Finite Group Databasebeta

← Group #13137988

Character table — Group #13137988

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111222222444444446666666699991212121212121212181818181818181818181818181824242424242424242424363636363636363636363636363636363636363672727272
order12223446664412121212121233666666444436661212121244888888881212121212121212121212121212222244666612122424242424242424661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111-1-111-1-1-1-11111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ61111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111
χ71111111111-1-111-1-1-1-111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-111
χ81111111111-1-111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1111111-1-1
χ911-1-111-11-1-1i−i1-1ii−i−i11-1-111-1-1ii−i−i1-11-11-11-1i−iii−i−i11-1-1ii−i−ii−ii−i1-1ii−i−i1-11-1i−i11-1-1i−iii−i−i11-1-11-1i−i
χ1011-1-111-11-1-1i−i1-1ii−i−i11-1-111-1-1ii−i−i1-11-11-11-1i−i−i−iii-1-111ii−i−ii−ii−i1-1ii−i−i1-1-11−ii11-1-1i−i−i−iii-1-111-11−ii
χ1111-1-111-11-1-1i−i1-1ii−i−i11-1-111-1-1−i−iii1-11-11-11-1−iiii−i−i-1-111−i−iiii−ii−i1-1ii−i−i-111-1−ii-1-111−iiii−i−i-1-1111-1−ii
χ1211-1-111-11-1-1i−i1-1ii−i−i11-1-111-1-1−i−iii1-11-11-11-1−ii−i−iii11-1-1−i−iiii−ii−i1-1ii−i−i-11-11i−i-1-111−ii−i−iii11-1-1-11i−i
χ1311-1-111-11-1-1−ii1-1−i−iii11-1-111-1-1ii−i−i1-11-11-11-1i−iii−i−i11-1-1ii−i−i−ii−ii1-1−i−iii-11-11−ii-1-111i−iii−i−i11-1-1-11−ii
χ1411-1-111-11-1-1−ii1-1−i−iii11-1-111-1-1ii−i−i1-11-11-11-1i−i−i−iii-1-111ii−i−i−ii−ii1-1−i−iii-111-1i−i-1-111i−i−i−iii-1-1111-1i−i
χ1511-1-111-11-1-1−ii1-1−i−iii11-1-111-1-1−i−iii1-11-11-11-1−iiii−i−i-1-111−i−iii−ii−ii1-1−i−iii1-1-11i−i11-1-1−iiii−i−i-1-111-11i−i
χ1611-1-111-11-1-1−ii1-1−i−iii11-1-111-1-1−i−iii1-11-11-11-1−ii−i−iii11-1-1−i−iii−ii−ii1-1−i−iii1-11-1−ii11-1-1−ii−i−iii11-1-11-1−ii
χ172222222222222222222-12-12-1-120000-1-1-1-1-122-100222200000000-1-122-1-1-1-1-1-1002200000000-1-1-1-10000-1-100
χ182222222222222222222-12-12-1-120000-1-1-1-1-122-100-2-2-2-200000000-1-122-1-1-1-1-1-100-2-200000000111100001100
χ19222222222222222222-12-12-122-10000-1-1-1-12-1-120000002222000022-1-1-1-1-1-1-1-10000220000000000-1-1-1-100-1-1
χ20222222222222222222-12-12-122-10000-1-1-1-12-1-12000000-2-2-2-2000022-1-1-1-1-1-1-1-10000-2-2000000000011110011
χ212222222222-2-222-2-2-2-22-12-12-1-120000-1-1-1-1-122-10022220000000011-2-2-1-1111100-2-200000000-1-1-1-100001100
χ222222222222-2-222-2-2-2-22-12-12-1-120000-1-1-1-1-122-100-2-2-2-20000000011-2-2-1-1111100220000000011110000-1-100
χ232222222222-2-222-2-2-2-2-12-12-122-10000-1-1-1-12-1-1200000022220000-2-211-1-111110000-2-20000000000-1-1-1-10011
χ242222222222-2-222-2-2-2-2-12-12-122-10000-1-1-1-12-1-12000000-2-2-2-20000-2-211-1-111110000220000000000111100-1-1
χ2522222-2-222200-2-200002222222222222222-2-2-2-2-2-20000000022220000-2-200000000000000-2-2000000000000
χ2622222-2-222200-2-2000022222222-2-2-2-22222-2-2-2-22200000000-2-2-2-20000-2-20000000000000022000000000000
χ2722-2-222-22-2-22i−2i2-22i2i−2i−2i2-1-212-11-20000-11-11-1-221002i2i−2i−2i00000000−ii2i−2i-11−i−iii002-200000000−i−iii0000-1100
χ2822-2-222-22-2-22i−2i2-22i2i−2i−2i2-1-212-11-20000-11-11-1-22100−2i−2i2i2i00000000−ii2i−2i-11−i−iii00-2200000000ii−i−i00001-100
χ2922-2-222-22-2-22i−2i2-22i2i−2i−2i-121-2-12-210000-11-1121-1-200000022-2-200002i−2i−ii-11−i−iii00002i−2i0000000000-1-11100−ii
χ3022-2-222-22-2-22i−2i2-22i2i−2i−2i-121-2-12-210000-11-1121-1-2000000-2-22200002i−2i−ii-11−i−iii0000−2i2i000000000011-1-100i−i
χ3122-2-222-22-2-2−2i2i2-2−2i−2i2i2i2-1-212-11-20000-11-11-1-221002i2i−2i−2i00000000i−i−2i2i-11ii−i−i00-2200000000−i−iii00001-100
χ3222-2-222-22-2-2−2i2i2-2−2i−2i2i2i2-1-212-11-20000-11-11-1-22100−2i−2i2i2i00000000i−i−2i2i-11ii−i−i002-200000000ii−i−i0000-1100
χ3322-2-222-22-2-2−2i2i2-2−2i−2i2i2i-121-2-12-210000-11-1121-1-200000022-2-20000−2i2ii−i-11ii−i−i0000−2i2i0000000000-1-11100i−i
χ3422-2-222-22-2-2−2i2i2-2−2i−2i2i2i-121-2-12-210000-11-1121-1-2000000-2-2220000−2i2ii−i-11ii−i−i00002i−2i000000000011-1-100−ii
χ3522-2-22-222-2-200-22000022-2-222-2-22i2i−2i−2i2-22-2-22-22−2i2i000000002i2i−2i−2i0000-2200000000000000−2i2i000000000000
χ3622-2-22-222-2-200-22000022-2-222-2-2−2i−2i2i2i2-22-2-22-222i−2i00000000−2i−2i2i2i0000-22000000000000002i−2i000000000000
χ372-22-2200-22-2000000002222-2-2-2-22i−2i2i−2i22-2-2000000−i2i2−i2i22−22−22i−2i2i−2i0000000000000000000000−i2i2−i2i22−22−20000
χ382-22-2200-22-2000000002222-2-2-2-22i−2i2i−2i22-2-2000000i2−i2i2−i2−22−222i−2i2i−2i0000000000000000000000i2−i2i2−i2−22−220000
χ392-22-2200-22-2000000002222-2-2-2-2−2i2i−2i2i22-2-2000000−i2i2−i2i2−22−22−2i2i−2i2i0000000000000000000000−i2i2−i2i2−22−220000
χ402-22-2200-22-2000000002222-2-2-2-2−2i2i−2i2i22-2-2000000i2−i2i2−i22−22−2−2i2i−2i2i0000000000000000000000i2−i2i2−i22−22−20000
χ412-2-22200-2-220000000022-2-2-2-2222-2-222-2-220000002−2−22−222−22-2-2200000000000000000000002−2−22−222−20000
χ422-2-22200-2-220000000022-2-2-2-2222-2-222-2-22000000−222−22−2−222-2-220000000000000000000000−222−22−2−220000
χ432-2-22200-2-220000000022-2-2-2-222-222-22-2-220000002−2−222−2−22-222-200000000000000000000002−2−222−2−220000
χ442-2-22200-2-220000000022-2-2-2-222-222-22-2-22000000−222−2−222−2-222-20000000000000000000000−222−2−222−20000
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
χ4744444-4-444400-4-400004-24-24-2-240000-2-2-2-22-4-42000000000000000000220000000000000000000000000000
χ4844444-4-444400-4-40000-24-24-244-20000-2-2-2-2-422-4000000000000000000220000000000000000000000000000
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
χ5144-4-444-44-4-44i−4i4-44i4i−4i−4i-2-222-2-22200001-11-1-22-2200000000000000−2i2i−2i2i1-1ii−i−i000000000000000000000000
χ5244-4-444-44-4-4−4i4i4-4−4i−4i4i4i-2-222-2-22200001-11-1-22-22000000000000002i−2i2i−2i1-1−i−iii000000000000000000000000
χ5344-4-44-444-4-400-4400004-2-424-22-40000-22-2224-4-20000000000000000002-20000000000000000000000000000
χ5444-4-44-444-4-400-440000-242-4-24-420000-22-22-4-2240000000000000000002-20000000000000000000000000000
χ5544-4-44-444-4-400-440000-2-222-2-22200001-11-12-22-2000000000000000000-113i−3i−3i3i000000000000000000000000
χ5644-4-44-444-4-400-440000-2-222-2-22200001-11-12-22-2000000000000000000-11−3i3i3i−3i000000000000000000000000
χ574-44-4400-44-4000000004-24-2-422-40000-2-222000000−2i22i2−2i22i2000000000000000000000000000000i2−i2i2−i200000000
χ584-44-4400-44-4000000004-24-2-422-40000-2-2220000002i2−2i22i2−2i2000000000000000000000000000000−i2i2−i2i200000000
χ594-44-4400-44-400000000-24-242-4-420000-2-222000000000022−2222−22000000000000000000000000000000−22−220000
χ604-44-4400-44-400000000-24-242-4-420000-2-2220000000000−2222−22220000000000000000000000000000002−22−20000
χ614-4-44400-4-44000000004-2-42-42-240000-222-200000022−22−2222000000000000000000000000000000−222−200000000
χ624-4-44400-4-44000000004-2-42-42-240000-222-2000000−222222−220000000000000000000000000000002−2−2200000000
χ634-4-44400-4-4400000000-242-42-44-20000-222-2000000000022−22−2222000000000000000000000000000000−222−20000
χ644-4-44400-4-4400000000-242-42-44-20000-222-20000000000−222222−220000000000000000000000000000002−2−220000
χ656666-366-3-3-366-3-3-3-3-3-3000000002222000000002200000000-1-1-1-10000000000220000-1-1-1-1-1-1000000000000
χ666666-366-3-3-366-3-3-3-3-3-300000000-2-2-2-200000000-2-20000000011110000000000-2-20000111111000000000000
χ676666-366-3-3-3-6-6-3-33333000000002222000000002200000000-1-1-1-10000000000-2-200001111-1-1000000000000
χ686666-366-3-3-3-6-6-3-3333300000000-2-2-2-200000000-2-20000000011110000000000220000-1-1-1-111000000000000
χ696666-3-6-6-3-3-30033−3i33i3−3i33i300000000222200000000-2-200000000-1-1-1-10000000000000000−i3i3−i3i311000000000000
χ706666-3-6-6-3-3-30033−3i33i3−3i33i300000000-2-2-2-200000000220000000011110000000000000000i3−i3i3−i3-1-1000000000000
χ716666-3-6-6-3-3-300333i3−3i33i3−3i300000000222200000000-2-200000000-1-1-1-10000000000000000i3−i3i3−i311000000000000
χ726666-3-6-6-3-3-300333i3−3i33i3−3i300000000-2-2-2-200000000220000000011110000000000000000−i3i3−i3i3-1-1000000000000
χ7366-6-6-36-6-3336i−6i-33−3i−3i3i3i000000002i2i−2i−2i000000002i−2i00000000−i−iii00000000002-20000-1-111−ii000000000000
χ7466-6-6-36-6-3336i−6i-33−3i−3i3i3i00000000−2i−2i2i2i00000000−2i2i00000000ii−i−i0000000000-22000011-1-1i−i000000000000
χ7566-6-6-36-6-333−6i6i-333i3i−3i−3i000000002i2i−2i−2i000000002i−2i00000000−i−iii0000000000-22000011-1-1−ii000000000000
χ7666-6-6-36-6-333−6i6i-333i3i−3i−3i00000000−2i−2i2i2i00000000−2i2i00000000ii−i−i00000000002-20000-1-111i−i000000000000
χ7766-6-6-3-66-333003-333−33−3333000000002i2i−2i−2i00000000−2i2i00000000−i−iii0000000000000000−i3i3i3−i3i−i000000000000
χ7866-6-6-3-66-333003-333−33−333300000000−2i−2i2i2i000000002i−2i00000000ii−i−i0000000000000000i3−i3−i3i3−ii000000000000
χ7966-6-6-3-66-333003-3−333333−33000000002i2i−2i−2i00000000−2i2i00000000−i−iii0000000000000000i3−i3−i3i3i−i000000000000
χ8066-6-6-3-66-333003-3−333333−3300000000−2i−2i2i2i000000002i−2i00000000ii−i−i0000000000000000−i3i3i3−i3−ii000000000000
χ818-88-8800-88-800000000-4-4-4-44444000022-2-20000000000000000000000000000000000000000000000000000
χ828-8-88800-8-8800000000-4-44444-4-400002-2-220000000000000000000000000000000000000000000000000000
χ8312-1212-12-6006-6600000000000000004i−4i4i−4i000000000000000000−2i2i−2i2i0000000000000000000000000000000000
χ8412-1212-12-6006-660000000000000000−4i4i−4i4i0000000000000000002i−2i2i−2i0000000000000000000000000000000000
χ8512-12-1212-60066-600000000000000004-4-44000000000000000000-222-20000000000000000000000000000000000
χ8612-12-1212-60066-60000000000000000-444-40000000000000000002-2-220000000000000000000000000000000000

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