Finite Group Databasebeta

← Group #13137964

Character table — Group #13137964

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11112222224444444466666666121212121212121218181818181818182424242424242424242436363636363636363636363636363636363636363636363672727272
order122234466644121212121212336666663666121212122244121212121212121212121212121244444466888812121212242424242424242412121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111
χ51111111111-1-1-1-1-1-111111111111111111111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111-1-1-1-1-1-111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1
χ71111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ81111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-111111111-1-1-1-1-1-111
χ911-1-11-11-11-1i−iii−i−i1-111-1-111-1-11-11-1-1-1111-11-111-1-1ii−i−i1-1ii−i−ii−ii−ii−i1-11-11-1ii−i−i11-1-111-1-1i−ii−i
χ1011-1-11-11-11-1i−iii−i−i1-111-1-111-1-11-11-1-1-1111-11-111-1-1ii−i−i1-1ii−i−ii−i−ii−ii1-1-11-11ii−i−i-1-111-1-111−ii−ii
χ1111-1-11-11-11-1i−iii−i−i1-111-1-111-1-11-11-1-1-111-11-11-1-111ii−i−i1-1ii−i−i−iii−i−ii-111-1-11−i−iii11-1-1-1-111i−i−ii
χ1211-1-11-11-11-1i−iii−i−i1-111-1-111-1-11-11-1-1-111-11-11-1-111ii−i−i1-1ii−i−i−ii−iii−i-11-111-1−i−iii-1-11111-1-1−iii−i
χ1311-1-11-11-11-1−ii−i−iii1-111-1-111-1-11-11-1-1-1111-11-111-1-1−i−iii1-1−i−iii−iii−ii−i1-1-11-11−i−iii-1-111-1-111i−ii−i
χ1411-1-11-11-11-1−ii−i−iii1-111-1-111-1-11-11-1-1-1111-11-111-1-1−i−iii1-1−i−iii−ii−ii−ii1-11-11-1−i−iii11-1-111-1-1−ii−ii
χ1511-1-11-11-11-1−ii−i−iii1-111-1-111-1-11-11-1-1-111-11-11-1-111−i−iii1-1−i−iiii−ii−i−ii-11-111-1ii−i−i-1-11111-1-1i−i−ii
χ1611-1-11-11-11-1−ii−i−iii1-111-1-111-1-11-11-1-1-111-11-11-1-111−i−iii1-1−i−iiii−i−iii−i-111-1-11ii−i−i11-1-1-1-111−iii−i
χ172222222222222222222-12-12-12-1-1-1-1-12-12-1000000002-12-1-1-1-1-1-1-100002200002200000000-1-1-1-100-1-1
χ182222222222222222222-12-12-12-1-1-1-1-12-12-1000000002-12-1-1-1-1-1-1-10000-2-20000-2-20000000011110011
χ19222222222222222222-12-12-12-12-1-1-1-1-12-1200000000-12-12-1-1-1-1-1-10022000022000000-1-1-1-10000-1-100
χ20222222222222222222-12-12-12-12-1-1-1-1-12-1200000000-12-12-1-1-1-1-1-100-2-20000-2-2000000111100001100
χ212222222222-2-2-2-2-2-2222-12-12-12-1-1-1-1-12-12-100000000-21-21-1-111110000220000-2-200000000111100-1-1
χ222222222222-2-2-2-2-2-2222-12-12-12-1-1-1-1-12-12-100000000-21-21-1-111110000-2-200002200000000-1-1-1-10011
χ232222222222-2-2-2-2-2-222-12-12-12-12-1-1-1-1-12-12000000001-21-2-1-1111100220000-2-200000011110000-1-100
χ242222222222-2-2-2-2-2-222-12-12-12-12-1-1-1-1-12-12000000001-21-2-1-1111100-2-2000022000000-1-1-1-100001100
χ2522222-2-2222000000-2-2222222222222-2-2-2-222-2-2-2-2-2-20000-2-200000000002200000000000000000000
χ2622222-2-2222000000-2-2222222222222-2-2-2-2-2-22222220000-2-20000000000-2-200000000000000000000
χ2722-2-222-2-22-2000000-2222-2-222-2-22-22-222-2-22-2-22-2-2220000-2200000000002-200000000000000000000
χ2822-2-222-2-22-2000000-2222-2-222-2-22-22-222-2-2-222-222-2-20000-220000000000-2200000000000000000000
χ2922-2-22-22-22-22i−2i2i2i−2i−2i2-22-1-212-1-21-11-11-212-1000000002i−i−2ii-11−i−iii00002i−2i00002-200000000-1-11100−ii
χ3022-2-22-22-22-22i−2i2i2i−2i−2i2-22-1-212-1-21-11-11-212-1000000002i−i−2ii-11−i−iii0000−2i2i0000-220000000011-1-100i−i
χ3122-2-22-22-22-22i−2i2i2i−2i−2i2-2-121-2-121-2-11-111-2-1200000000−i2ii−2i-11−i−iii002i−2i00002-2000000-1-1110000−ii00
χ3222-2-22-22-22-22i−2i2i2i−2i−2i2-2-121-2-121-2-11-111-2-1200000000−i2ii−2i-11−i−iii00−2i2i0000-2200000011-1-10000i−i00
χ3322-2-22-22-22-2−2i2i−2i−2i2i2i2-22-1-212-1-21-11-11-212-100000000−2ii2i−i-11ii−i−i00002i−2i0000-220000000011-1-100−ii
χ3422-2-22-22-22-2−2i2i−2i−2i2i2i2-22-1-212-1-21-11-11-212-100000000−2ii2i−i-11ii−i−i0000−2i2i00002-200000000-1-11100i−i
χ3522-2-22-22-22-2−2i2i−2i−2i2i2i2-2-121-2-121-2-11-111-2-1200000000i−2i−i2i-11ii−i−i002i−2i0000-2200000011-1-10000−ii00
χ3622-2-22-22-22-2−2i2i−2i−2i2i2i2-2-121-2-121-2-11-111-2-1200000000i−2i−i2i-11ii−i−i00−2i2i00002-2000000-1-1110000i−i00
χ37444444444444444444-2-2-2-2-2-2-2-21111-2-2-2-200000000-2-2-2-21111110000000000000000000000000000
χ384444444444-4-4-4-4-4-444-2-2-2-2-2-2-2-21111-2-2-2-200000000222211-1-1-1-10000000000000000000000000000
χ3944444-4-4444000000-4-44-24-24-24-2-2-2-2-2-42-420000000000002200000000000000000000000000000000
χ4044444-4-4444000000-4-4-24-24-24-24-2-2-2-22-42-40000000000002200000000000000000000000000000000
χ4144444-4-4444000000-4-4-2-2-2-2-2-2-2-211112222000000000000-1-13-33-30000000000000000000000000000
χ4244444-4-4444000000-4-4-2-2-2-2-2-2-2-211112222000000000000-1-1-33-330000000000000000000000000000
χ4344-4-444-4-44-4000000-444-2-424-2-42-22-224-2-420000000000002-200000000000000000000000000000000
χ4444-4-444-4-44-4000000-44-242-4-242-4-22-22-242-40000000000002-200000000000000000000000000000000
χ4544-4-444-4-44-4000000-44-2-222-2-2221-11-1-2-222000000000000-113i−3i−3i3i0000000000000000000000000000
χ4644-4-444-4-44-4000000-44-2-222-2-2221-11-1-2-222000000000000-11−3i3i3i−3i0000000000000000000000000000
χ4744-4-44-44-44-44i−4i4i4i−4i−4i4-4-2-222-2-2221-11-122-2-200000000−2i−2i2i2i1-1ii−i−i0000000000000000000000000000
χ4844-4-44-44-44-4−4i4i−4i−4i4i4i4-4-2-222-2-2221-11-122-2-2000000002i2i−2i−2i1-1−i−iii0000000000000000000000000000
χ494-44-4400-4-44000000004444-4-4-4-444-4-400000000000000000000000000000000000000000000000000
χ504-44-4400-4-44000000004-24-2-42-42-2-222000000000000000000000000000000000000000000i6−i6i6−i60000
χ514-44-4400-4-44000000004-24-2-42-42-2-222000000000000000000000000000000000000000000−i6i6−i6i60000
χ524-44-4400-4-4400000000-24-242-42-4-2-22200000000000000000000000000000000000000i6−i6i6−i600000000
χ534-44-4400-4-4400000000-24-242-42-4-2-22200000000000000000000000000000000000000−i6i6−i6i600000000
χ544-4-444004-4-40000000044-4-4-4-4444-4-4400000000000000000000000000000000000000000000000000
χ554-4-444004-4-4000000004-2-42-424-2-222-2000000000000000000000000000000000000000000i6−i6−i6i60000
χ564-4-444004-4-4000000004-2-42-424-2-222-2000000000000000000000000000000000000000000−i6i6i6−i60000
χ574-4-444004-4-400000000-242-42-4-24-222-200000000000000000000000000000000000000i6−i6−i6i600000000
χ584-4-444004-4-400000000-242-42-4-24-222-200000000000000000000000000000000000000−i6i6i6−i600000000
χ596666-366-3-3-366-3-3-3-3-3-300000000000000002222-1-1-1-10000000000220000-1-10000-1-1-1-1000000000000
χ606666-366-3-3-366-3-3-3-3-3-30000000000000000-2-2-2-211110000000000-2-200001100001111000000000000
χ616666-366-3-3-3-6-63333-3-300000000000000002222-1-1-1-10000000000-2-20000-1-100001111000000000000
χ626666-366-3-3-3-6-63333-3-30000000000000000-2-2-2-211110000000000220000110000-1-1-1-1000000000000
χ636666-3-6-6-3-3-300−3i33i3−3i33i333000000000000000022-2-211110000000000000000-1-10000−i3i3−i3i3000000000000
χ646666-3-6-6-3-3-300−3i33i3−3i33i3330000000000000000-2-222-1-1-1-10000000000000000110000i3−i3i3−i3000000000000
χ656666-3-6-6-3-3-3003i3−3i33i3−3i333000000000000000022-2-211110000000000000000-1-10000i3−i3i3−i3000000000000
χ666666-3-6-6-3-3-3003i3−3i33i3−3i3330000000000000000-2-222-1-1-1-10000000000000000110000−i3i3−i3i3000000000000
χ6766-6-6-36-63-330033−33−33333-300000000000000002-2-2211-1-10000000000000000-1100003−3−33000000000000
χ6866-6-6-36-63-330033−33−33333-30000000000000000-222-2-1-11100000000000000001-10000−333−3000000000000
χ6966-6-6-36-63-3300−333333−333-300000000000000002-2-2211-1-10000000000000000-110000−333−3000000000000
χ7066-6-6-36-63-3300−333333−333-30000000000000000-222-2-1-11100000000000000001-100003−3−33000000000000
χ7166-6-6-3-663-336i−6i−3i−3i3i3i-3300000000000000002-22-2-1-11100000000002i−2i0000-110000−i−iii000000000000
χ7266-6-6-3-663-336i−6i−3i−3i3i3i-330000000000000000-22-2211-1-10000000000−2i2i00001-10000ii−i−i000000000000
χ7366-6-6-3-663-33−6i6i3i3i−3i−3i-3300000000000000002-22-2-1-1110000000000−2i2i0000-110000ii−i−i000000000000
χ7466-6-6-3-663-33−6i6i3i3i−3i−3i-330000000000000000-22-2211-1-100000000002i−2i00001-10000−i−iii000000000000
χ758-88-8800-8-8800000000-4-4-4-4444422-2-200000000000000000000000000000000000000000000000000
χ768-8-888008-8-800000000-4-44444-4-42-2-2200000000000000000000000000000000000000000000000000
χ7712-1212-12-60066-6000000000000000000000000000023−2323−2300000000000000000000000000000000000000
χ7812-1212-12-60066-60000000000000000000000000000−2323−232300000000000000000000000000000000000000
χ7912-12-1212-600-666000000000000000000000000000023−23−232300000000000000000000000000000000000000
χ8012-12-1212-600-6660000000000000000000000000000−232323−2300000000000000000000000000000000000000

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