Finite Group Databasebeta

← Group #13140905

Character table — Group #13140905

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222244446666666688999912121212121212121212121218181818181818181818181818182424242424242424363636363636363636363636363636363636363672727272
order1222344666441212336666661212222236661212121212121212446666888888881212121212121212444444121212121212242424242424242412121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111-1-11111111111-1-111111111111-1-1-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ61111111111-1-11111111111-1-111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111-1-11111111111-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-111111111-1-1-1-1-1-111
χ81111111111-1-11111111111-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1
χ91-11-111-1-11-11-11-111-1-1-11-111-111-1-11-1-1111-111-1-1-11-111-1-1ii−i−iii−i−i1-11-111-1-11-1i−ii−i1-111-1-1ii−i−iii−i−ii−ii−i
χ101-11-111-1-11-11-11-111-1-1-11-111-111-1-11-1-1111-111-1-1-11-111-1-1−i−iii−i−iii1-11-111-1-11-1−ii−ii1-111-1-1−i−iii−i−iii−ii−ii
χ111-11-111-1-11-11-11-111-1-1-11-111-1-1-1111-1-1111-111-1-1-1-11-1-111ii−i−i−i−iii1-11-111-1-1-11i−i−ii-11-1-111ii−i−i−i−iiii−i−ii
χ121-11-111-1-11-11-11-111-1-1-11-111-1-1-1111-1-1111-111-1-1-1-11-1-111−i−iiiii−i−i1-11-111-1-1-11−iii−i-11-1-111−i−iiiii−i−i−iii−i
χ131-11-111-1-11-1-111-111-1-1-11-11-1111-1-11-1-1111-1-1-111-11-111-1-1ii−i−iii−i−i-111-1-1-111-11−ii−ii1-1-1-111ii−i−iii−i−i−ii−ii
χ141-11-111-1-11-1-111-111-1-1-11-11-1111-1-11-1-1111-1-1-111-11-111-1-1−i−iii−i−iii-111-1-1-111-11i−ii−i1-1-1-111−i−iii−i−iiii−ii−i
χ151-11-111-1-11-1-111-111-1-1-11-11-11-1-1111-1-1111-1-1-111-1-11-1-111ii−i−i−i−iii-111-1-1-1111-1−iii−i-1111-1-1ii−i−i−i−iii−iii−i
χ161-11-111-1-11-1-111-111-1-1-11-11-11-1-1111-1-1111-1-1-111-1-11-1-111−i−iiiii−i−i-111-1-1-1111-1i−i−ii-1111-1-1−i−iiiii−i−ii−i−ii
χ17222222222222222-12-1-122-1222222-1-1-1-12-1-1-1-1-1-1222-1-1-1-10000000022-1-1-1-1-1-1220000-1-1-1-1-1-1000000000000
χ18222222222222222-12-1-122-122-2-2-2-2-1-1-1-12-1-1-1-1-1-12-2-211110000000022-1-1-1-1-1-1-2-20000111111000000000000
χ1922222222222222-12-122-1-12220000-1-1-1-1-1222222-100000000002222-1-1-1-1-1-1-1-10000220000000000-1-1-1-100-1-1
χ2022222222222222-12-122-1-12220000-1-1-1-1-1222222-10000000000-2-2-2-2-1-1-1-1-1-1-1-10000-2-2000000000011110011
χ212222222222-2-2222-12-1-122-1-2-22222-1-1-1-12-1-11111222-1-1-1-100000000-2-2-1-11111-2-20000-1-11111000000000000
χ222222222222-2-2222-12-1-122-1-2-2-2-2-2-2-1-1-1-12-1-111112-2-2111100000000-2-2-1-1111122000011-1-1-1-1000000000000
χ232222222222-2-222-12-122-1-12-2-20000-1-1-1-1-122-2-2-2-2-10000000000222211-1-111110000-2-20000000000-1-1-1-10011
χ242222222222-2-222-12-122-1-12-2-20000-1-1-1-1-122-2-2-2-2-10000000000-2-2-2-211-1-111110000220000000000111100-1-1
χ2522222-2-222200-2-2222222220022222222-2-2-20000-2-2-222220000000000-2-20000000000-2-20000000000000000
χ2622222-2-222200-2-22222222200-2-2-2-22222-2-2-20000-222-2-2-2-20000000000-2-20000000000220000000000000000
χ2722222-2-222200-2-22-12-1-122-1002222-1-1-1-1-211−i3i3−i3i3-2-2-2-1-1-1-1000000000011−i3i3−i3i300000011−i3i3−i3i3000000000000
χ2822222-2-222200-2-22-12-1-122-1002222-1-1-1-1-211i3−i3i3−i3-2-2-2-1-1-1-1000000000011i3−i3i3−i300000011i3−i3i3−i3000000000000
χ2922222-2-222200-2-22-12-1-122-100-2-2-2-2-1-1-1-1-211−i3i3−i3i3-2221111000000000011−i3i3−i3i3000000-1-1i3−i3i3−i3000000000000
χ3022222-2-222200-2-22-12-1-122-100-2-2-2-2-1-1-1-1-211i3−i3i3−i3-2221111000000000011i3−i3i3−i3000000-1-1−i3i3−i3i3000000000000
χ3122-2-22002-2-200002222-2-2-2-2002-22-222-2-200000000002-22-22−22−22−22−2000000000000000000002−22−22−22−20000
χ3222-2-22002-2-200002222-2-2-2-2002-22-222-2-200000000002-22-2−22−22−22−2200000000000000000000−22−22−22−220000
χ3322-2-22002-2-200002222-2-2-2-200-22-2222-2-20000000000-22-222−22−2−22−22000000000000000000002−22−2−22−220000
χ3422-2-22002-2-200002222-2-2-2-200-22-2222-2-20000000000-22-22−22−222−22−200000000000000000000−22−222−22−20000
χ352-22-222-2-22-22-22-22-1-2112-2-12-222-2-2-111-12-11-1-111-22-2-1-111000000002-2-11-1-1112-20000-11-1-111000000000000
χ362-22-222-2-22-22-22-22-1-2112-2-12-2-2-222-111-12-11-1-111-2-2211-1-1000000002-2-11-1-111-2200001-111-1-1000000000000
χ372-22-222-2-22-22-22-2-121-2-2-1122-20000-111-1-12-222-2-2100000000002i2i−2i−2i-11-11-1-11100002i−2i0000000000−i−iii00−ii
χ382-22-222-2-22-22-22-2-121-2-2-1122-20000-111-1-12-222-2-210000000000−2i−2i2i2i-11-11-1-1110000−2i2i0000000000ii−i−i00i−i
χ392-22-222-2-22-2-222-22-1-2112-2-1-2222-2-2-111-12-1111-1-1-22-2-1-11100000000-22-1111-1-1-220000-1111-1-1000000000000
χ402-22-222-2-22-2-222-22-1-2112-2-1-22-2-222-111-12-1111-1-1-2-2211-1-100000000-22-1111-1-12-200001-1-1-111000000000000
χ412-22-222-2-22-2-222-2-121-2-2-112-220000-111-1-12-2-2-222100000000002i2i−2i−2i1-1-1111-1-10000−2i2i0000000000−i−iii00i−i
χ422-22-222-2-22-2-222-2-121-2-2-112-220000-111-1-12-2-2-22210000000000−2i−2i2i2i1-1-1111-1-100002i−2i0000000000ii−i−i00−ii
χ432-22-22-22-22-200-2222-2-2-22-220022-2-22-2-22-2-2200002-2222-2-20000000000-220000000000-220000000000000000
χ442-22-22-22-22-200-2222-2-2-22-2200-2-2222-2-22-2-22000022-2-2-2220000000000-2200000000002-20000000000000000
χ452-22-22-22-22-200-222-1-2112-2-10022-2-2-111-1-21-1−i3i3i3−i32-22-1-11100000000001-1−i3i3i3−i30000001-1−i3i3i3−i3000000000000
χ462-22-22-22-22-200-222-1-2112-2-10022-2-2-111-1-21-1i3−i3−i3i32-22-1-11100000000001-1i3−i3−i3i30000001-1i3−i3−i3i3000000000000
χ472-22-22-22-22-200-222-1-2112-2-100-2-222-111-1-21-1−i3i3i3−i322-211-1-100000000001-1−i3i3i3−i3000000-11i3−i3−i3i3000000000000
χ482-22-22-22-22-200-222-1-2112-2-100-2-222-111-1-21-1i3−i3−i3i322-211-1-100000000001-1i3−i3−i3i3000000-11−i3i3i3−i3000000000000
χ492-2-22200-2-22000022-2-22-22-2002-2-222-22-200000000002-2-22−i2i2i2−i2−i2i2i2−i200000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ502-2-22200-2-22000022-2-22-22-2002-2-222-22-200000000002-2-22i2−i2−i2i2i2−i2−i2i200000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ512-2-22200-2-22000022-2-22-22-200-222-22-22-20000000000-222-2−i2i2i2−i2i2−i2−i2i200000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ522-2-22200-2-22000022-2-22-22-200-222-22-22-20000000000-222-2i2−i2−i2i2−i2i2i2−i200000000000000000000i2−i2−i2i2−i2i2i2−i20000
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
χ5544444-4-444400-4-4-24-244-2-24000000-2-2-2-22-4-4000020000000000000000220000000000000000000000000000
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
χ5844-4-44004-4-400004-24-22-4-42004-44-4-2-2220000000000-22-220000000000000000000000000000000000000000
χ5944-4-44004-4-400004-24-22-4-4200-44-44-2-22200000000002-22-20000000000000000000000000000000000000000
χ6044-4-44004-4-40000-24-24-422-4000000-2-22200000000000000000022−2222−22000000000000000000000000−22−220000
χ6144-4-44004-4-40000-24-24-422-4000000-2-222000000000000000000−2222−22220000000000000000000000002−22−20000
χ624-44-444-4-44-44-44-4-2-2222-22-24-400001-1-11-2-22-2-222200000000000000-221-111-1-1000000000000000000000000
χ634-44-444-4-44-4-444-4-2-2222-22-2-4400001-1-11-2-2222-2-22000000000000002-21-1-1-111000000000000000000000000
χ644-44-44-44-44-400-44-242-4-4-224000000-222-22-440000-200000000000000002-20000000000000000000000000000
χ654-44-44-44-44-400-44-2-2222-22-20000001-1-1122-2−2i32i32i3−2i3-20000000000000000-11i3−i3−i3i3000000000000000000000000
χ664-44-44-44-44-400-44-2-2222-22-20000001-1-1122-22i3−2i3−2i32i3-20000000000000000-11−i3i3i3−i3000000000000000000000000
χ674-4-44400-4-4400004-2-42-2-442004-4-44-22-220000000000-222-20000000000000000000000000000000000000000
χ684-4-44400-4-4400004-2-42-2-44200-444-4-22-2200000000002-2-220000000000000000000000000000000000000000
χ694-4-44400-4-440000-242-442-2-4000000-22-22000000000000000000−2i22i22i2−2i2000000000000000000000000i2−i2−i2i20000
χ704-4-44400-4-440000-242-442-2-4000000-22-220000000000000000002i2−2i2−2i22i2000000000000000000000000−i2i2i2−i20000
χ716666-366-3-3-366-3-300000000-3-300000000000000000000002222000000000000002200000000-1-1-1-10000-1-100
χ726666-366-3-3-366-3-300000000-3-30000000000000000000000-2-2-2-200000000000000-2-200000000111100001100
χ736666-366-3-3-3-6-6-3-300000000330000000000000000000000222200000000000000-2-200000000-1-1-1-100001100
χ746666-366-3-3-3-6-6-3-300000000330000000000000000000000-2-2-2-200000000000000220000000011110000-1-100
χ756-66-6-36-63-336-6-3300000000-3300000000000000000000002i2i−2i−2i000000000000002i−2i00000000−i−iii0000−ii00
χ766-66-6-36-63-336-6-3300000000-330000000000000000000000−2i−2i2i2i00000000000000−2i2i00000000ii−i−i0000i−i00
χ776-66-6-36-63-33-66-33000000003-300000000000000000000002i2i−2i−2i00000000000000−2i2i00000000−i−iii0000i−i00
χ786-66-6-36-63-33-66-33000000003-30000000000000000000000−2i−2i2i2i000000000000002i−2i00000000ii−i−i0000−ii00
χ7988-8-88008-8-80000-4-4-4-4444400000022-2-2000000000000000000000000000000000000000000000000000000
χ808-8-88800-8-880000-4-444-44-440000002-22-2000000000000000000000000000000000000000000000000000000
χ8112121212-6-12-12-6-6-60066000000000000000000000000000000000000000000000000000000000000000000000000
χ821212-12-12-600-66600000000000000000000000000000000000022−2222−22000000000000000000000000−22−2200000000
χ831212-12-12-600-666000000000000000000000000000000000000−2222−22220000000000000000000000002−22−200000000
χ8412-1212-12-6-12126-66006-6000000000000000000000000000000000000000000000000000000000000000000000000
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).