Finite Group Databasebeta

← Group #13137942

Character table — Group #13137942

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222244446666666688999912121212121212121212121218181818181818181818181818182424242424242424363636363636363636363636363636363636363672727272
order122234466644121233666666121244443666121212121212121222888888881212121212121212121212124444446612121212242424242424242412121212
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
χ3111111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ4111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1
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
χ71111111111-1-11111111111-1-1-1-1-1-111111-1-1-1-1111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1
χ81111111111-1-11111111111-1-1-1-1-1-111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111
χ911-1-11-111-1-1i−i-1111-11-11-1-1i−i11-1-11-11-1-1ii−i−i1-111-111-1-111-1-111-1-1i−i1-1ii−i−ii−ii−ii−i1-1ii−i−i11-1-111-1-1i−ii−i
χ1011-1-11-111-1-1i−i-1111-11-11-1-1i−i11-1-11-11-1-1ii−i−i1-111-1-1-111-1-11111-1-1i−i1-1ii−i−i−iii−i−ii1-1ii−i−i-1-111-1-111−ii−ii
χ1111-1-11-111-1-1i−i-1111-11-11-1-1i−i-1-1111-11-1-1ii−i−i1-11-1111-1-1-1-111-1-111i−i1-1ii−i−ii−i−ii−ii-11−i−iii-1-11111-1-1−iii−i
χ1211-1-11-111-1-1i−i-1111-11-11-1-1i−i-1-1111-11-1-1ii−i−i1-11-11-1-11111-1-1-1-111i−i1-1ii−i−i−ii−iii−i-11−i−iii11-1-1-1-111i−i−ii
χ1311-1-11-111-1-1−ii-1111-11-11-1-1−ii11-1-11-11-1-1−i−iii1-111-111-1-111-1-111-1-1−ii1-1−i−iii−ii−ii−ii1-1−i−iii11-1-111-1-1−ii−ii
χ1411-1-11-111-1-1−ii-1111-11-11-1-1−ii11-1-11-11-1-1−i−iii1-111-1-1-111-1-11111-1-1−ii1-1−i−iiii−i−iii−i1-1−i−iii-1-111-1-111i−ii−i
χ1511-1-11-111-1-1−ii-1111-11-11-1-1−ii-1-1111-11-1-1−i−iii1-11-1111-1-1-1-111-1-111−ii1-1−i−iii−iii−ii−i-11ii−i−i-1-11111-1-1i−i−ii
χ1611-1-11-111-1-1−ii-1111-11-11-1-1−ii-1-1111-11-1-1−i−iii1-11-11-1-11111-1-1-1-111−ii1-1−i−iiii−ii−i−ii-11ii−i−i11-1-1-1-111−iii−i
χ17222222222222222-122-1-1-12222222-1-1-1-12-1-1-1-1-1-122200000000-1-1-1-122-1-1-1-1-1-1002200-1-1-1-1-1-1000000000000
χ18222222222222222-122-1-1-1222-2-2-2-2-1-1-1-12-1-1-1-1-1-12-2-200000000111122-1-1-1-1-1-100-2-200111111000000000000
χ1922222222222222-12-1-1222-1220000-1-1-1-1-1222222-100222200000000-1-1-1-1-1-1-1-12200000000000000-1-1-1-100-1-1
χ2022222222222222-12-1-1222-1220000-1-1-1-1-1222222-100-2-2-2-200000000-1-1-1-1-1-1-1-1-2-20000000000000011110011
χ212222222222-2-2222-122-1-1-12-2-22222-1-1-1-121111-1-122200000000-1-1-1-1-2-2-1-1111100-2-200-1-11111000000000000
χ222222222222-2-2222-122-1-1-12-2-2-2-2-2-2-1-1-1-121111-1-12-2-2000000001111-2-2-1-1111100220011-1-1-1-1000000000000
χ232222222222-2-222-12-1-1222-1-2-20000-1-1-1-1-1-2-2-2-222-10022220000000011-1-11111-2-200000000000000-1-1-1-10011
χ242222222222-2-222-12-1-1222-1-2-20000-1-1-1-1-1-2-2-2-222-100-2-2-2-20000000011-1-111112200000000000000111100-1-1
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
χ2722222-2-222200-2-22-122-1-1-12002222-1-1-1-1-2−i3i3−i3i311-2-2-200000000-1-1-1-10011−i3i3−i3i300000011−i3i3−i3i3000000000000
χ2822222-2-222200-2-22-122-1-1-12002222-1-1-1-1-2i3−i3i3−i311-2-2-200000000-1-1-1-10011i3−i3i3−i300000011i3−i3i3−i3000000000000
χ2922222-2-222200-2-22-122-1-1-1200-2-2-2-2-1-1-1-1-2−i3i3−i3i311-2220000000011110011−i3i3−i3i3000000-1-1i3−i3i3−i3000000000000
χ3022222-2-222200-2-22-122-1-1-1200-2-2-2-2-1-1-1-1-2i3−i3i3−i311-2220000000011110011i3−i3i3−i3000000-1-1−i3i3−i3i3000000000000
χ3122-2-222-22-2-2002-222-22-22-2-20022-2-22-22-220000-22-2-220000000022-2-200-220000000000-220000000000000000
χ3222-2-222-22-2-2002-222-22-22-2-200-2-2222-22-220000-22-22-200000000-2-22200-2200000000002-20000000000000000
χ3322-2-222-22-2-2002-22-1-221-11-20022-2-2-11-1123−3−331-1-2-2200000000-1-111001-13−3−330000001-13−3−33000000000000
χ3422-2-222-22-2-2002-22-1-221-11-20022-2-2-11-112−333−31-1-2-2200000000-1-111001-1−333−30000001-1−333−3000000000000
χ3522-2-222-22-2-2002-22-1-221-11-200-2-222-11-1123−3−331-1-22-20000000011-1-1001-13−3−33000000-11−333−3000000000000
χ3622-2-222-22-2-2002-22-1-221-11-200-2-222-11-112−333−31-1-22-20000000011-1-1001-1−333−3000000-113−3−33000000000000
χ3722-2-22-222-2-22i−2i-222-1-221-11-22i−2i22-2-2-11-11-2−i−iii-1122-200000000-1-1112i−2i-11−i−iii002i−2i00-11−i−iii000000000000
χ3822-2-22-222-2-22i−2i-222-1-221-11-22i−2i-2-222-11-11-2−i−iii-112-220000000011-1-12i−2i-11−i−iii00−2i2i001-1ii−i−i000000000000
χ3922-2-22-222-2-22i−2i-22-121-1-22-212i−2i0000-11-1112i2i−2i−2i2-2-10022-2-200000000−ii-11−i−iii2i−2i00000000000000-1-11100−ii
χ4022-2-22-222-2-22i−2i-22-121-1-22-212i−2i0000-11-1112i2i−2i−2i2-2-100-2-22200000000−ii-11−i−iii−2i2i0000000000000011-1-100i−i
χ4122-2-22-222-2-2−2i2i-222-1-221-11-2−2i2i22-2-2-11-11-2ii−i−i-1122-200000000-1-111−2i2i-11ii−i−i00−2i2i00-11ii−i−i000000000000
χ4222-2-22-222-2-2−2i2i-222-1-221-11-2−2i2i-2-222-11-11-2ii−i−i-112-220000000011-1-1−2i2i-11ii−i−i002i−2i001-1−i−iii000000000000
χ4322-2-22-222-2-2−2i2i-22-121-1-22-21−2i2i0000-11-111−2i−2i2i2i2-2-10022-2-200000000i−i-11ii−i−i−2i2i00000000000000-1-11100i−i
χ4422-2-22-222-2-2−2i2i-22-121-1-22-21−2i2i0000-11-111−2i−2i2i2i2-2-100-2-22200000000i−i-11ii−i−i2i−2i0000000000000011-1-100−ii
χ452-22-2200-22-2000022-2-22-2-22002i−2i2i−2i2-2-2200000000002−22−2−i2i2−i2i22i−2i2i−2i00000000000000000000−i2i2−i2i22−22−20000
χ462-22-2200-22-2000022-2-22-2-22002i−2i2i−2i2-2-220000000000−22−22i2−i2i2−i22i−2i2i−2i00000000000000000000i2−i2i2−i2−22−220000
χ472-22-2200-22-2000022-2-22-2-2200−2i2i−2i2i2-2-2200000000002−22−2i2−i2i2−i2−2i2i−2i2i00000000000000000000i2−i2i2−i22−22−20000
χ482-22-2200-22-2000022-2-22-2-2200−2i2i−2i2i2-2-220000000000−22−22−i2i2−i2i2−2i2i−2i2i00000000000000000000−i2i2−i2i2−22−220000
χ492-2-22200-2-220000222-2-2-22-2002i−2i−2i2i22-2-200000000002−2−22−i2i2i2−i22i−2i−2i2i00000000000000000000−i2i2i2−i22−2−220000
χ502-2-22200-2-220000222-2-2-22-2002i−2i−2i2i22-2-20000000000−222−2i2−i2−i2i22i−2i−2i2i00000000000000000000i2−i2−i2i2−222−20000
χ512-2-22200-2-220000222-2-2-22-200−2i2i2i−2i22-2-200000000002−2−22i2−i2−i2i2−2i2i2i−2i00000000000000000000i2−i2−i2i22−2−220000
χ522-2-22200-2-220000222-2-2-22-200−2i2i2i−2i22-2-20000000000−222−2−i2i2i2−i2−2i2i2i−2i00000000000000000000−i2i2i2−i2−222−20000
χ5344444444444444-2-2-2-2-2-2-2-24400001111-2-2-2-2-2-2-2-200000000000000-2-2111111000000000000000000000000
χ544444444444-4-444-2-2-2-2-2-2-2-2-4-400001111-22222-2-2-2000000000000002211-1-1-1-1000000000000000000000000
χ5544444-4-444400-4-4-24-2-2444-2000000-2-2-2-220000-4-420000000000000000220000000000000000000000000000
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
χ5844-4-444-44-4-4004-4-242-2-44-42000000-22-22-20000-44200000000000000002-20000000000000000000000000000
χ5944-4-444-44-4-4004-4-2-22-22-2220000001-11-1-223−23−23232-220000000000000000-11−333−3000000000000000000000000
χ6044-4-444-44-4-4004-4-2-22-22-2220000001-11-1-2−232323−232-220000000000000000-113−3−33000000000000000000000000
χ6144-4-44-444-4-44i−4i-44-2-22-22-2224i−4i00001-11-12−2i−2i2i2i-22-200000000000000−2i2i1-1ii−i−i000000000000000000000000
χ6244-4-44-444-4-4−4i4i-44-2-22-22-222−4i4i00001-11-122i2i−2i−2i-22-2000000000000002i−2i1-1−i−iii000000000000000000000000
χ634-44-4400-44-400004-2-4-4-2224004i−4i4i−4i-222-2000000000000000000−2i2i−2i2i00000000000000000000000000000000
χ644-44-4400-44-400004-2-4-4-222400−4i4i−4i4i-222-20000000000000000002i−2i2i−2i00000000000000000000000000000000
χ654-44-4400-44-40000-24224-4-4-2000000-222-2000000000022−2222−2200000000000000000000000000000000−22−220000
χ664-44-4400-44-40000-24224-4-4-2000000-222-20000000000−2222−2222000000000000000000000000000000002−22−20000
χ674-4-44400-4-4400004-24-422-2-4004i−4i−4i4i-2-222000000000000000000−2i2i2i−2i00000000000000000000000000000000
χ684-4-44400-4-4400004-24-422-2-400−4i4i4i−4i-2-2220000000000000000002i−2i−2i2i00000000000000000000000000000000
χ694-4-44400-4-440000-24-22-4-442000000-2-222000000000022−22−222200000000000000000000000000000000−222−20000
χ704-4-44400-4-440000-24-22-4-442000000-2-2220000000000−222222−22000000000000000000000000000000002−2−220000
χ716666-366-3-3-366-3-300000000-3-300000000000000000000002222000000000000000022000000-1-1-1-10000-1-100
χ726666-366-3-3-366-3-300000000-3-30000000000000000000000-2-2-2-20000000000000000-2-2000000111100001100
χ736666-366-3-3-3-6-6-3-30000000033000000000000000000000022220000000000000000-2-2000000-1-1-1-100001100
χ746666-366-3-3-3-6-6-3-300000000330000000000000000000000-2-2-2-200000000000000002200000011110000-1-100
χ7566-6-6-3-66-3336i−6i3-300000000−3i3i000000000000000000000022-2-200000000000000002i−2i000000-1-1110000−ii00
χ7666-6-6-3-66-3336i−6i3-300000000−3i3i0000000000000000000000-2-2220000000000000000−2i2i00000011-1-10000i−i00
χ7766-6-6-3-66-333−6i6i3-3000000003i−3i000000000000000000000022-2-20000000000000000−2i2i000000-1-1110000i−i00
χ7866-6-6-3-66-333−6i6i3-3000000003i−3i0000000000000000000000-2-22200000000000000002i−2i00000011-1-10000−ii00
χ798-88-8800-88-80000-4-444-444-40000002-2-22000000000000000000000000000000000000000000000000000000
χ808-8-88800-8-880000-4-4-4444-4400000022-2-2000000000000000000000000000000000000000000000000000000
χ8112121212-6-12-12-6-6-60066000000000000000000000000000000000000000000000000000000000000000000000000
χ821212-12-12-612-12-66600-66000000000000000000000000000000000000000000000000000000000000000000000000
χ8312-1212-12-6006-66000000000000000000000000000000000000−2i22i2−2i22i2000000000000000000000000i2−i2i2−i200000000
χ8412-1212-12-6006-660000000000000000000000000000000000002i2−2i22i2−2i2000000000000000000000000−i2i2−i2i200000000
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).