-2200002-2-2000000−i2i2−i2i2−i2i2−i2i22-22-200000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ462-22-22002-2-20000222-2-2-2-22002-22-2200002-2-2000000i2−i2i2−i2i2−i2i2−i22-22-200000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ472-22-22002-2-20000222-2-2-2-2200-22-22200002-2-2000000−i2i2−i2i2i2−i2i2−i2-22-2200000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ482-22-22002-2-20000222-2-2-2-2200-22-22200002-2-2000000i2−i2i2−i2−i2i2−i2i2-22-2200000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ492-2-22200-22-2000022-2-2-222-2002i−2i−2i2i20000-22-2000000−i2i2i2−i22−2−222i−2i−2i2i00000000000000000000−i2i2i2−i22−2−220000
χ502-2-22200-22-2000022-2-2-222-2002i−2i−2i2i20000-22-2000000i2−i2−i2i2−222−22i−2i−2i2i00000000000000000000i2−i2−i2i2−222−20000
χ512-2-22200-22-2000022-2-2-222-200−2i2i2i−2i20000-22-2000000−i2i2i2−i2−222−2−2i2i2i−2i00000000000000000000−i2i2i2−i2−222−20000
χ522-2-22200-22-2000022-2-2-222-200−2i2i2i−2i20000-22-2000000i2−i2−i2i22−2−22−2i2i2i−2i00000000000000000000i2−i2−i2i22−2−220000
χ5344444444444444-2-2-2-2-2-2-2-24400001-2-2-2-2111-2-2-2-200000000000000-2-2111111000000000000000000000000
χ544444444444-4-444-2-2-2-2-2-2-2-2-4-4000012222111-2-2-2-20000000000000022-1-1-1-111000000000000000000000000
χ5544444-4-444400-4-4-24-2-244-24000000-20000-2-2-22-4-420000000000000000000022000000000000000000000000
χ5644444-4-444400-4-4-2-2-2-2-2-2-2-20000001−2i32i3−2i32i311122220000000000000000i3−i3i3−i3-1-1000000000000000000000000
χ5744444-4-444400-4-4-2-2-2-2-2-2-2-200000012i3−2i32i3−2i311122220000000000000000−i3i3−i3i3-1-1000000000000000000000000
χ5844-4-444-4-4-444-4-44-2-22-2-22224-400001-2-222-1-11-2-22200000000000000-2211-1-11-1000000000000000000000000
χ5944-4-444-4-4-44-44-44-2-22-2-2222-440000122-2-2-1-11-2-222000000000000002-2-1-1111-1000000000000000000000000
χ6044-4-44-44-4-44004-4-242-24-42-4000000-2000022-22-44-2000000000000000000002-2000000000000000000000000
χ6144-4-44-44-4-44004-4-2-22-2-22220000001−2i32i32i3−2i3-1-1122-2-20000000000000000i3−i3−i3i3-11000000000000000000000000
χ6244-4-44-44-4-44004-4-2-22-2-222200000012i3−2i3−2i32i3-1-1122-2-20000000000000000−i3i3i3−i3-11000000000000000000000000
χ634-44-44004-4-400004-24-422-4-2004-44-4-20000-22200000000000000-22-2200000000000000000000000000000000
χ644-44-44004-4-400004-24-422-4-200-44-44-20000-222000000000000002-22-200000000000000000000000000000000
χ654-44-44004-4-40000-24-22-4-424000000-20000-2220000000000−2i22i2−2i22i20000000000000000000000000000i2−i2i2−i20000
χ664-44-44004-4-40000-24-22-4-424000000-20000-22200000000002i2−2i22i2−2i20000000000000000000000000000−i2i2−i2i20000
χ674-4-44400-44-400004-2-4-42-242004i−4i−4i4i-200002-2200000000000000−2i2i2i−2i00000000000000000000000000000000
χ684-4-44400-44-400004-2-4-42-24200−4i4i4i−4i-200002-22000000000000002i−2i−2i2i00000000000000000000000000000000
χ694-4-44400-44-40000-2422-44-2-4000000-200002-22000000000022−22−22220000000000000000000000000000−222−20000
χ704-4-44400-44-40000-2422-44-2-4000000-200002-220000000000−222222−2200000000000000000000000000002−2−220000
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
χ7566-6-6-36-633-36-63-300000000-3300000000000000000022-2-200000000000000002-20000000000-1-1110000-1100
χ7666-6-6-36-633-36-63-300000000-33000000000000000000-2-2220000000000000000-22000000000011-1-100001-100
χ7766-6-6-36-633-3-663-3000000003-300000000000000000022-2-20000000000000000-220000000000-1-11100001-100
χ7866-6-6-36-633-3-663-3000000003-3000000000000000000-2-22200000000000000002-2000000000011-1-10000-1100
χ798-88-88008-8-80000-4-4-44444-4000000200002-2-200000000000000000000000000000000000000000000000000
χ808-8-88800-88-80000-4-4444-4-4400000020000-22-200000000000000000000000000000000000000000000000000
χ8112121212-6-12-12-6-6-60066000000000000000000000000000000000000000000000000000000000000000000000000
χ821212-12-12-6-121266-600-66000000000000000000000000000000000000000000000000000000000000000000000000
χ8312-1212-12-600-66600000000000000000000000000000000−2i22i2−2i22i20000000000000000000000000000i2−i2i2−i200000000
χ8412-1212-12-600-666000000000000000000000000000000002i2−2i22i2−2i20000000000000000000000000000−i2i2−i2i200000000
χ8512-12-1212-6006-6600000000000000000000000000000000−2i22i22i2−2i20000000000000000000000000000i2−i2−i2i200000000
χ8612-12-1212-6006-66000000000000000000000000000000002i2−2i2−2i22i20000000000000000000000000000−i2i2i2−i200000000

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