Finite Group Databasebeta

← Group #13137943

Character table — Group #13137943

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
χ911-1-11-111-1-1i−i-1111-11-11-1-1i−i11-1-11-11-1-11-1ii−i−i11-111-1-111-1-111-1-1i−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−i11-1-11-11-1-11-1ii−i−i11-111-1-1-1-111-1-111i−i1-1ii−i−ii−i−ii−ii1-1ii−i−i-1-111-1-111−ii−ii
χ1111-1-11-111-1-1i−i-1111-11-11-1-1i−i-1-1111-11-1-11-1ii−i−i1-11-1-11111-1-1-1-111i−i1-1ii−i−i−iii−i−ii-11−i−iii11-1-1-1-111i−i−ii
χ1211-1-11-111-1-1i−i-1111-11-11-1-1i−i-1-1111-11-1-11-1ii−i−i1-11-1-111-1-11111-1-1i−i1-1ii−i−i−ii−iii−i-11−i−iii-1-11111-1-1−iii−i
χ1311-1-11-111-1-1−ii-1111-11-11-1-1−ii11-1-11-11-1-11-1−i−iii11-111-1-111-1-111-1-1−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−ii11-1-11-11-1-11-1−i−iii11-111-1-1-1-111-1-111−ii1-1−i−iii−iii−ii−i1-1−i−iii-1-111-1-111i−ii−i
χ1511-1-11-111-1-1−ii-1111-11-11-1-1−ii-1-1111-11-1-11-1−i−iii1-11-1-11111-1-1-1-111−ii1-1−i−iiii−i−iii−i-11ii−i−i11-1-1-1-111−iii−i
χ1611-1-11-111-1-1−ii-1111-11-11-1-1−ii-1-1111-11-1-11-1−i−iii1-11-1-111-1-11111-1-1−ii1-1−i−iiii−ii−i−ii-11ii−i−i-1-11111-1-1i−i−ii
χ17222222222222222-1-122-12-1222222-1-1-1-12-1-1-1-1-1-1222-1-1-1-10000000022-1-1-1-1-1-1220000-1-1-1-1-1-1000000000000
χ18222222222222222-1-122-12-122-2-2-2-2-1-1-1-12-1-1-1-1-1-12-2-211110000000022-1-1-1-1-1-1-2-20000111111000000000000
χ1922222222222222-122-1-12-12220000-1-1-1-1-1222222-100000000002222-1-1-1-1-1-1-1-10000220000000000-1-1-1-100-1-1
χ2022222222222222-122-1-12-12220000-1-1-1-1-1222222-10000000000-2-2-2-2-1-1-1-1-1-1-1-10000-2-2000000000011110011
χ212222222222-2-2222-1-122-12-1-2-22222-1-1-1-12-1-11111222-1-1-1-100000000-2-2-1-11111-2-20000-1-11111000000000000
χ222222222222-2-2222-1-122-12-1-2-2-2-2-2-2-1-1-1-12-1-111112-2-2111100000000-2-2-1-1111122000011-1-1-1-1000000000000
χ232222222222-2-222-122-1-12-12-2-20000-1-1-1-1-122-2-2-2-2-10000000000222211-1-111110000-2-20000000000-1-1-1-10011
χ242222222222-2-222-122-1-12-12-2-20000-1-1-1-1-122-2-2-2-2-10000000000-2-2-2-211-1-111110000220000000000111100-1-1
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
χ2722222-2-222200-2-22-1-122-12-1002222-1-1-1-1-211−i3i3−i3i3-2-2-2-1-1-1-1000000000011−i3i3−i3i300000011−i3i3−i3i3000000000000
χ2822222-2-222200-2-22-1-122-12-1002222-1-1-1-1-211i3−i3i3−i3-2-2-2-1-1-1-1000000000011i3−i3i3−i300000011i3−i3i3−i3000000000000
χ2922222-2-222200-2-22-1-122-12-100-2-2-2-2-1-1-1-1-211−i3i3−i3i3-2221111000000000011−i3i3−i3i3000000-1-1i3−i3i3−i3000000000000
χ3022222-2-222200-2-22-1-122-12-100-2-2-2-2-1-1-1-1-211i3−i3i3−i3-2221111000000000011i3−i3i3−i3000000-1-1−i3i3−i3i3000000000000
χ3122-2-222-22-2-2002-222-22-22-2-20022-2-22-22-22-220000-2-2222-2-20000000000-220000000000-220000000000000000
χ3222-2-222-22-2-2002-222-22-22-2-200-2-2222-22-22-220000-22-2-2-2220000000000-2200000000002-20000000000000000
χ3322-2-222-22-2-2002-22-112-2-1-210022-2-2-11-1121-13−3−33-2-22-1-11100000000001-13−3−330000001-13−3−33000000000000
χ3422-2-222-22-2-2002-22-112-2-1-210022-2-2-11-1121-1−333−3-2-22-1-11100000000001-1−333−30000001-1−333−3000000000000
χ3522-2-222-22-2-2002-22-112-2-1-2100-2-222-11-1121-13−3−33-22-211-1-100000000001-13−3−33000000-11−333−3000000000000
χ3622-2-222-22-2-2002-22-112-2-1-2100-2-222-11-1121-1−333−3-22-211-1-100000000001-1−333−3000000-113−3−33000000000000
χ3722-2-22-222-2-22i−2i-222-112-2-1-212i−2i22-2-2-11-11-2-11−i−iii22-2-1-111000000002i−2i-11−i−iii2i−2i0000-11−i−iii000000000000
χ3822-2-22-222-2-22i−2i-222-112-2-1-212i−2i-2-222-11-11-2-11−i−iii2-2211-1-1000000002i−2i-11−i−iii−2i2i00001-1ii−i−i000000000000
χ3922-2-22-222-2-22i−2i-22-12-2-1121-22i−2i0000-11-1112-22i2i−2i−2i-1000000000022-2-2−ii-11−i−iii00002i−2i0000000000-1-11100−ii
χ4022-2-22-222-2-22i−2i-22-12-2-1121-22i−2i0000-11-1112-22i2i−2i−2i-10000000000-2-222−ii-11−i−iii0000−2i2i000000000011-1-100i−i
χ4122-2-22-222-2-2−2i2i-222-112-2-1-21−2i2i22-2-2-11-11-2-11ii−i−i22-2-1-11100000000−2i2i-11ii−i−i−2i2i0000-11ii−i−i000000000000
χ4222-2-22-222-2-2−2i2i-222-112-2-1-21−2i2i-2-222-11-11-2-11ii−i−i2-2211-1-100000000−2i2i-11ii−i−i2i−2i00001-1−i−iii000000000000
χ4322-2-22-222-2-2−2i2i-22-12-2-1121-2−2i2i0000-11-1112-2−2i−2i2i2i-1000000000022-2-2i−i-11ii−i−i0000−2i2i0000000000-1-11100i−i
χ4422-2-22-222-2-2−2i2i-22-12-2-1121-2−2i2i0000-11-1112-2−2i−2i2i2i-10000000000-2-222i−i-11ii−i−i00002i−2i000000000011-1-100−ii
χ452-22-2200-22-2000022-2-22-2-22002-22-22-2-2200000000002-22-2−i2i2−i2i2−i2i2−i2i200000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ462-22-2200-22-2000022-2-22-2-22002-22-22-2-2200000000002-22-2i2−i2i2−i2i2−i2i2−i200000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ472-22-2200-22-2000022-2-22-2-2200-22-222-2-220000000000-22-22−i2i2−i2i2i2−i2i2−i200000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ482-22-2200-22-2000022-2-22-2-2200-22-222-2-220000000000-22-22i2−i2i2−i2−i2i2−i2i200000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ492-2-22200-2-220000222-2-2-22-2002-2-2222-2-200000000002-2-22−i2i2i2−i2−i2i2i2−i200000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ502-2-22200-2-220000222-2-2-22-2002-2-2222-2-200000000002-2-22i2−i2−i2i2i2−i2−i2i200000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ512-2-22200-2-220000222-2-2-22-200-222-222-2-20000000000-222-2−i2i2i2−i2i2−i2−i2i200000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ522-2-22200-2-220000222-2-2-22-200-222-222-2-20000000000-222-2i2−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
χ5544444-4-444400-4-4-244-2-24-24000000-2-2-2-22-4-4000020000000000000000220000000000000000000000000000
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
χ5844-4-444-44-4-4004-4-24-4-2242-4000000-22-22-2-440000200000000000000002-20000000000000000000000000000
χ5944-4-444-44-4-4004-4-2-22-22-2220000001-11-1-22-223−23−232320000000000000000-11−333−3000000000000000000000000
χ6044-4-444-44-4-4004-4-2-22-22-2220000001-11-1-22-2−232323−2320000000000000000-113−3−33000000000000000000000000
χ6144-4-44-444-4-44i−4i-44-2-22-22-2224i−4i00001-11-12-22−2i−2i2i2i-200000000000000−2i2i1-1ii−i−i000000000000000000000000
χ6244-4-44-444-4-4−4i4i-44-2-22-22-222−4i4i00001-11-12-222i2i−2i−2i-2000000000000002i−2i1-1−i−iii000000000000000000000000
χ634-44-4400-44-400004-22-442-4-2004-44-4-222-20000000000-22-220000000000000000000000000000000000000000
χ644-44-4400-44-400004-22-442-4-200-44-44-222-200000000002-22-20000000000000000000000000000000000000000
χ654-44-4400-44-40000-24-42-2-424000000-222-2000000000000000000−2i22i2−2i22i2000000000000000000000000i2−i2i2−i20000
χ664-44-4400-44-40000-24-42-2-424000000-222-20000000000000000002i2−2i22i2−2i2000000000000000000000000−i2i2−i2i20000
χ674-4-44400-4-4400004-2-2-4-4242004-4-44-2-2220000000000-222-20000000000000000000000000000000000000000
χ684-4-44400-4-4400004-2-2-4-424200-444-4-2-22200000000002-2-220000000000000000000000000000000000000000
χ694-4-44400-4-440000-24422-4-2-4000000-2-222000000000000000000−2i22i22i2−2i2000000000000000000000000i2−i2−i2i20000
χ704-4-44400-4-440000-24422-4-2-4000000-2-2220000000000000000002i2−2i2−2i22i2000000000000000000000000−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
χ7566-6-6-3-66-3336i−6i3-300000000−3i3i000000000000000000000022-2-2000000000000002i−2i00000000-1-1110000−ii00
χ7666-6-6-3-66-3336i−6i3-300000000−3i3i0000000000000000000000-2-22200000000000000−2i2i0000000011-1-10000i−i00
χ7766-6-6-3-66-333−6i6i3-3000000003i−3i000000000000000000000022-2-200000000000000−2i2i00000000-1-1110000i−i00
χ7866-6-6-3-66-333−6i6i3-3000000003i−3i0000000000000000000000-2-222000000000000002i−2i0000000011-1-10000−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).