Finite Group Databasebeta

← Group #13138049

Character table — Group #13138049

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111222222444444446666666699991212121212121212181818181818181818181818181824242424242424242424363636363636363636363636363636363636363672727272
order1222344666441212121212123366666644443666121212122288888888121212121212121212121212121222444466121212122424242424242424661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ61111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111-1-1-1-1-1-11111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-111
χ81111111111-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1
χ91-1-1111-1-11-1i−iii−i−i1-111-1-11-1-1111-1-11-11-111-1-11-1ii−i−iii−i−i11-1-1ii−i−i1-1ii−i−i1-1i−i1-11-1ii−i−iii−i−iii−i−i1-11-1
χ101-1-1111-1-11-1i−iii−i−i1-111-1-11-1-1111-1-11-11-111-1-11-1−i−iii−i−iii11-1-1ii−i−i1-1ii−i−i-11i−i-111-1ii−i−i−i−iii−i−iii-11-11
χ111-1-1111-1-11-1i−iii−i−i1-111-1-11-1-11-1-1111-11-111-1-1-11ii−i−i−i−iii-1-111ii−i−i1-1ii−i−i1-1−ii-11-11−i−iiiii−i−i−i−iii1-1-11
χ121-1-1111-1-11-1i−iii−i−i1-111-1-11-1-11-1-1111-11-111-1-1-11−i−iiiii−i−i-1-111ii−i−i1-1ii−i−i-11−ii1-1-11−i−iii−i−iiiii−i−i-111-1
χ131-1-1111-1-11-1−ii−i−iii1-111-1-11-1-1111-1-11-11-111-1-11-1ii−i−iii−i−i11-1-1−i−iii1-1−i−iii-11−ii-111-1−i−iiiii−i−iii−i−i-11-11
χ141-1-1111-1-11-1−ii−i−iii1-111-1-11-1-1111-1-11-11-111-1-11-1−i−iii−i−iii11-1-1−i−iii1-1−i−iii1-1−ii1-11-1−i−iii−i−iii−i−iii1-11-1
χ151-1-1111-1-11-1−ii−i−iii1-111-1-11-1-11-1-1111-11-111-1-1-11ii−i−i−i−iii-1-111−i−iii1-1−i−iii-11i−i1-1-11ii−i−iii−i−i−i−iii-111-1
χ161-1-1111-1-11-1−ii−i−iii1-111-1-11-1-11-1-1111-11-111-1-1-11−i−iiiii−i−i-1-111−i−iii1-1−i−iii1-1i−i-11-11ii−i−i−i−iiiii−i−i1-1-11
χ172222222222222222222-12-1-12-120000-1-1-1-1-12-12002222000000002-12-1-1-1-1-1-1-1220000000000-1-1-1-10000-1-100
χ182222222222222222222-12-1-12-120000-1-1-1-1-12-1200-2-2-2-2000000002-12-1-1-1-1-1-1-1-2-20000000000111100001100
χ19222222222222222222-12-122-12-10000-1-1-1-12-12-100000022220000-12-12-1-1-1-1-1-10000220000000000-1-1-1-100-1-1
χ20222222222222222222-12-122-12-10000-1-1-1-12-12-1000000-2-2-2-20000-12-12-1-1-1-1-1-10000-2-2000000000011110011
χ212222222222-2-2-2-2-2-2222-12-1-12-120000-1-1-1-1-12-1200222200000000-21-21-1-11111-2-20000000000-1-1-1-100001100
χ222222222222-2-2-2-2-2-2222-12-1-12-120000-1-1-1-1-12-1200-2-2-2-200000000-21-21-1-1111122000000000011110000-1-100
χ232222222222-2-2-2-2-2-222-12-122-12-10000-1-1-1-12-12-1000000222200001-21-2-1-111110000-2-20000000000-1-1-1-10011
χ242222222222-2-2-2-2-2-222-12-122-12-10000-1-1-1-12-12-1000000-2-2-2-200001-21-2-1-111110000220000000000111100-1-1
χ2522222-2-2222000000-2-22222222222222222-2-2-2-2-2-20000000022220000-2-20000000000-2-20000000000000000
χ2622222-2-2222000000-2-222222222-2-2-2-22222-2-2-2-22200000000-2-2-2-20000-2-20000000000220000000000000000
χ2722-2-22002-2-20000000022-2-2-222-22i−2i2i−2i2-2-220000002−22−2−i2i2−i2i22i−2i2i−2i00000000000000000000002−22−2−i2i2−i2i20000
χ2822-2-22002-2-20000000022-2-2-222-22i−2i2i−2i2-2-22000000−22−22i2−i2i2−i22i−2i2i−2i0000000000000000000000−22−22i2−i2i2−i20000
χ2922-2-22002-2-20000000022-2-2-222-2−2i2i−2i2i2-2-220000002−22−2i2−i2i2−i2−2i2i−2i2i00000000000000000000002−22−2i2−i2i2−i20000
χ3022-2-22002-2-20000000022-2-2-222-2−2i2i−2i2i2-2-22000000−22−22−i2i2−i2i2−2i2i−2i2i0000000000000000000000−22−22−i2i2−i2i20000
χ312-22-2200-2-22000000002222-2-2-2-22i−2i−2i2i22-2-2000000−i2i2i2−i2−222−22i−2i−2i2i0000000000000000000000−i2i2i2−i2−222−20000
χ322-22-2200-2-22000000002222-2-2-2-22i−2i−2i2i22-2-2000000i2−i2−i2i22−2−222i−2i−2i2i0000000000000000000000i2−i2−i2i22−2−220000
χ332-22-2200-2-22000000002222-2-2-2-2−2i2i2i−2i22-2-2000000−i2i2i2−i22−2−22−2i2i2i−2i0000000000000000000000−i2i2i2−i22−2−220000
χ342-22-2200-2-22000000002222-2-2-2-2−2i2i2i−2i22-2-2000000i2−i2−i2i2−222−2−2i2i2i−2i0000000000000000000000i2−i2−i2i2−222−20000
χ352-2-2222-2-22-22i−2i2i2i−2i−2i2-22-1-21-1-2120000-11-11-121-2002i2i−2i−2i000000002i−i−2ii-11−i−iii2-20000000000−i−iii0000-1100
χ362-2-2222-2-22-22i−2i2i2i−2i−2i2-22-1-21-1-2120000-11-11-121-200−2i−2i2i2i000000002i−i−2ii-11−i−iii-220000000000ii−i−i00001-100
χ372-2-2222-2-22-22i−2i2i2i−2i−2i2-2-121-221-2-10000-11-112-1-210000002i2i−2i−2i0000−i2ii−2i-11−i−iii00002-20000000000−i−iii00-11
χ382-2-2222-2-22-22i−2i2i2i−2i−2i2-2-121-221-2-10000-11-112-1-21000000−2i−2i2i2i0000−i2ii−2i-11−i−iii0000-220000000000ii−i−i001-1
χ392-2-2222-2-22-2−2i2i−2i−2i2i2i2-22-1-21-1-2120000-11-11-121-2002i2i−2i−2i00000000−2ii2i−i-11ii−i−i-220000000000−i−iii00001-100
χ402-2-2222-2-22-2−2i2i−2i−2i2i2i2-22-1-21-1-2120000-11-11-121-200−2i−2i2i2i00000000−2ii2i−i-11ii−i−i2-20000000000ii−i−i0000-1100
χ412-2-2222-2-22-2−2i2i−2i−2i2i2i2-2-121-221-2-10000-11-112-1-210000002i2i−2i−2i0000i−2i−i2i-11ii−i−i0000-220000000000−i−iii001-1
χ422-2-2222-2-22-2−2i2i−2i−2i2i2i2-2-121-221-2-10000-11-112-1-21000000−2i−2i2i2i0000i−2i−i2i-11ii−i−i00002-20000000000ii−i−i00-11
χ432-2-222-22-22-2000000-2222-2-22-2-2222-2-22-22-2-2-222-220000000022-2-20000-220000000000-220000000000000000
χ442-2-222-22-22-2000000-2222-2-22-2-22-2-2222-22-2-2-2222-200000000-2-2220000-2200000000002-20000000000000000
χ45444444444444444444-2-2-2-2-2-2-2-200001111-2-2-2-200000000000000-2-2-2-2111111000000000000000000000000
χ464444444444-4-4-4-4-4-444-2-2-2-2-2-2-2-200001111-2-2-2-200000000000000222211-1-1-1-1000000000000000000000000
χ4744444-4-4444000000-4-44-24-2-24-240000-2-2-2-22-42-4000000000000000000220000000000000000000000000000
χ4844444-4-4444000000-4-4-24-244-24-20000-2-2-2-2-42-42000000000000000000220000000000000000000000000000
χ4944444-4-4444000000-4-4-2-2-2-2-2-2-2-2000011112222000000000000000000-1-13-33-3000000000000000000000000
χ5044444-4-4444000000-4-4-2-2-2-2-2-2-2-2000011112222000000000000000000-1-1-33-33000000000000000000000000
χ5144-4-44004-4-4000000004-2-4224-2-40000-222-200000022−2222−22000000000000000000000000000000−22−2200000000
χ5244-4-44004-4-4000000004-2-4224-2-40000-222-2000000−2222−22220000000000000000000000000000002−22−200000000
χ5344-4-44004-4-400000000-242-4-4-2420000-222-20000000000−2i22i2−2i22i2000000000000000000000000000000i2−i2i2−i20000
χ5444-4-44004-4-400000000-242-4-4-2420000-222-200000000002i2−2i22i2−2i2000000000000000000000000000000−i2i2−i2i20000
χ554-44-4400-4-44000000004-24-22-42-40000-2-222000000−2i22i22i2−2i2000000000000000000000000000000i2−i2−i2i200000000
χ564-44-4400-4-44000000004-24-22-42-40000-2-2220000002i2−2i2−2i22i2000000000000000000000000000000−i2i2i2−i200000000
χ574-44-4400-4-4400000000-24-24-42-420000-2-222000000000022−22−2222000000000000000000000000000000−222−20000
χ584-44-4400-4-4400000000-24-24-42-420000-2-2220000000000−222222−220000000000000000000000000000002−2−220000
χ594-4-4444-4-44-44i−4i4i4i−4i−4i4-4-2-222-222-200001-11-1-2-22200000000000000−2i−2i2i2i1-1ii−i−i000000000000000000000000
χ604-4-4444-4-44-4−4i4i−4i−4i4i4i4-4-2-222-222-200001-11-1-2-222000000000000002i2i−2i−2i1-1−i−iii000000000000000000000000
χ614-4-444-44-44-4000000-444-2-42-2-4240000-22-222-4-240000000000000000002-20000000000000000000000000000
χ624-4-444-44-44-4000000-44-242-442-4-20000-22-22-424-20000000000000000002-20000000000000000000000000000
χ634-4-444-44-44-4000000-44-2-222-222-200001-11-122-2-2000000000000000000-113i−3i−3i3i000000000000000000000000
χ644-4-444-44-44-4000000-44-2-222-222-200001-11-122-2-2000000000000000000-11−3i3i3i−3i000000000000000000000000
χ656666-366-3-3-366-3-3-3-3-3-3000000002222000000002200000000-1-1-1-10000000000002200-1-1-1-1-1-1000000000000
χ666666-366-3-3-366-3-3-3-3-3-300000000-2-2-2-200000000-2-2000000001111000000000000-2-200111111000000000000
χ676666-366-3-3-3-6-63333-3-3000000002222000000002200000000-1-1-1-1000000000000-2-200-1-11111000000000000
χ686666-366-3-3-3-6-63333-3-300000000-2-2-2-200000000-2-2000000001111000000000000220011-1-1-1-1000000000000
χ696666-3-6-6-3-3-300−3i33i3−3i33i33300000000222200000000-2-200000000-1-1-1-1000000000000000011−i3i3−i3i3000000000000
χ706666-3-6-6-3-3-300−3i33i3−3i33i33300000000-2-2-2-200000000220000000011110000000000000000-1-1i3−i3i3−i3000000000000
χ716666-3-6-6-3-3-3003i3−3i33i3−3i33300000000222200000000-2-200000000-1-1-1-1000000000000000011i3−i3i3−i3000000000000
χ726666-3-6-6-3-3-3003i3−3i33i3−3i33300000000-2-2-2-200000000220000000011110000000000000000-1-1−i3i3−i3i3000000000000
χ736-6-66-36-63-336i−6i−3i−3i3i3i-330000000022-2-2000000002-200000000-1-1110000000000002i−2i00-11−i−iii000000000000
χ746-6-66-36-63-336i−6i−3i−3i3i3i-3300000000-2-22200000000-220000000011-1-1000000000000−2i2i001-1ii−i−i000000000000
χ756-6-66-36-63-33−6i6i3i3i−3i−3i-330000000022-2-2000000002-200000000-1-111000000000000−2i2i00-11ii−i−i000000000000
χ766-6-66-36-63-33−6i6i3i3i−3i−3i-3300000000-2-22200000000-220000000011-1-10000000000002i−2i001-1−i−iii000000000000
χ776-6-66-3-663-330033−33−33333-30000000022-2-200000000-2200000000-1-11100000000000000001-13−3−33000000000000
χ786-6-66-3-663-330033−33−33333-300000000-2-222000000002-20000000011-1-10000000000000000-11−333−3000000000000
χ796-6-66-3-663-3300−333333−333-30000000022-2-200000000-2200000000-1-11100000000000000001-1−333−3000000000000
χ806-6-66-3-663-3300−333333−333-300000000-2-222000000002-20000000011-1-10000000000000000-113−3−33000000000000
χ8188-8-88008-8-800000000-4-4444-4-4400002-2-220000000000000000000000000000000000000000000000000000
χ828-88-8800-8-8800000000-4-4-4-44444000022-2-20000000000000000000000000000000000000000000000000000
χ831212-12-12-600-66600000000000000004i−4i4i−4i000000000000000000−2i2i−2i2i0000000000000000000000000000000000
χ841212-12-12-600-6660000000000000000−4i4i−4i4i0000000000000000002i−2i2i−2i0000000000000000000000000000000000
χ8512-1212-12-60066-600000000000000004i−4i−4i4i000000000000000000−2i2i2i−2i0000000000000000000000000000000000
χ8612-1212-12-60066-60000000000000000−4i4i4i−4i0000000000000000002i−2i−2i2i0000000000000000000000000000000000

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