Finite Group Databasebeta

← Group #13137986

Character table — Group #13137986

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
χ3111111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
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
χ51111111111-1-11111111111-1-111111111111-1-1-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
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
χ71111111111-1-11111111111-1-1-1-1-1-11111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-111
χ81111111111-1-11111111111-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1111111-1-1
χ911-1-111-1-11-1i−i1-111-111-1-1-1i−iii−i−i1-11-11-1-1ii−i−i1i−iii−i−i11-1-1ii−i−ii−i1-1ii−i−i1-11-1i−i11-1-1i−iii−i−i11-1-11-1i−i
χ1011-1-111-1-11-1i−i1-111-111-1-1-1i−iii−i−i1-11-11-1-1ii−i−i1i−i−i−iii-1-111ii−i−ii−i1-1ii−i−i1-1-11−ii11-1-1i−i−i−iii-1-111-11−ii
χ1111-1-111-1-11-1i−i1-111-111-1-1-1i−i−i−iii1-11-11-1-1ii−i−i1−iiii−i−i-1-111−i−iiii−i1-1ii−i−i-111-1−ii-1-111−iiii−i−i-1-1111-1−ii
χ1211-1-111-1-11-1i−i1-111-111-1-1-1i−i−i−iii1-11-11-1-1ii−i−i1−ii−i−iii11-1-1−i−iiii−i1-1ii−i−i-11-11i−i-1-111−ii−i−iii11-1-1-11i−i
χ1311-1-111-1-11-1−ii1-111-111-1-1-1−iiii−i−i1-11-11-1-1−i−iii1i−iii−i−i11-1-1ii−i−i−ii1-1−i−iii-11-11−ii-1-111i−iii−i−i11-1-1-11−ii
χ1411-1-111-1-11-1−ii1-111-111-1-1-1−iiii−i−i1-11-11-1-1−i−iii1i−i−i−iii-1-111ii−i−i−ii1-1−i−iii-111-1i−i-1-111i−i−i−iii-1-1111-1i−i
χ1511-1-111-1-11-1−ii1-111-111-1-1-1−ii−i−iii1-11-11-1-1−i−iii1−iiii−i−i-1-111−i−iii−ii1-1−i−iii1-1-11i−i11-1-1−iiii−i−i-1-111-11i−i
χ1611-1-111-1-11-1−ii1-111-111-1-1-1−ii−i−iii1-11-11-1-1−i−iii1−ii−i−iii11-1-1−i−iii−ii1-1−i−iii1-11-1−ii11-1-1−ii−i−iii11-1-11-1−ii
χ17222222222222222-122-1-1-12222222-1-1-1-1-12-1-1-1-1-122200000000-1-1-1-122-1-1-1-1-1-1220000-1-1-1-1-1-1000000000000
χ18222222222222222-122-1-1-1222-2-2-2-2-1-1-1-1-12-1-1-1-1-12-2-200000000111122-1-1-1-1-1-1-2-20000111111000000000000
χ1922222222222222-12-1-1222-1220000-1-1-1-12-122222-100000022220000-1-1-1-1-1-1-1-10000220000000000-1-1-1-100-1-1
χ2022222222222222-12-1-1222-1220000-1-1-1-12-122222-1000000-2-2-2-20000-1-1-1-1-1-1-1-10000-2-2000000000011110011
χ212222222222-2-2222-122-1-1-12-2-22222-1-1-1-1-12-1111122200000000-1-1-1-1-2-2-1-11111-2-200001111-1-1000000000000
χ222222222222-2-2222-122-1-1-12-2-2-2-2-2-2-1-1-1-1-12-111112-2-2000000001111-2-2-1-11111220000-1-1-1-111000000000000
χ232222222222-2-222-12-1-1222-1-2-20000-1-1-1-12-12-2-2-2-2-10000002222000011-1-111110000-2-20000000000-1-1-1-10011
χ242222222222-2-222-12-1-1222-1-2-20000-1-1-1-12-12-2-2-2-2-1000000-2-2-2-2000011-1-111110000220000000000111100-1-1
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
χ2722222-2-222200-2-22-122-1-1-12002222-1-1-1-11-21−i3i3−i3i3-2-2-200000000-1-1-1-10011−i3i3−i3i3000000−i3i3−i3i311000000000000
χ2822222-2-222200-2-22-122-1-1-12002222-1-1-1-11-21i3−i3i3−i3-2-2-200000000-1-1-1-10011i3−i3i3−i3000000i3−i3i3−i311000000000000
χ2922222-2-222200-2-22-122-1-1-1200-2-2-2-2-1-1-1-11-21−i3i3−i3i3-2220000000011110011−i3i3−i3i3000000i3−i3i3−i3-1-1000000000000
χ3022222-2-222200-2-22-122-1-1-1200-2-2-2-2-1-1-1-11-21i3−i3i3−i3-2220000000011110011i3−i3i3−i3000000−i3i3−i3i3-1-1000000000000
χ3122-2-222-2-22-22i−2i2-22-1-22-111-22i−2i2i2i−2i−2i-11-11-1-21−i−iii22i−2i00000000−i−iii2i−2i-11−i−iii2-20000-1-111−ii000000000000
χ3222-2-222-2-22-22i−2i2-22-1-22-111-22i−2i−2i−2i2i2i-11-11-1-21−i−iii2−2i2i00000000ii−i−i2i−2i-11−i−iii-22000011-1-1i−i000000000000
χ3322-2-222-2-22-22i−2i2-2-121-12-2-212i−2i0000-11-1121-22i2i−2i−2i-100000022-2-20000−ii-11−i−iii00002i−2i0000000000-1-11100−ii
χ3422-2-222-2-22-22i−2i2-2-121-12-2-212i−2i0000-11-1121-22i2i−2i−2i-1000000-2-2220000−ii-11−i−iii0000−2i2i000000000011-1-100i−i
χ3522-2-222-2-22-2−2i2i2-22-1-22-111-2−2i2i2i2i−2i−2i-11-11-1-21ii−i−i22i−2i00000000−i−iii−2i2i-11ii−i−i-22000011-1-1−ii000000000000
χ3622-2-222-2-22-2−2i2i2-22-1-22-111-2−2i2i−2i−2i2i2i-11-11-1-21ii−i−i2−2i2i00000000ii−i−i−2i2i-11ii−i−i2-20000-1-111i−i000000000000
χ3722-2-222-2-22-2−2i2i2-2-121-12-2-21−2i2i0000-11-1121-2−2i−2i2i2i-100000022-2-20000i−i-11ii−i−i0000−2i2i0000000000-1-11100i−i
χ3822-2-222-2-22-2−2i2i2-2-121-12-2-21−2i2i0000-11-1121-2−2i−2i2i2i-1000000-2-2220000i−i-11ii−i−i00002i−2i000000000011-1-100−ii
χ3922-2-22-22-22-200-2222-222-2-2-2002i2i−2i−2i2-22-2-2220000-2−2i2i000000002i2i−2i−2i00-2200000000000000−2i2i000000000000
χ4022-2-22-22-22-200-2222-222-2-2-200−2i−2i2i2i2-22-2-2220000-22i−2i00000000−2i−2i2i2i00-22000000000000002i−2i000000000000
χ4122-2-22-22-22-200-222-1-22-111-2002i2i−2i−2i-11-1112-13−3−33-2−2i2i00000000−i−iii001-13−3−33000000−i3i3i3−i3i−i000000000000
χ4222-2-22-22-22-200-222-1-22-111-2002i2i−2i−2i-11-1112-1−333−3-2−2i2i00000000−i−iii001-1−333−3000000i3−i3−i3i3i−i000000000000
χ4322-2-22-22-22-200-222-1-22-111-200−2i−2i2i2i-11-1112-13−3−33-22i−2i00000000ii−i−i001-13−3−33000000i3−i3−i3i3−ii000000000000
χ4422-2-22-22-22-200-222-1-22-111-200−2i−2i2i2i-11-1112-1−333−3-22i−2i00000000ii−i−i001-1−333−3000000−i3i3i3−i3−ii000000000000
χ452-22-22002-2-20000222-2-22-2-2002i−2i2i−2i22-2-20000000000−i2i2−i2i22−22−22i−2i2i−2i00000000000000000000−i2i2−i2i22−22−20000
χ462-22-22002-2-20000222-2-22-2-2002i−2i2i−2i22-2-20000000000i2−i2i2−i2−22−222i−2i2i−2i00000000000000000000i2−i2i2−i2−22−220000
χ472-22-22002-2-20000222-2-22-2-200−2i2i−2i2i22-2-20000000000−i2i2−i2i2−22−22−2i2i−2i2i00000000000000000000−i2i2−i2i2−22−220000
χ482-22-22002-2-20000222-2-22-2-200−2i2i−2i2i22-2-20000000000i2−i2i2−i22−22−2−2i2i−2i2i00000000000000000000i2−i2i2−i22−22−20000
χ492-2-22200-2-22000022-2-2-2-222002-2-222-2-2200000000002−2−22−222−22-2-22000000000000000000002−2−22−222−20000
χ502-2-22200-2-22000022-2-2-2-222002-2-222-2-220000000000−222−22−2−222-2-2200000000000000000000−222−22−2−220000
χ512-2-22200-2-22000022-2-2-2-22200-222-22-2-2200000000002−2−222−2−22-222-2000000000000000000002−2−222−2−220000
χ522-2-22200-2-22000022-2-2-2-22200-222-22-2-220000000000−222−2−222−2-222-200000000000000000000−222−2−222−20000
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
χ5544444-4-444400-4-4-24-2-2444-2000000-2-2-2-2-42-4000020000000000000000220000000000000000000000000000
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−4i4-4-2-22-2-22224i−4i00001-11-1-222−2i−2i2i2i-200000000000000−2i2i1-1ii−i−i000000000000000000000000
χ5944-4-444-4-44-4−4i4i4-4-2-22-2-2222−4i4i00001-11-1-2222i2i−2i−2i-2000000000000002i−2i1-1−i−iii000000000000000000000000
χ6044-4-44-44-44-400-44-242-24-4-42000000-22-22-4-240000200000000000000002-20000000000000000000000000000
χ6144-4-44-44-44-400-44-2-22-2-22220000001-11-12-2-223−23−232320000000000000000-11−333−3000000000000000000000000
χ6244-4-44-44-44-400-44-2-22-2-22220000001-11-12-2-2−232323−2320000000000000000-113−3−33000000000000000000000000
χ634-44-44004-4-400004-24-42-22-4004i−4i4i−4i-2-222000000000000000000−2i2i−2i2i00000000000000000000000000000000
χ644-44-44004-4-400004-24-42-22-400−4i4i−4i4i-2-2220000000000000000002i−2i2i−2i00000000000000000000000000000000
χ654-44-44004-4-40000-24-22-44-42000000-2-2220000000000000022−2222−220000000000000000000000000000−22−220000
χ664-44-44004-4-40000-24-22-44-42000000-2-22200000000000000−2222−222200000000000000000000000000002−22−20000
χ674-4-44400-4-4400004-2-4-422-24004-4-44-222-2000000000000000000-222-200000000000000000000000000000000
χ684-4-44400-4-4400004-2-4-422-2400-444-4-222-20000000000000000002-2-2200000000000000000000000000000000
χ694-4-44400-4-440000-2422-4-44-2000000-222-20000000000000022−22−22220000000000000000000000000000−222−20000
χ704-4-44400-4-440000-2422-4-44-2000000-222-200000000000000−222222−2200000000000000000000000000002−2−220000
χ716666-366-3-3-366-3-300000000-3-300000000000000000022220000000000000000002200000000-1-1-1-10000-1-100
χ726666-366-3-3-366-3-300000000-3-3000000000000000000-2-2-2-2000000000000000000-2-200000000111100001100
χ736666-366-3-3-3-6-6-3-300000000330000000000000000002222000000000000000000-2-200000000-1-1-1-100001100
χ746666-366-3-3-3-6-6-3-30000000033000000000000000000-2-2-2-2000000000000000000220000000011110000-1-100
χ7566-6-6-36-63-336i−6i-3300000000−3i3i0000000000000000002i2i−2i−2i0000000000000000002-200000000−i−iii0000-1100
χ7666-6-6-36-63-336i−6i-3300000000−3i3i000000000000000000−2i−2i2i2i000000000000000000-2200000000ii−i−i00001-100
χ7766-6-6-36-63-33−6i6i-33000000003i−3i0000000000000000002i2i−2i−2i000000000000000000-2200000000−i−iii00001-100
χ7866-6-6-36-63-33−6i6i-33000000003i−3i000000000000000000−2i−2i2i2i0000000000000000002-200000000ii−i−i0000-1100
χ798-88-88008-8-80000-4-4-444-44400000022-2-2000000000000000000000000000000000000000000000000000000
χ808-8-88800-8-880000-4-44444-4-40000002-2-22000000000000000000000000000000000000000000000000000000
χ8112121212-6-12-12-6-6-60066000000000000000000000000000000000000000000000000000000000000000000000000
χ821212-12-12-6-12126-66006-6000000000000000000000000000000000000000000000000000000000000000000000000
χ8312-1212-12-600-66600000000000000000000000000000000−2i22i2−2i22i20000000000000000000000000000i2−i2i2−i200000000
χ8412-1212-12-600-666000000000000000000000000000000002i2−2i22i2−2i20000000000000000000000000000−i2i2−i2i200000000
χ8512-12-1212-60066-60000000000000000000000000000000022−22−22220000000000000000000000000000−222−200000000
χ8612-12-1212-60066-600000000000000000000000000000000−222222−2200000000000000000000000000002−2−2200000000

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