Finite Group Databasebeta

← Group #13137958

Character table — Group #13137958

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111222222444444446666666699991212121212121212181818181818181818181818181824242424242424242424363636363636363636363636363636363636363672727272
order122234466644121212121212336666664444366612121212228888888812121212121212121212121212124444446612121212242424242424242412121212
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
χ311111111111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1
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
χ71111111111-1-1-1-1-1-11111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111111111-1-1-1-111-1-1
χ81111111111-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111
χ911-1-11-11-11-1i−iii−i−i1-111-111-1-1-111-1-11-11-1-1-1111-111-1-111-1-111-1-1i−ii−i1-1ii−i−ii−ii−ii−i1-1ii−i−i11-1-111-1-1i−ii−i
χ1011-1-11-11-11-1i−iii−i−i1-111-111-1-1-111-1-11-11-1-1-1111-1-1-111-1-11111-1-1i−ii−i1-1ii−i−i−iii−i−ii1-1ii−i−i-1-111-1-111−ii−ii
χ1111-1-11-11-11-1i−iii−i−i1-111-111-1-1-1-1-1111-11-1-1-111-1111-1-1-1-111-1-111i−ii−i1-1ii−i−ii−i−ii−ii-11−i−iii11-1-1-1-111−iii−i
χ1211-1-11-11-11-1i−iii−i−i1-111-111-1-1-1-1-1111-11-1-1-111-11-1-11111-1-1-1-111i−ii−i1-1ii−i−i−ii−iii−i-11−i−iii-1-11111-1-1i−i−ii
χ1311-1-11-11-11-1−ii−i−iii1-111-111-1-1-111-1-11-11-1-1-1111-111-1-111-1-111-1-1−ii−ii1-1−i−iii−ii−ii−ii1-1−i−iii11-1-111-1-1−ii−ii
χ1411-1-11-11-11-1−ii−i−iii1-111-111-1-1-111-1-11-11-1-1-1111-1-1-111-1-11111-1-1−ii−ii1-1−i−iiii−i−iii−i1-1−i−iii-1-111-1-111i−ii−i
χ1511-1-11-11-11-1−ii−i−iii1-111-111-1-1-1-1-1111-11-1-1-111-1111-1-1-1-111-1-111−ii−ii1-1−i−iii−iii−ii−i-11ii−i−i11-1-1-1-111i−i−ii
χ1611-1-11-11-11-1−ii−i−iii1-111-111-1-1-1-1-1111-11-1-1-111-11-1-11111-1-1-1-111−ii−ii1-1−i−iiii−ii−i−ii-11ii−i−i-1-11111-1-1−iii−i
χ172222222222222222222-122-1-1-120000-1-1-1-12-12-100000022220000-1-122-1-1-1-1-1-10000220000000000-1-1-1-1-1-100
χ182222222222222222222-122-1-1-120000-1-1-1-12-12-1000000-2-2-2-20000-1-122-1-1-1-1-1-10000-2-2000000000011111100
χ19222222222222222222-12-1-1222-10000-1-1-1-1-12-120022220000000022-1-1-1-1-1-1-1-1220000000000-1-1-1-1000000-1-1
χ20222222222222222222-12-1-1222-10000-1-1-1-1-12-1200-2-2-2-20000000022-1-1-1-1-1-1-1-1-2-20000000000111100000011
χ212222222222-2-2-2-2-2-2222-122-1-1-120000-1-1-1-12-12-10000002222000011-2-2-1-111110000-2-20000000000-1-1-1-11100
χ222222222222-2-2-2-2-2-2222-122-1-1-120000-1-1-1-12-12-1000000-2-2-2-2000011-2-2-1-1111100002200000000001111-1-100
χ232222222222-2-2-2-2-2-222-12-1-1222-10000-1-1-1-1-12-1200222200000000-2-211-1-11111-2-20000000000-1-1-1-100000011
χ242222222222-2-2-2-2-2-222-12-1-1222-10000-1-1-1-1-12-1200-2-2-2-200000000-2-211-1-111112200000000001111000000-1-1
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
χ2722-2-222-2-22-2000000-2222-222-2-2-222-2-22-22-222-2-2-220000000022-2-20000-220000000000-220000000000000000
χ2822-2-222-2-22-2000000-2222-222-2-2-2-2-2222-22-222-2-22-200000000-2-2220000-2200000000002-20000000000000000
χ2922-2-22-22-22-22i−2i2i2i−2i−2i2-22-1-22-111-20000-11-11-212-100000022-2-20000−ii2i−2i-11−i−iii00002i−2i0000000000-1-111−ii00
χ3022-2-22-22-22-22i−2i2i2i−2i−2i2-22-1-22-111-20000-11-11-212-1000000-2-2220000−ii2i−2i-11−i−iii0000−2i2i000000000011-1-1i−i00
χ3122-2-22-22-22-22i−2i2i2i−2i−2i2-2-121-12-2-210000-11-111-2-120022-2-2000000002i−2i−ii-11−i−iii2i−2i0000000000-1-111000000−ii
χ3222-2-22-22-22-22i−2i2i2i−2i−2i2-2-121-12-2-210000-11-111-2-1200-2-222000000002i−2i−ii-11−i−iii−2i2i000000000011-1-1000000i−i
χ3322-2-22-22-22-2−2i2i−2i−2i2i2i2-22-1-22-111-20000-11-11-212-100000022-2-20000i−i−2i2i-11ii−i−i0000−2i2i0000000000-1-111i−i00
χ3422-2-22-22-22-2−2i2i−2i−2i2i2i2-22-1-22-111-20000-11-11-212-1000000-2-2220000i−i−2i2i-11ii−i−i00002i−2i000000000011-1-1−ii00
χ3522-2-22-22-22-2−2i2i−2i−2i2i2i2-2-121-12-2-210000-11-111-2-120022-2-200000000−2i2ii−i-11ii−i−i−2i2i0000000000-1-111000000i−i
χ3622-2-22-22-22-2−2i2i−2i−2i2i2i2-2-121-12-2-210000-11-111-2-1200-2-22200000000−2i2ii−i-11ii−i−i2i−2i000000000011-1-1000000−ii
χ372-22-22002-2-20000000022-2-2-22-222i−2i2i−2i2-2-220000002−22−2−i2i2−i2i22i−2i2i−2i00000000000000000000002−22−2−i2i2−i2i20000
χ382-22-22002-2-20000000022-2-2-22-222i−2i2i−2i2-2-22000000−22−22i2−i2i2−i22i−2i2i−2i0000000000000000000000−22−22i2−i2i2−i20000
χ392-22-22002-2-20000000022-2-2-22-22−2i2i−2i2i2-2-220000002−22−2i2−i2i2−i2−2i2i−2i2i00000000000000000000002−22−2i2−i2i2−i20000
χ402-22-22002-2-20000000022-2-2-22-22−2i2i−2i2i2-2-22000000−22−22−i2i2−i2i2−2i2i−2i2i0000000000000000000000−22−22−i2i2−i2i20000
χ412-2-22200-2-2200000000222-2-2-22-22i−2i−2i2i22-2-20000002−2−22−i2i2i2−i22i−2i−2i2i00000000000000000000002−2−22−i2i2i2−i20000
χ422-2-22200-2-2200000000222-2-2-22-22i−2i−2i2i22-2-2000000−222−2i2−i2−i2i22i−2i−2i2i0000000000000000000000−222−2i2−i2−i2i20000
χ432-2-22200-2-2200000000222-2-2-22-2−2i2i2i−2i22-2-20000002−2−22i2−i2−i2i2−2i2i2i−2i00000000000000000000002−2−22i2−i2−i2i20000
χ442-2-22200-2-2200000000222-2-2-22-2−2i2i2i−2i22-2-2000000−222−2−i2i2i2−i2−2i2i2i−2i0000000000000000000000−222−2−i2i2i2−i20000
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
χ4744444-4-4444000000-4-44-244-2-2-240000-2-2-2-2-42-42000000000000000000220000000000000000000000000000
χ4844444-4-4444000000-4-4-24-2-2444-20000-2-2-2-22-42-4000000000000000000220000000000000000000000000000
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
χ5144-4-444-4-44-4000000-444-2-44-222-40000-22-224-2-420000000000000000002-20000000000000000000000000000
χ5244-4-444-4-44-4000000-44-242-24-4-420000-22-22-242-40000000000000000002-20000000000000000000000000000
χ5344-4-444-4-44-4000000-44-2-22-2-222200001-11-1-2-222000000000000000000-113i−3i−3i3i000000000000000000000000
χ5444-4-444-4-44-4000000-44-2-22-2-222200001-11-1-2-222000000000000000000-11−3i3i3i−3i000000000000000000000000
χ5544-4-44-44-44-44i−4i4i4i−4i−4i4-4-2-22-2-222200001-11-122-2-200000000000000−2i2i−2i2i1-1ii−i−i000000000000000000000000
χ5644-4-44-44-44-4−4i4i−4i−4i4i4i4-4-2-22-2-222200001-11-122-2-2000000000000002i−2i2i−2i1-1−i−iii000000000000000000000000
χ574-44-44004-4-4000000004-2-4-42-2240000-222-20000000000−2i22i2−2i22i2000000000000000000000000000000i2−i2i2−i20000
χ584-44-44004-4-4000000004-2-4-42-2240000-222-200000000002i2−2i22i2−2i2000000000000000000000000000000−i2i2−i2i20000
χ594-44-44004-4-400000000-2422-44-4-20000-222-200000022−2222−22000000000000000000000000000000−22−2200000000
χ604-44-44004-4-400000000-2422-44-4-20000-222-2000000−2222−22220000000000000000000000000000002−22−200000000
χ614-4-44400-4-44000000004-24-422-2-40000-2-2220000000000−2i22i22i2−2i2000000000000000000000000000000i2−i2−i2i20000
χ624-4-44400-4-44000000004-24-422-2-40000-2-22200000000002i2−2i2−2i22i2000000000000000000000000000000−i2i2i2−i20000
χ634-4-44400-4-4400000000-24-22-4-4420000-2-22200000022−22−2222000000000000000000000000000000−222−200000000
χ644-4-44400-4-4400000000-24-22-4-4420000-2-222000000−222222−220000000000000000000000000000002−2−2200000000
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
χ7366-6-6-36-63-330033−33−33333-30000000022-2-200000000-2200000000-1-11100000000000000001-13−3−33000000000000
χ7466-6-6-36-63-330033−33−33333-300000000-2-222000000002-20000000011-1-10000000000000000-11−333−3000000000000
χ7566-6-6-36-63-3300−333333−333-30000000022-2-200000000-2200000000-1-11100000000000000001-1−333−3000000000000
χ7666-6-6-36-63-3300−333333−333-300000000-2-222000000002-20000000011-1-10000000000000000-113−3−33000000000000
χ7766-6-6-3-663-336i−6i−3i−3i3i3i-330000000022-2-2000000002-200000000-1-1110000000000002i−2i00-11−i−iii000000000000
χ7866-6-6-3-663-336i−6i−3i−3i3i3i-3300000000-2-22200000000-220000000011-1-1000000000000−2i2i001-1ii−i−i000000000000
χ7966-6-6-3-663-33−6i6i3i3i−3i−3i-330000000022-2-2000000002-200000000-1-111000000000000−2i2i00-11ii−i−i000000000000
χ8066-6-6-3-663-33−6i6i3i3i−3i−3i-3300000000-2-22200000000-220000000011-1-10000000000002i−2i001-1−i−iii000000000000
χ818-88-88008-8-800000000-4-4444-44-400002-2-220000000000000000000000000000000000000000000000000000
χ828-8-88800-8-8800000000-4-4-4444-44000022-2-20000000000000000000000000000000000000000000000000000
χ8312-1212-12-600-66600000000000000004i−4i4i−4i000000000000000000−2i2i−2i2i0000000000000000000000000000000000
χ8412-1212-12-600-6660000000000000000−4i4i−4i4i0000000000000000002i−2i2i−2i0000000000000000000000000000000000
χ8512-12-1212-60066-600000000000000004i−4i−4i4i000000000000000000−2i2i2i−2i0000000000000000000000000000000000
χ8612-12-1212-60066-60000000000000000−4i4i4i−4i0000000000000000002i−2i−2i2i0000000000000000000000000000000000

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