Finite Group Databasebeta

← Group #13137987

Character table — Group #13137987

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11112222224444444466666666121212121212121218181818181818182424242424242424242436363636363636363636363636363636363636363636363672727272
order12223446664412121212121233666666366612121212444412121212121212121212121212122222446666888812122424242424242424661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111
χ51111111111-1-111-1-1-1-1111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ61111111111-1-111-1-1-1-1111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ71111111111-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-111-1-1-1-1-1-1111111-1-1
χ81111111111-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ911-1-111-11-1-1i−i1-1ii−i−i11-111-1-1-11-11-11-11-1i−ii−iii−i−iii−i−i1-1ii−i−i1-11-1i−i11-1-1i−i1-1i−iii−i−i11-1-11-1i−i
χ1011-1-111-11-1-1i−i1-1ii−i−i11-111-1-1-11-11-11-11-1i−ii−iii−i−iii−i−i1-1ii−i−i1-1-11−ii11-1-1−ii-11i−i−i−iii-1-111-11−ii
χ1111-1-111-11-1-1i−i1-1ii−i−i11-111-1-1-11-11-11-11-1−ii−ii−i−iiiii−i−i1-1ii−i−i-111-1−ii-1-111i−i-11−iiii−i−i-1-1111-1−ii
χ1211-1-111-11-1-1i−i1-1ii−i−i11-111-1-1-11-11-11-11-1−ii−ii−i−iiiii−i−i1-1ii−i−i-11-11i−i-1-111−ii1-1−ii−i−iii11-1-1-11i−i
χ1311-1-111-11-1-1−ii1-1−i−iii11-111-1-1-11-11-11-11-1i−ii−iii−i−i−i−iii1-1−i−iii-111-1i−i-1-111−ii-11i−i−i−iii-1-1111-1i−i
χ1411-1-111-11-1-1−ii1-1−i−iii11-111-1-1-11-11-11-11-1i−ii−iii−i−i−i−iii1-1−i−iii-11-11−ii-1-111i−i1-1i−iii−i−i11-1-1-11−ii
χ1511-1-111-11-1-1−ii1-1−i−iii11-111-1-1-11-11-11-11-1−ii−ii−i−iii−i−iii1-1−i−iii1-11-1−ii11-1-1−ii1-1−ii−i−iii11-1-11-1−ii
χ1611-1-111-11-1-1−ii1-1−i−iii11-111-1-1-11-11-11-11-1−ii−ii−i−iii−i−iii1-1−i−iii1-1-11i−i11-1-1i−i-11−iiii−i−i-1-111-11i−i
χ172222222222222222222-1-12-12-12-1-1-1-1-122-1000000002-12-1-1-1-1-1-1-10022000000220000-1-1-1-10000-1-100
χ182222222222222222222-1-12-12-12-1-1-1-1-122-1000000002-12-1-1-1-1-1-1-100-2-2000000-2-20000111100001100
χ19222222222222222222-122-12-12-1-1-1-1-12-1-1200000000-12-12-1-1-1-1-1-100002200000022000000-1-1-1-100-1-1
χ20222222222222222222-122-12-12-1-1-1-1-12-1-1200000000-12-12-1-1-1-1-1-10000-2-2000000-2-200000011110011
χ212222222222-2-222-2-2-2-22-1-12-12-12-1-1-1-1-122-100000000-21-21-1-111110022000000-2-2000011110000-1-100
χ222222222222-2-222-2-2-2-22-1-12-12-12-1-1-1-1-122-100000000-21-21-1-1111100-2-2000000220000-1-1-1-100001100
χ232222222222-2-222-2-2-2-2-122-12-12-1-1-1-1-12-1-12000000001-21-2-1-11111000022000000-2-2000000111100-1-1
χ242222222222-2-222-2-2-2-2-122-12-12-1-1-1-1-12-1-12000000001-21-2-1-111110000-2-200000022000000-1-1-1-10011
χ2522222-2-222200-2-20000222222222222-2-2-2-222-2-222220000-2-2000000000000000000-2-2000000000000
χ2622222-2-222200-2-20000222222222222-2-2-2-2-2-222-2-2-2-20000-2-200000000000000000022000000000000
χ2722-2-222-22-2-22i−2i2-22i2i−2i−2i2-112-1-21-2-11-11-1-221000000002i−i−2ii-11−i−iii002-20000002i−2i0000−i−iii0000-1100
χ2822-2-222-22-2-22i−2i2-22i2i−2i−2i2-112-1-21-2-11-11-1-221000000002i−i−2ii-11−i−iii00-22000000−2i2i0000ii−i−i00001-100
χ2922-2-222-22-2-22i−2i2-22i2i−2i−2i-12-2-121-21-11-1121-1-200000000−i2ii−2i-11−i−iii00002i−2i0000002-2000000-1-11100−ii
χ3022-2-222-22-2-22i−2i2-22i2i−2i−2i-12-2-121-21-11-1121-1-200000000−i2ii−2i-11−i−iii0000−2i2i000000-2200000011-1-100i−i
χ3122-2-222-22-2-2−2i2i2-2−2i−2i2i2i2-112-1-21-2-11-11-1-22100000000−2ii2i−i-11ii−i−i002-2000000−2i2i0000ii−i−i0000-1100
χ3222-2-222-22-2-2−2i2i2-2−2i−2i2i2i2-112-1-21-2-11-11-1-22100000000−2ii2i−i-11ii−i−i00-220000002i−2i0000−i−iii00001-100
χ3322-2-222-22-2-2−2i2i2-2−2i−2i2i2i-12-2-121-21-11-1121-1-200000000i−2i−i2i-11ii−i−i00002i−2i000000-2200000011-1-100−ii
χ3422-2-222-22-2-2−2i2i2-2−2i−2i2i2i-12-2-121-21-11-1121-1-200000000i−2i−i2i-11ii−i−i0000−2i2i0000002-2000000-1-11100i−i
χ3522-2-22-222-2-200-22000022-222-2-2-22-22-2-22-222i−2i−2i2i2i2i−2i−2i0000-22000000000000000000−2i2i000000000000
χ3622-2-22-222-2-200-22000022-222-2-2-22-22-2-22-22−2i2i2i−2i−2i−2i2i2i0000-220000000000000000002i−2i000000000000
χ37444444444444444444-2-2-2-2-2-2-2-21111-2-2-2-200000000-2-2-2-21111110000000000000000000000000000
χ384444444444-4-444-4-4-4-4-2-2-2-2-2-2-2-21111-2-2-2-200000000222211-1-1-1-10000000000000000000000000000
χ3944444-4-444400-4-400004-2-24-24-24-2-2-2-22-4-420000000000002200000000000000000000000000000000
χ4044444-4-444400-4-40000-244-24-24-2-2-2-2-2-422-40000000000002200000000000000000000000000000000
χ4144444-4-444400-4-40000-2-2-2-2-2-2-2-211112222000000000000-1-13-33-30000000000000000000000000000
χ4244444-4-444400-4-40000-2-2-2-2-2-2-2-211112222000000000000-1-1-33-330000000000000000000000000000
χ4344-4-444-44-4-44i−4i4-44i4i−4i−4i-2-22-2-22221-11-1-22-2200000000−2i−2i2i2i1-1ii−i−i0000000000000000000000000000
χ4444-4-444-44-4-4−4i4i4-4−4i−4i4i4i-2-22-2-22221-11-1-22-22000000002i2i−2i−2i1-1−i−iii0000000000000000000000000000
χ4544-4-44-444-4-400-4400004-224-2-42-4-22-2224-4-20000000000002-200000000000000000000000000000000
χ4644-4-44-444-4-400-440000-24-4-242-42-22-22-4-2240000000000002-200000000000000000000000000000000
χ4744-4-44-444-4-400-440000-2-22-2-22221-11-12-22-2000000000000-113i−3i−3i3i0000000000000000000000000000
χ4844-4-44-444-4-400-440000-2-22-2-22221-11-12-22-2000000000000-11−3i3i3i−3i0000000000000000000000000000
χ494-44-4400-4-440000000044-4-4-444-44-4-4400000000000000000000000000000000000000000000000000
χ504-44-4400-4-44000000004-22-424-2-4-222-200000000000000000000000000000000000000i6−i6i6−i600000000
χ514-44-4400-4-44000000004-22-424-2-4-222-200000000000000000000000000000000000000−i6i6−i6i600000000
χ524-44-4400-4-4400000000-24-42-4-242-222-20000000000000000000000000000000000000000006−66−60000
χ534-44-4400-4-4400000000-24-42-4-242-222-2000000000000000000000000000000000000000000−66−660000
χ544-4-44400-44-400000000444-4-4-4-4444-4-400000000000000000000000000000000000000000000000000
χ554-4-44400-44-4000000004-2-2-42-424-2-222000000000000000000000000000000000000006−6−6600000000
χ564-4-44400-44-4000000004-2-2-42-424-2-22200000000000000000000000000000000000000−666−600000000
χ574-4-44400-44-400000000-2442-42-4-2-2-2220000000000000000000000000000000000000000006−6−660000
χ584-4-44400-44-400000000-2442-42-4-2-2-222000000000000000000000000000000000000000000−666−60000
χ596666-366-3-3-366-3-3-3-3-3-300000000000000002222-1-1-1-10000000000220000-1-1-1-10000-1-1000000000000
χ606666-366-3-3-366-3-3-3-3-3-30000000000000000-2-2-2-211110000000000-2-200001111000011000000000000
χ616666-366-3-3-3-6-6-3-3333300000000000000002222-1-1-1-10000000000-2-2000011110000-1-1000000000000
χ626666-366-3-3-3-6-6-3-333330000000000000000-2-2-2-211110000000000220000-1-1-1-1000011000000000000
χ636666-3-6-6-3-3-30033−3i33i3−3i33i3000000000000000022-2-2-1-1-1-10000000000000000−i3i3−i3i3000011000000000000
χ646666-3-6-6-3-3-30033−3i33i3−3i33i30000000000000000-2-22211110000000000000000i3−i3i3−i30000-1-1000000000000
χ656666-3-6-6-3-3-300333i3−3i33i3−3i3000000000000000022-2-2-1-1-1-10000000000000000i3−i3i3−i3000011000000000000
χ666666-3-6-6-3-3-300333i3−3i33i3−3i30000000000000000-2-22211110000000000000000−i3i3−i3i30000-1-1000000000000
χ6766-6-6-36-6-3336i−6i-33−3i−3i3i3i00000000000000002i−2i2i−2i−i−iii00000000002-20000-1-1110000−ii000000000000
χ6866-6-6-36-6-3336i−6i-33−3i−3i3i3i0000000000000000−2i2i−2i2iii−i−i0000000000-22000011-1-10000i−i000000000000
χ6966-6-6-36-6-333−6i6i-333i3i−3i−3i00000000000000002i−2i2i−2i−i−iii0000000000-22000011-1-10000−ii000000000000
χ7066-6-6-36-6-333−6i6i-333i3i−3i−3i0000000000000000−2i2i−2i2iii−i−i00000000002-20000-1-1110000i−i000000000000
χ7166-6-6-3-66-333003-333−33−333300000000000000002i−2i−2i2i−i−iii0000000000000000−i3i3i3−i30000i−i000000000000
χ7266-6-6-3-66-333003-333−33−33330000000000000000−2i2i2i−2iii−i−i0000000000000000i3−i3−i3i30000−ii000000000000
χ7366-6-6-3-66-333003-3−333333−3300000000000000002i−2i−2i2i−i−iii0000000000000000i3−i3−i3i30000i−i000000000000
χ7466-6-6-3-66-333003-3−333333−330000000000000000−2i2i2i−2iii−i−i0000000000000000−i3i3i3−i30000−ii000000000000
χ758-88-8800-8-8800000000-4-4444-4-442-2-2200000000000000000000000000000000000000000000000000
χ768-8-88800-88-800000000-4-4-44444-422-2-200000000000000000000000000000000000000000000000000
χ7712-1212-12-60066-60000000000000000000000000000−2i32i3−2i32i300000000000000000000000000000000000000
χ7812-1212-12-60066-600000000000000000000000000002i3−2i32i3−2i300000000000000000000000000000000000000
χ7912-12-1212-6006-66000000000000000000000000000023−23−232300000000000000000000000000000000000000
χ8012-12-1212-6006-660000000000000000000000000000−232323−2300000000000000000000000000000000000000

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