Finite Group Databasebeta

← Group #13138050

Character table — Group #13138050

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11112222224444444466666666121212121212121218181818181818182424242424242424242436363636363636363636363636363636363636363636363672727272
order12223446664412121212121233666666366612121212224466661212121212121212121222444488881212121212122424242424242424661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111-1-111-1-1-1-1111111111111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111-1-111-1-1-1-1111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1
χ71111111111-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1111111-1-1
χ81111111111-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-111
χ91-1-1111-1-11-1i−i1-1ii−i−i11-1-11-1-111-11-111-1-11-11-111-1-1ii−i−i1-1ii−i−i1-1i−i1-1i−ii−i1-1ii−i−iii−i−iii−i−i1-11-1
χ101-1-1111-1-11-1i−i1-1ii−i−i11-1-11-1-111-11-111-1-11-11-111-1-1ii−i−i1-1ii−i−i-11i−i-11−ii−ii1-1ii−i−i−i−iii−i−iii-11-11
χ111-1-1111-1-11-1i−i1-1ii−i−i11-1-11-1-111-11-111-1-1-11-11-1-111ii−i−i1-1ii−i−i1-1−ii-11i−i−ii-11−i−iiiii−i−i−i−iii1-1-11
χ121-1-1111-1-11-1i−i1-1ii−i−i11-1-11-1-111-11-111-1-1-11-11-1-111ii−i−i1-1ii−i−i-11−ii1-1−iii−i-11−i−iii−i−iiiii−i−i-111-1
χ131-1-1111-1-11-1−ii1-1−i−iii11-1-11-1-111-11-111-1-11-11-111-1-1−i−iii1-1−i−iii1-1−ii1-1−ii−ii1-1−i−iii−i−iii−i−iii1-11-1
χ141-1-1111-1-11-1−ii1-1−i−iii11-1-11-1-111-11-111-1-11-11-111-1-1−i−iii1-1−i−iii-11−ii-11i−ii−i1-1−i−iiiii−i−iii−i−i-11-11
χ151-1-1111-1-11-1−ii1-1−i−iii11-1-11-1-111-11-111-1-1-11-11-1-111−i−iii1-1−i−iii1-1i−i-11−iii−i-11ii−i−i−i−iiiii−i−i1-1-11
χ161-1-1111-1-11-1−ii1-1−i−iii11-1-11-1-111-11-111-1-1-11-11-1-111−i−iii1-1−i−iii-11i−i1-1i−i−ii-11ii−i−iii−i−i−i−iii-111-1
χ172222222222222222222-12-1-12-12-1-1-1-1-12-12000000002-12-1-1-1-1-1-1-12200002200000000-1-1-1-10000-1-100
χ182222222222222222222-12-1-12-12-1-1-1-1-12-12000000002-12-1-1-1-1-1-1-1-2-20000-2-200000000111100001100
χ19222222222222222222-12-122-12-1-1-1-1-12-12-100000000-12-12-1-1-1-1-1-100002200220000000000-1-1-1-100-1-1
χ20222222222222222222-12-122-12-1-1-1-1-12-12-100000000-12-12-1-1-1-1-1-10000-2-200-2-2000000000011110011
χ212222222222-2-222-2-2-2-22-12-1-12-12-1-1-1-1-12-1200000000-21-21-1-11111220000-2-20000000011110000-1-100
χ222222222222-2-222-2-2-2-22-12-1-12-12-1-1-1-1-12-1200000000-21-21-1-11111-2-200002200000000-1-1-1-100001100
χ232222222222-2-222-2-2-2-2-12-122-12-1-1-1-1-12-12-1000000001-21-2-1-1111100002200-2-20000000000111100-1-1
χ242222222222-2-222-2-2-2-2-12-122-12-1-1-1-1-12-12-1000000001-21-2-1-111110000-2-200220000000000-1-1-1-10011
χ2522222-2-222200-2-20000222222222222-2-2-2-222-2-222220000-2-200000000000000-2-20000000000000000
χ2622222-2-222200-2-20000222222222222-2-2-2-2-2-222-2-2-2-20000-2-200000000000000220000000000000000
χ272-2-2222-2-22-22i−2i2-22i2i−2i−2i2-1-21-1-212-11-11-121-2000000002i−i−2ii-11−i−iii2-200002i−2i00000000−i−iii0000-1100
χ282-2-2222-2-22-22i−2i2-22i2i−2i−2i2-1-21-1-212-11-11-121-2000000002i−i−2ii-11−i−iii-220000−2i2i00000000ii−i−i00001-100
χ292-2-2222-2-22-22i−2i2-22i2i−2i−2i-121-221-2-1-11-112-1-2100000000−i2ii−2i-11−i−iii00002-2002i−2i0000000000−i−iii00-11
χ302-2-2222-2-22-22i−2i2-22i2i−2i−2i-121-221-2-1-11-112-1-2100000000−i2ii−2i-11−i−iii0000-2200−2i2i0000000000ii−i−i001-1
χ312-2-2222-2-22-2−2i2i2-2−2i−2i2i2i2-1-21-1-212-11-11-121-200000000−2ii2i−i-11ii−i−i2-20000−2i2i00000000ii−i−i0000-1100
χ322-2-2222-2-22-2−2i2i2-2−2i−2i2i2i2-1-21-1-212-11-11-121-200000000−2ii2i−i-11ii−i−i-2200002i−2i00000000−i−iii00001-100
χ332-2-2222-2-22-2−2i2i2-2−2i−2i2i2i-121-221-2-1-11-112-1-2100000000i−2i−i2i-11ii−i−i00002-200−2i2i0000000000ii−i−i00-11
χ342-2-2222-2-22-2−2i2i2-2−2i−2i2i2i-121-221-2-1-11-112-1-2100000000i−2i−i2i-11ii−i−i0000-22002i−2i0000000000−i−iii001-1
χ352-2-222-22-22-200-22000022-2-22-2-222-22-2-2-2222-2-2222-2-20000-2200000000000000-220000000000000000
χ362-2-222-22-22-200-22000022-2-22-2-222-22-2-2-222-222-2-2-2220000-22000000000000002-20000000000000000
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
χ3944444-4-444400-4-400004-24-2-24-24-2-2-2-22-42-40000000000002200000000000000000000000000000000
χ4044444-4-444400-4-40000-24-244-24-2-2-2-2-2-42-420000000000002200000000000000000000000000000000
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
χ4344-4-44004-4-4000000004444-4-4-4-444-4-400000000000000000000000000000000000000000000000000
χ4444-4-44004-4-4000000004-24-22-42-4-2-222000000000000000000000000000000000000006−66−600000000
χ4544-4-44004-4-4000000004-24-22-42-4-2-22200000000000000000000000000000000000000−66−6600000000
χ4644-4-44004-4-400000000-24-24-42-42-2-222000000000000000000000000000000000000000000i6−i6i6−i60000
χ4744-4-44004-4-400000000-24-24-42-42-2-222000000000000000000000000000000000000000000−i6i6−i6i60000
χ484-44-4400-4-440000000044-4-4-444-44-4-4400000000000000000000000000000000000000000000000000
χ494-44-4400-4-44000000004-2-4224-2-4-222-200000000000000000000000000000000000000i6−i6−i6i600000000
χ504-44-4400-4-44000000004-2-4224-2-4-222-200000000000000000000000000000000000000−i6i6i6−i600000000
χ514-44-4400-4-4400000000-242-4-4-242-222-20000000000000000000000000000000000000000006−6−660000
χ524-44-4400-4-4400000000-242-4-4-242-222-2000000000000000000000000000000000000000000−666−60000
χ534-4-4444-4-44-44i−4i4-44i4i−4i−4i-2-222-222-21-11-1-2-22200000000−2i−2i2i2i1-1ii−i−i0000000000000000000000000000
χ544-4-4444-4-44-4−4i4i4-4−4i−4i4i4i-2-222-222-21-11-1-2-222000000002i2i−2i−2i1-1−i−iii0000000000000000000000000000
χ554-4-444-44-44-400-4400004-2-42-2-424-22-222-4-240000000000002-200000000000000000000000000000000
χ564-4-444-44-44-400-440000-242-442-4-2-22-22-424-20000000000002-200000000000000000000000000000000
χ574-4-444-44-44-400-440000-2-222-222-21-11-122-2-2000000000000-113i−3i−3i3i0000000000000000000000000000
χ584-4-444-44-44-400-440000-2-222-222-21-11-122-2-2000000000000-11−3i3i3i−3i0000000000000000000000000000
χ596666-366-3-3-366-3-3-3-3-3-300000000000000002222-1-1-1-100000000000022000000-1-1-1-1-1-1000000000000
χ606666-366-3-3-366-3-3-3-3-3-30000000000000000-2-2-2-21111000000000000-2-2000000111111000000000000
χ616666-366-3-3-3-6-6-3-3333300000000000000002222-1-1-1-1000000000000-2-2000000-1-11111000000000000
χ626666-366-3-3-3-6-6-3-333330000000000000000-2-2-2-211110000000000002200000011-1-1-1-1000000000000
χ636666-3-6-6-3-3-30033−3i33i3−3i33i3000000000000000022-2-2-1-1-1-10000000000000000000011−i3i3−i3i3000000000000
χ646666-3-6-6-3-3-30033−3i33i3−3i33i30000000000000000-2-222111100000000000000000000-1-1i3−i3i3−i3000000000000
χ656666-3-6-6-3-3-300333i3−3i33i3−3i3000000000000000022-2-2-1-1-1-10000000000000000000011i3−i3i3−i3000000000000
χ666666-3-6-6-3-3-300333i3−3i33i3−3i30000000000000000-2-222111100000000000000000000-1-1−i3i3−i3i3000000000000
χ676-6-66-36-63-336i−6i-33−3i−3i3i3i00000000000000002-22-2-1-1110000000000002i−2i000000-11−i−iii000000000000
χ686-6-66-36-63-336i−6i-33−3i−3i3i3i0000000000000000-22-2211-1-1000000000000−2i2i0000001-1ii−i−i000000000000
χ696-6-66-36-63-33−6i6i-333i3i−3i−3i00000000000000002-22-2-1-111000000000000−2i2i000000-11ii−i−i000000000000
χ706-6-66-36-63-33−6i6i-333i3i−3i−3i0000000000000000-22-2211-1-10000000000002i−2i0000001-1−i−iii000000000000
χ716-6-66-3-663-33003-333−33−333300000000000000002-2-22-1-111000000000000000000001-13−3−33000000000000
χ726-6-66-3-663-33003-333−33−33330000000000000000-222-211-1-100000000000000000000-11−333−3000000000000
χ736-6-66-3-663-33003-3−333333−3300000000000000002-2-22-1-111000000000000000000001-1−333−3000000000000
χ746-6-66-3-663-33003-3−333333−330000000000000000-222-211-1-100000000000000000000-113−3−33000000000000
χ7588-8-88008-8-800000000-4-4-4-4444422-2-200000000000000000000000000000000000000000000000000
χ768-88-8800-8-8800000000-4-4444-4-442-2-2200000000000000000000000000000000000000000000000000
χ771212-12-12-600-6660000000000000000000000000000−2i32i3−2i32i300000000000000000000000000000000000000
χ781212-12-12-600-66600000000000000000000000000002i3−2i32i3−2i300000000000000000000000000000000000000
χ7912-1212-12-60066-60000000000000000000000000000−2i32i32i3−2i300000000000000000000000000000000000000
χ8012-1212-12-60066-600000000000000000000000000002i3−2i3−2i32i300000000000000000000000000000000000000

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