Finite Group Databasebeta

← Group #13137951

Character table — Group #13137951

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444466666666881212121212121212121212121818181818181818242424242424242436363636363636363636363636363636363636363636363672727272
order122234466644121233666666121236661212121212121212444412121212121212121212121222444488881212121212122424242424242424661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111
χ51111111111-1-11111111111-1-111111-1-1-1-111111111111-1-111-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111-1-11111111111-1-111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1
χ71111111111-1-11111111111-1-111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-111-1-1
χ81111111111-1-11111111111-1-111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-111
χ91-11-111-1-11-1i−i-1111-11-1-1-11i−i1-11-11ii−i−i1-1-1i−ii−iii−i−ii−i1-1ii−i−i1-11-1i−ii−i1-1i−i11-1-111-1-1ii−i−i1-1i−i
χ101-11-111-1-11-1i−i-1111-11-1-1-11i−i1-11-11ii−i−i1-1-1i−ii−iii−i−ii−i1-1ii−i−i-111-1−ii−ii-11i−i11-1-1-1-111−i−iii-11−ii
χ111-11-111-1-11-1i−i-1111-11-1-1-11i−i1-11-11ii−i−i1-1-1−ii−ii−i−iiii−i1-1ii−i−i1-1-11−iii−i-11−ii-1-111-1-111ii−i−i1-1−ii
χ121-11-111-1-11-1i−i-1111-11-1-1-11i−i1-11-11ii−i−i1-1-1−ii−ii−i−iiii−i1-1ii−i−i-11-11i−i−ii1-1−ii-1-11111-1-1−i−iii-11i−i
χ131-11-111-1-11-1−ii-1111-11-1-1-11−ii1-11-11−i−iii1-1-1i−ii−iii−i−i−ii1-1−i−iii1-1-11i−i−ii-11i−i-1-111-1-111−i−iii1-1i−i
χ141-11-111-1-11-1−ii-1111-11-1-1-11−ii1-11-11−i−iii1-1-1i−ii−iii−i−i−ii1-1−i−iii-11-11−iii−i1-1i−i-1-11111-1-1ii−i−i-11−ii
χ151-11-111-1-11-1−ii-1111-11-1-1-11−ii1-11-11−i−iii1-1-1−ii−ii−i−iii−ii1-1−i−iii1-11-1−ii−ii1-1−ii11-1-111-1-1−i−iii1-1−ii
χ161-11-111-1-11-1−ii-1111-11-1-1-11−ii1-11-11−i−iii1-1-1−ii−ii−i−iii−ii1-1−i−iii-111-1i−ii−i-11−ii11-1-1-1-111ii−i−i-11i−i
χ17222222222222222-1-1-1-122222-1-1-1-1-1222222-100000000-1-1-1-1-1-1-1-122000022000000000000-1-1-1-1-1-100
χ18222222222222222-1-1-1-122222-1-1-1-1-1222222-100000000-1-1-1-1-1-1-1-1-2-20000-2-200000000000011111100
χ1922222222222222-12222-1-1-122-1-1-1-12-1-1-1-1-1-122222-1-1-1-122-1-1-1-1-1-10022000000-1-1-1-1-1-1000000000000
χ2022222222222222-12222-1-1-122-1-1-1-12-1-1-1-1-1-12-2-2-2-2111122-1-1-1-1-1-100-2-2000000111111000000000000
χ212222222222-2-2222-1-1-1-1222-2-2-1-1-1-1-1-2-2-2-222-10000000011-1-11111220000-2-20000000000001111-1-100
χ222222222222-2-2222-1-1-1-1222-2-2-1-1-1-1-1-2-2-2-222-10000000011-1-11111-2-2000022000000000000-1-1-1-11100
χ232222222222-2-222-12222-1-1-1-2-2-1-1-1-121111-1-122222-1-1-1-1-2-2-1-1111100-2-2000000-1-11111000000000000
χ242222222222-2-222-12222-1-1-1-2-2-1-1-1-121111-1-12-2-2-2-21111-2-2-1-11111002200000011-1-1-1-1000000000000
χ2522222-2-222200-2-222222222002222-20000-2-2-222-2-2222200-2-200000000000000-2-20000000000000000
χ2622222-2-222200-2-222222222002222-20000-2-2-2-2-222-2-2-2-200-2-200000000000000220000000000000000
χ2722222-2-222200-2-2-12222-1-1-100-1-1-1-1-2−i3i3−i3i311-222-2-2-1-1-1-10011−i3i3−i3i3000000000011−i3i3−i3i3000000000000
χ2822222-2-222200-2-2-12222-1-1-100-1-1-1-1-2−i3i3−i3i311-2-2-22211110011−i3i3−i3i30000000000-1-1i3−i3i3−i3000000000000
χ2922222-2-222200-2-2-12222-1-1-100-1-1-1-1-2i3−i3i3−i311-222-2-2-1-1-1-10011i3−i3i3−i3000000000011i3−i3i3−i3000000000000
χ3022222-2-222200-2-2-12222-1-1-100-1-1-1-1-2i3−i3i3−i311-2-2-22211110011i3−i3i3−i30000000000-1-1−i3i3−i3i3000000000000
χ312-22-222-2-22-22i−2i-222-11-11-2-222i−2i-11-11-12i2i−2i−2i2-2100000000−ii-11−i−iii2-200002i−2i000000000000−i−iii-1100
χ322-22-222-2-22-22i−2i-222-11-11-2-222i−2i-11-11-12i2i−2i−2i2-2100000000−ii-11−i−iii-220000−2i2i000000000000ii−i−i1-100
χ332-22-222-2-22-22i−2i-22-12-22-211-12i−2i-11-112−i−iii-11-22i−2i2i−2i−i−iii2i−2i-11−i−iii002-2000000−ii-1-111000000000000
χ342-22-222-2-22-22i−2i-22-12-22-211-12i−2i-11-112−i−iii-11-2−2i2i−2i2iii−i−i2i−2i-11−i−iii00-22000000i−i11-1-1000000000000
χ352-22-222-2-22-2−2i2i-222-11-11-2-22−2i2i-11-11-1−2i−2i2i2i2-2100000000i−i-11ii−i−i2-20000−2i2i000000000000ii−i−i-1100
χ362-22-222-2-22-2−2i2i-222-11-11-2-22−2i2i-11-11-1−2i−2i2i2i2-2100000000i−i-11ii−i−i-2200002i−2i000000000000−i−iii1-100
χ372-22-222-2-22-2−2i2i-22-12-22-211-1−2i2i-11-112ii−i−i-11-22i−2i2i−2i−i−iii−2i2i-11ii−i−i00-22000000−ii11-1-1000000000000
χ382-22-222-2-22-2−2i2i-22-12-22-211-1−2i2i-11-112ii−i−i-11-2−2i2i−2i2iii−i−i−2i2i-11ii−i−i002-2000000i−i-1-111000000000000
χ392-22-22-22-22-2002-222-22-2-2-22002-22-2-20000-2222i−2i−2i2i2i2i−2i−2i00-2200000000000000−2i2i0000000000000000
χ402-22-22-22-22-2002-222-22-2-2-22002-22-2-20000-222−2i2i2i−2i−2i−2i2i2i00-22000000000000002i−2i0000000000000000
χ412-22-22-22-22-2002-2-12-22-211-100-11-11-23−3−331-122i−2i−2i2i−i−iii001-13−3−330000000000i−i−i3i3i3−i3000000000000
χ422-22-22-22-22-2002-2-12-22-211-100-11-11-23−3−331-12−2i2i2i−2iii−i−i001-13−3−330000000000−iii3−i3−i3i3000000000000
χ432-22-22-22-22-2002-2-12-22-211-100-11-11-2−333−31-122i−2i−2i2i−i−iii001-1−333−30000000000i−ii3−i3−i3i3000000000000
χ442-22-22-22-22-2002-2-12-22-211-100-11-11-2−333−31-12−2i2i2i−2iii−i−i001-1−333−30000000000−ii−i3i3i3−i3000000000000
χ4544444444444444-2-2-2-2-2-2-2-2441111-2-2-2-2-2-2-2-200000000-2-21111110000000000000000000000000000
χ464444444444-4-444-2-2-2-2-2-2-2-2-4-41111-22222-2-2-2000000002211-1-1-1-10000000000000000000000000000
χ4744444-4-444400-4-44-2-2-2-244400-2-2-2-220000-4-4200000000002200000000000000000000000000000000
χ4844444-4-444400-4-4-2-2-2-2-2-2-2-20011112−2i32i3−2i32i32220000000000-1-1i3−i3i3−i30000000000000000000000000000
χ4944444-4-444400-4-4-2-2-2-2-2-2-2-200111122i3−2i32i3−2i32220000000000-1-1−i3i3−i3i30000000000000000000000000000
χ5044-4-44004-4-40000444-4-44-4-40044-4-40000000000000000000000000000000000000000000000000000
χ5144-4-44004-4-400004-2-2224-4-400-2-222000000000000000000000000000000000000000000006−66−60000
χ5244-4-44004-4-400004-2-2224-4-400-2-22200000000000000000000000000000000000000000000−66−660000
χ5344-4-44004-4-40000-244-4-4-22200-2-222000000000000−2i32i3−2i32i3000000000000000000000000000000000000
χ5444-4-44004-4-40000-244-4-4-22200-2-2220000000000002i3−2i32i3−2i3000000000000000000000000000000000000
χ554-44-444-4-44-44i−4i-44-2-22-2222-24i−4i1-11-1-2−2i−2i2i2i-22200000000−2i2i1-1ii−i−i0000000000000000000000000000
χ564-44-444-4-44-4−4i4i-44-2-22-2222-2−4i4i1-11-1-22i2i−2i−2i-222000000002i−2i1-1−i−iii0000000000000000000000000000
χ574-44-44-44-44-4004-44-22-22-4-4400-22-2220000-44-200000000002-200000000000000000000000000000000
χ584-44-44-44-44-4004-4-2-22-2222-2001-11-1223−23−23232-2-20000000000-11−333−30000000000000000000000000000
χ594-44-44-44-44-4004-4-2-22-2222-2001-11-12−232323−232-2-20000000000-113−3−330000000000000000000000000000
χ604-4-44400-4-44000044-4-44-44-4004-4-440000000000000000000000000000000000000000000000000000
χ614-4-44400-4-4400004-222-2-44-400-222-200000000000000000000000000000000000000000000i6−i6−i6i60000
χ624-4-44400-4-4400004-222-2-44-400-222-200000000000000000000000000000000000000000000−i6i6i6−i60000
χ634-4-44400-4-440000-24-4-442-2200-222-200000000000023−23−2323000000000000000000000000000000000000
χ644-4-44400-4-440000-24-4-442-2200-222-2000000000000−232323−23000000000000000000000000000000000000
χ656666-366-3-3-366-3-300000000-3-300000000000000000000000000000000220022000000-1-1-1-1000000-1-1
χ666666-366-3-3-366-3-300000000-3-300000000000000000000000000000000-2-200-2-2000000111100000011
χ676666-366-3-3-3-6-6-3-30000000033000000000000000000000000000000002200-2-20000001111000000-1-1
χ686666-366-3-3-3-6-6-3-3000000003300000000000000000000000000000000-2-20022000000-1-1-1-100000011
χ696-66-6-36-63-336i−6i3-300000000−3i3i000000000000000000000000000000002i−2i002-2000000-1-111000000−ii
χ706-66-6-36-63-336i−6i3-300000000−3i3i00000000000000000000000000000000−2i2i00-2200000011-1-1000000i−i
χ716-66-6-36-63-33−6i6i3-3000000003i−3i000000000000000000000000000000002i−2i00-2200000011-1-1000000−ii
χ726-66-6-36-63-33−6i6i3-3000000003i−3i00000000000000000000000000000000−2i2i002-2000000-1-111000000i−i
χ7388-8-88008-8-80000-4-4-444-4440022-2-20000000000000000000000000000000000000000000000000000
χ748-8-88800-8-880000-4-444-44-44002-2-220000000000000000000000000000000000000000000000000000
χ7512121212-6-12-12-6-6-60066000000000000000000000000000000000000000000000000000000000000000000
χ761212-12-12-600-6660000000000000000000000000000000000000000000000000000000000i6−i6i6−i600000000
χ771212-12-12-600-6660000000000000000000000000000000000000000000000000000000000−i6i6−i6i600000000
χ7812-1212-12-6-12126-6600-66000000000000000000000000000000000000000000000000000000000000000000
χ7912-12-1212-60066-60000000000000000000000000000000000000000000000000000000000i6−i6−i6i600000000
χ8012-12-1212-60066-60000000000000000000000000000000000000000000000000000000000−i6i6i6−i600000000

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