Finite Group Databasebeta

← Group #13138041

Character table — Group #13138041

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111222222444444446666666699991212121212121212181818181818181818181818181824242424242424242424363636363636363636363636363636363636363672727272
order1222344666441212121212123366666622223666121212124466668888888812121212121212121212444444121212121212242424242424242412121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111-1-111-1-1-1-11111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ61111111111-1-111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111-1-111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-111111111-1-1-1-1-1-111
χ81111111111-1-111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1
χ91-1-1111-1-11-1i−i1-1ii−i−i11-1-1-1-11111-1-11-11-111-1-11-111-1-1ii−i−iii−i−iii−i−i1-1ii−i−ii−i1-11-11-1ii−i−iii−i−iii−i−i1-11-1
χ101-1-1111-1-11-1i−i1-1ii−i−i11-1-1-1-11111-1-11-11-111-1-11-111-1-1−i−iii−i−iiiii−i−i1-1ii−i−ii−i-11-111-1ii−i−i−i−iii−i−iii-11-11
χ111-1-1111-1-11-1i−i1-1ii−i−i11-1-1-1-111-1-1111-11-111-1-1-11-1-111ii−i−i−i−iiiii−i−i1-1ii−i−i−ii1-1-11-11−i−iiiii−i−i−i−iii1-1-11
χ121-1-1111-1-11-1i−i1-1ii−i−i11-1-1-1-111-1-1111-11-111-1-1-11-1-111−i−iiiii−i−iii−i−i1-1ii−i−i−ii-111-1-11−i−iii−i−iiiii−i−i-111-1
χ131-1-1111-1-11-1−ii1-1−i−iii11-1-1-1-11111-1-11-11-111-1-11-111-1-1ii−i−iii−i−i−i−iii1-1−i−iii−ii-11-111-1−i−iiiii−i−iii−i−i-11-11
χ141-1-1111-1-11-1−ii1-1−i−iii11-1-1-1-11111-1-11-11-111-1-11-111-1-1−i−iii−i−iii−i−iii1-1−i−iii−ii1-11-11-1−i−iii−i−iii−i−iii1-11-1
χ151-1-1111-1-11-1−ii1-1−i−iii11-1-1-1-111-1-1111-11-111-1-1-11-1-111ii−i−i−i−iii−i−iii1-1−i−iiii−i-111-1-11ii−i−iii−i−i−i−iii-111-1
χ161-1-1111-1-11-1−ii1-1−i−iii11-1-1-1-111-1-1111-11-111-1-1-11-1-111−i−iiiii−i−i−i−iii1-1−i−iiii−i1-1-11-11ii−i−i−i−iiiii−i−i1-1-11
χ172222222222222222222-12-12-12-10000-1-1-1-12-12-1000000000022222-12-1-1-1-1-1-1-10000220000000000-1-1-1-100-1-1
χ182222222222222222222-12-12-12-10000-1-1-1-12-12-10000000000-2-2-2-22-12-1-1-1-1-1-1-10000-2-2000000000011110011
χ19222222222222222222-12-12-12-120000-1-1-1-1-12-1200000022220000-12-12-1-1-1-1-1-1002200000000-1-1-1-10000-1-100
χ20222222222222222222-12-12-12-120000-1-1-1-1-12-12000000-2-2-2-20000-12-12-1-1-1-1-1-100-2-200000000111100001100
χ212222222222-2-222-2-2-2-22-12-12-12-10000-1-1-1-12-12-100000000002222-21-21-1-111110000-2-20000000000-1-1-1-10011
χ222222222222-2-222-2-2-2-22-12-12-12-10000-1-1-1-12-12-10000000000-2-2-2-2-21-21-1-111110000220000000000111100-1-1
χ232222222222-2-222-2-2-2-2-12-12-12-120000-1-1-1-1-12-12000000222200001-21-2-1-1111100-2-200000000-1-1-1-100001100
χ242222222222-2-222-2-2-2-2-12-12-12-120000-1-1-1-1-12-12000000-2-2-2-200001-21-2-1-1111100220000000011110000-1-100
χ2522222-2-222200-2-200002222222222222222-2-2-2-2-2-22222000000000000-2-20000000000-2-20000000000000000
χ2622222-2-222200-2-2000022222222-2-2-2-22222-2-2-2-222-2-2-2-2000000000000-2-20000000000220000000000000000
χ2722-2-22002-2-2000000002222-2-2-2-22-22-222-2-20000002-22-22−22−22−22−200000000000000000000002−22−22−22−20000
χ2822-2-22002-2-2000000002222-2-2-2-22-22-222-2-20000002-22-2−22−22−22−220000000000000000000000−22−22−22−220000
χ2922-2-22002-2-2000000002222-2-2-2-2-22-2222-2-2000000-22-222−22−2−22−2200000000000000000000002−22−2−22−220000
χ3022-2-22002-2-2000000002222-2-2-2-2-22-2222-2-2000000-22-22−22−222−22−20000000000000000000000−22−222−22−20000
χ312-22-2200-2-220000000022-2-222-2-22-2-222-2-220000002-2-22−i2i2i2−i2−i2i2i2−i20000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ322-22-2200-2-220000000022-2-222-2-22-2-222-2-220000002-2-22i2−i2−i2i2i2−i2−i2i20000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ332-22-2200-2-220000000022-2-222-2-2-222-22-2-22000000-222-2−i2i2i2−i2i2−i2−i2i20000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ342-22-2200-2-220000000022-2-222-2-2-222-22-2-22000000-222-2i2−i2−i2i2−i2i2i2−i20000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ352-2-2222-2-22-22i−2i2-22i2i−2i−2i2-1-21-212-10000-11-112-1-2100000000002i2i−2i−2i2i−i−2ii-11−i−iii00002-20000000000−i−iii00-11
χ362-2-2222-2-22-22i−2i2-22i2i−2i−2i2-1-21-212-10000-11-112-1-210000000000−2i−2i2i2i2i−i−2ii-11−i−iii0000-220000000000ii−i−i001-1
χ372-2-2222-2-22-22i−2i2-22i2i−2i−2i-121-21-2-120000-11-11-121-20000002i2i−2i−2i0000−i2ii−2i-11−i−iii002-200000000−i−iii0000-1100
χ382-2-2222-2-22-22i−2i2-22i2i−2i−2i-121-21-2-120000-11-11-121-2000000−2i−2i2i2i0000−i2ii−2i-11−i−iii00-2200000000ii−i−i00001-100
χ392-2-2222-2-22-2−2i2i2-2−2i−2i2i2i2-1-21-212-10000-11-112-1-2100000000002i2i−2i−2i−2ii2i−i-11ii−i−i0000-220000000000−i−iii001-1
χ402-2-2222-2-22-2−2i2i2-2−2i−2i2i2i2-1-21-212-10000-11-112-1-210000000000−2i−2i2i2i−2ii2i−i-11ii−i−i00002-20000000000ii−i−i00-11
χ412-2-2222-2-22-2−2i2i2-2−2i−2i2i2i-121-21-2-120000-11-11-121-20000002i2i−2i−2i0000i−2i−i2i-11ii−i−i00-2200000000−i−iii00001-100
χ422-2-2222-2-22-2−2i2i2-2−2i−2i2i2i-121-21-2-120000-11-11-121-2000000−2i−2i2i2i0000i−2i−i2i-11ii−i−i002-200000000ii−i−i0000-1100
χ432-2-222-22-22-200-22000022-2-2-2-22222-2-22-22-2-2-222-2222-2-2000000000000-220000000000-220000000000000000
χ442-2-222-22-22-200-22000022-2-2-2-222-2-2222-22-2-2-2222-2-2-222000000000000-2200000000002-20000000000000000
χ45444444444444444444-2-2-2-2-2-2-2-200001111-2-2-2-200000000000000-2-2-2-2111111000000000000000000000000
χ464444444444-4-444-4-4-4-4-2-2-2-2-2-2-2-200001111-2-2-2-200000000000000222211-1-1-1-1000000000000000000000000
χ4744444-4-444400-4-400004-24-24-24-20000-2-2-2-2-42-42000000000000000000220000000000000000000000000000
χ4844444-4-444400-4-40000-24-24-24-240000-2-2-2-22-42-4000000000000000000220000000000000000000000000000
χ4944444-4-444400-4-40000-2-2-2-2-2-2-2-2000011112222000000000000000000-1-13-33-3000000000000000000000000
χ5044444-4-444400-4-40000-2-2-2-2-2-2-2-2000011112222000000000000000000-1-1-33-33000000000000000000000000
χ5144-4-44004-4-4000000004-24-2-42-420000-2-2220000000000000022−2222−2200000000000000000000000000−22−220000
χ5244-4-44004-4-4000000004-24-2-42-420000-2-22200000000000000−2222−2222000000000000000000000000002−22−20000
χ5344-4-44004-4-400000000-24-242-42-40000-2-222000000000022−2222−2200000000000000000000000000−22−2200000000
χ5444-4-44004-4-400000000-24-242-42-40000-2-2220000000000−2222−2222000000000000000000000000002−22−200000000
χ554-44-4400-4-44000000004-2-424-2-420000-222-200000000000000−2i22i22i2−2i200000000000000000000000000i2−i2−i2i20000
χ564-44-4400-4-44000000004-2-424-2-420000-222-2000000000000002i2−2i2−2i22i200000000000000000000000000−i2i2i2−i20000
χ574-44-4400-4-4400000000-242-4-242-40000-222-20000000000−2i22i22i2−2i200000000000000000000000000i2−i2−i2i200000000
χ584-44-4400-4-4400000000-242-4-242-40000-222-200000000002i2−2i2−2i22i200000000000000000000000000−i2i2i2−i200000000
χ594-4-4444-4-44-44i−4i4-44i4i−4i−4i-2-22222-2-200001-11-1-2-22200000000000000−2i−2i2i2i1-1ii−i−i000000000000000000000000
χ604-4-4444-4-44-4−4i4i4-4−4i−4i4i4i-2-22222-2-200001-11-1-2-222000000000000002i2i−2i−2i1-1−i−iii000000000000000000000000
χ614-4-444-44-44-400-4400004-2-42-424-20000-22-22-424-20000000000000000002-20000000000000000000000000000
χ624-4-444-44-44-400-440000-242-42-4-240000-22-222-4-240000000000000000002-20000000000000000000000000000
χ634-4-444-44-44-400-440000-2-22222-2-200001-11-122-2-2000000000000000000-113i−3i−3i3i000000000000000000000000
χ644-4-444-44-44-400-440000-2-22222-2-200001-11-122-2-2000000000000000000-11−3i3i3i−3i000000000000000000000000
χ656666-366-3-3-366-3-3-3-3-3-30000000022220000000022-1-1-1-1000000000000000000220000-1-1-1-1-1-1000000000000
χ666666-366-3-3-366-3-3-3-3-3-300000000-2-2-2-200000000-2-21111000000000000000000-2-20000111111000000000000
χ676666-366-3-3-3-6-6-3-333330000000022220000000022-1-1-1-1000000000000000000-2-20000-1-11111000000000000
χ686666-366-3-3-3-6-6-3-3333300000000-2-2-2-200000000-2-2111100000000000000000022000011-1-1-1-1000000000000
χ696666-3-6-6-3-3-30033−3i33i3−3i33i300000000222200000000-2-2-1-1-1-100000000000000000000000011−i3i3−i3i3000000000000
χ706666-3-6-6-3-3-30033−3i33i3−3i33i300000000-2-2-2-200000000221111000000000000000000000000-1-1i3−i3i3−i3000000000000
χ716666-3-6-6-3-3-300333i3−3i33i3−3i300000000222200000000-2-2-1-1-1-100000000000000000000000011i3−i3i3−i3000000000000
χ726666-3-6-6-3-3-300333i3−3i33i3−3i300000000-2-2-2-200000000221111000000000000000000000000-1-1−i3i3−i3i3000000000000
χ736-6-66-36-63-336i−6i-33−3i−3i3i3i0000000022-2-2000000002-2-1-1110000000000000000002i−2i0000-11−i−iii000000000000
χ746-6-66-36-63-336i−6i-33−3i−3i3i3i00000000-2-22200000000-2211-1-1000000000000000000−2i2i00001-1ii−i−i000000000000
χ756-6-66-36-63-33−6i6i-333i3i−3i−3i0000000022-2-2000000002-2-1-111000000000000000000−2i2i0000-11ii−i−i000000000000
χ766-6-66-36-63-33−6i6i-333i3i−3i−3i00000000-2-22200000000-2211-1-10000000000000000002i−2i00001-1−i−iii000000000000
χ776-6-66-3-663-33003-333−33−33330000000022-2-200000000-22-1-1110000000000000000000000001-13−3−33000000000000
χ786-6-66-3-663-33003-333−33−333300000000-2-222000000002-211-1-1000000000000000000000000-11−333−3000000000000
χ796-6-66-3-663-33003-3−333333−330000000022-2-200000000-22-1-1110000000000000000000000001-1−333−3000000000000
χ806-6-66-3-663-33003-3−333333−3300000000-2-222000000002-211-1-1000000000000000000000000-113−3−33000000000000
χ8188-8-88008-8-800000000-4-4-4-44444000022-2-20000000000000000000000000000000000000000000000000000
χ828-88-8800-8-8800000000-4-444-4-44400002-2-220000000000000000000000000000000000000000000000000000
χ831212-12-12-600-66600000000000000004-44-40000000000-22-22000000000000000000000000000000000000000000
χ841212-12-12-600-6660000000000000000-44-4400000000002-22-2000000000000000000000000000000000000000000
χ8512-1212-12-60066-600000000000000004-4-440000000000-222-2000000000000000000000000000000000000000000
χ8612-1212-12-60066-60000000000000000-444-400000000002-2-22000000000000000000000000000000000000000000

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