Finite Group Databasebeta

← Group #13151501

Character table — Group #13151501

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444466666666881212121212121212121212121818181818181818242424242424242436363636363636363636363636363636363636363636363672727272
order1222223666246633666666612366666666612124444121212126666612121222244444446666121212121212121212126121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1
χ51111111111-1-11111111111-1-1111-1-111111-1-111111111-111-1-1-1-1-111-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1
χ61111111111-1-11111111111-1-1111-1-111111-1-111111111-111-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ71111111111-1-11111111111-1-1111-1-111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-11111-1-1
χ81111111111-1-11111111111-1-1111-1-111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-111-1-111
χ91111-1-111111-1-1-1111111111-11-1-111-1-1111-1-111-1-111111-1-111-1-1-11-11-11-11-11-111-1-111-1-1-1-1-1-1111-11-1
χ101111-1-111111-1-1-1111111111-11-1-111-1-1111-1-111-1-111111-1-111-1-1-1-11-111-1-11-11-1-111-1-111-1-1-1-111-11-11
χ111111-1-111111-1-1-1111111111-11-1-111-1-1111-1-1-1-111-1-1-1-11-1-111-1-1-11-1-11-111-1-1111-1-1-1-1111111-1-1-111-1
χ121111-1-111111-1-1-1111111111-11-1-111-1-1111-1-1-1-111-1-1-1-11-1-111-1-1-1-111-1-11-111-1-1-11111-1-11111-1-11-1-11
χ131111-1-11111-11-1-111111111-111-1-1-1-1-1-11111111-1-11111-1-1-1-1-11111-1-11-11-111-111-1-111-1-111-1-1-1-1-11-11
χ141111-1-11111-11-1-111111111-111-1-1-1-1-1-11111111-1-11111-1-1-1-1-1111-111-1-111-1-11-1-111-1-11111-1-1-1-11-11-1
χ151111-1-11111-11-1-111111111-111-1-1-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-11111-11-11-1-11-1111-1-1-1-111-1-111111-1-11
χ161111-1-11111-11-1-111111111-111-1-1-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-1111-11-111-11-11-1-1-11111-1-1-1-11111-111-1
χ17222222222222222-12-12-1-1222-12222-1-1-1-1-12200000000-1-1-1-1-1-1-1-12200002200-1-1-1-1000000000000-1-1
χ18222222222222222-12-12-1-1222-12222-1-1-1-1-12200000000-1-1-1-1-1-1-1-1-2-20000-2-200111100000000000011
χ1922222222222222-12-12-122-122-1-1-1-1-122-1-1-1-1-12222-1-1-1-12-1-1-1-12-1-1000022000000000000-1-1-1-1-1-10000
χ2022222222222222-12-12-122-122-1-1-1-1-122-1-1-1-1-1-2-2-2-211112-1-1-1-12-1-10000-2-20000000000001111110000
χ212222222222-2-2222-12-12-1-12-2-2-122-2-2-1-1-1-1-1-2-2000000001-1-111111220000-2-200-1-1-1-100000000000011
χ222222222222-2-2222-12-12-1-12-2-2-122-2-2-1-1-1-1-1-2-2000000001-1-111111-2-2000022001111000000000000-1-1
χ232222222222-2-222-12-12-122-1-2-2-1-1-11122-1-1-1112222-1-1-1-1-2-1-111-2110000-2-200000000000011-1-1110000
χ242222222222-2-222-12-12-122-1-2-2-1-1-11122-1-1-111-2-2-2-21111-2-1-111-211000022000000000000-1-111-1-10000
χ252222-2-222222-2-2-22-12-12-1-122-2-1-2-22211-1-1-1-2-200000000-111-1-11112-200002-200-1-111000000000000-11
χ262222-2-222222-2-2-22-12-12-1-122-2-1-2-22211-1-1-1-2-200000000-111-1-1111-220000-220011-1-10000000000001-1
χ272222-2-222222-2-2-2-12-12-122-12-2-111-1-1-2-2-1-1-11122-2-2-1-1-1-1211-1-1-21100002-20000000000001111-1-10000
χ282222-2-222222-2-2-2-12-12-122-12-2-111-1-1-2-2-1-1-111-2-2221111211-1-1-2110000-22000000000000-1-1-1-1110000
χ292222-2-22222-22-2-22-12-12-1-12-22-1-2-2-2-211-1-1-1220000000011111-1-1-12-20000-2200-1-1110000000000001-1
χ302222-2-22222-22-2-22-12-12-1-12-22-1-2-2-2-211-1-1-1220000000011111-1-1-1-2200002-20011-1-1000000000000-11
χ312222-2-22222-22-2-2-12-12-122-1-22-11111-2-2-1-1-1-1-122-2-2-1-1-1-1-211112-1-10000-22000000000000-1-111110000
χ322222-2-22222-22-2-2-12-12-122-1-22-11111-2-2-1-1-1-1-1-2-2221111-211112-1-100002-200000000000011-1-1-1-10000
χ3322-2-22-22-22-2002-22222-2-2-2-20022-2002-2-2-22002i−2i2i−2i2i2i−2i−2i02-200000000000000000000000002i−2i000000
χ3422-2-22-22-22-2002-22222-2-2-2-20022-2002-2-2-2200−2i2i−2i2i−2i−2i2i2i02-20000000000000000000000000−2i2i000000
χ3522-2-22-22-22-2002-2-12-121-2-2100-1-11−i3i32-211-1−i3i32i−2i2i−2i−i−iii0-11−i3i30−i3i30000000000000000003−3−ii3−30000
χ3622-2-22-22-22-2002-2-12-121-2-2100-1-11−i3i32-211-1−i3i3−2i2i−2i2iii−i−i0-11−i3i30−i3i3000000000000000000−33i−i−330000
χ3722-2-22-22-22-2002-2-12-121-2-2100-1-11i3−i32-211-1i3−i32i−2i2i−2i−i−iii0-11i3−i30i3−i3000000000000000000−33−ii−330000
χ3822-2-22-22-22-2002-2-12-121-2-2100-1-11i3−i32-211-1i3−i3−2i2i−2i2iii−i−i0-11i3−i30i3−i30000000000000000003−3i−i3−30000
χ3922-2-2-222-22-200-222222-2-2-2-2002-2200-22-2-22002i−2i−2i2i2i2i−2i−2i0-220000000000000000000000000−2i2i000000
χ4022-2-2-222-22-200-222222-2-2-2-2002-2200-22-2-2200−2i2i2i−2i−2i−2i2i2i0-2200000000000000000000000002i−2i000000
χ4122-2-2-222-22-200-22-12-121-2-2100-11-1−i3i3-2211-1i3−i32i−2i−2i2i−i−iii01-1−i3i30i3−i3000000000000000000−33i−i3−30000
χ4222-2-2-222-22-200-22-12-121-2-2100-11-1−i3i3-2211-1i3−i3−2i2i2i−2iii−i−i01-1−i3i30i3−i30000000000000000003−3−ii−330000
χ4322-2-2-222-22-200-22-12-121-2-2100-11-1i3−i3-2211-1−i3i32i−2i−2i2i−i−iii01-1i3−i30−i3i30000000000000000003−3i−i−330000
χ4422-2-2-222-22-200-22-12-121-2-2100-11-1i3−i3-2211-1−i3i3−2i2i2i−2iii−i−i01-1i3−i30−i3i3000000000000000000−33−ii3−30000
χ4544444444444444-2-2-2-2-2-2-2-2441-2-2-2-2-2-2111-2-200000000-21111-2110000000000000000000000000000
χ464444444444-4-444-2-2-2-2-2-2-2-2-4-41-2-222-2-21112200000000211-1-12-1-10000000000000000000000000000
χ474444-4-444444-4-4-4-2-2-2-2-2-2-2-24-4122-2-2221112200000000-2-1-1112-1-10000000000000000000000000000
χ484444-4-44444-44-4-4-2-2-2-2-2-2-2-2-441222222111-2-2000000002-1-1-1-1-2110000000000000000000000000000
χ4944-4-44-44-44-4004-44-24-2-422-400-24-400-2222-200000000000-22000000000000000000000000000000000
χ5044-4-44-44-44-4004-4-2-2-2-22222001-22−2i32i3-22-1-11−2i32i30000000001-1i3−i30i3−i30000000000000000000000000000
χ5144-4-44-44-44-4004-4-2-2-2-22222001-222i3−2i3-22-1-112i3−2i30000000001-1−i3i30−i3i30000000000000000000000000000
χ5244-4-4-444-44-400-444-24-2-422-400-2-44002-222-2000000000002-2000000000000000000000000000000000
χ5344-4-4-444-44-400-44-2-2-2-222220012-2−2i32i32-2-1-112i3−2i3000000000-11i3−i30−i3i30000000000000000000000000000
χ5444-4-4-444-44-400-44-2-2-2-222220012-22i3−2i32-2-1-11−2i32i3000000000-11−i3i30i3−i30000000000000000000000000000
χ554-44-40044-4-4000044-4-4-44-440040000004-4-40000000000000000000000000000000000000000000000
χ564-44-40044-4-400004-2-42-4-22400-2000000-222000000000000000000000000000000−2i32i300000000000000
χ574-44-40044-4-400004-2-42-4-22400-2000000-2220000000000000000000000000000002i3−2i300000000000000
χ584-44-40044-4-40000-242-424-4-200-2000000-222000000−2i32i3−2i32i3000000000000000000000000000000000000
χ594-44-40044-4-40000-242-424-4-200-2000000-2220000002i3−2i32i3−2i3000000000000000000000000000000000000
χ604-4-44004-4-44000044-4-44-44-4004000000-44-40000000000000000000000000000000000000000000000
χ614-4-44004-4-4400004-2-4242-2-400-20000002-220000000000000000000000000000−2i32i30000000000000000
χ624-4-44004-4-4400004-2-4242-2-400-20000002-2200000000000000000000000000002i3−2i30000000000000000
χ634-4-44004-4-440000-242-4-2-44200-20000002-2200000023−23−2323000000000000000000000000000000000000
χ644-4-44004-4-440000-242-4-2-44200-20000002-22000000−232323−23000000000000000000000000000000000000
χ65666666-3-3-3-366-3-300000000-3-3000000000000000000000000000000220000220000-1-1-1-1000000-1-100
χ66666666-3-3-3-366-3-300000000-3-3000000000000000000000000000000-2-20000-2-2000011110000001100
χ67666666-3-3-3-3-6-6-3-30000000033000000000000000000000000000000220000-2-200001111000000-1-100
χ68666666-3-3-3-3-6-6-3-30000000033000000000000000000000000000000-2-20000220000-1-1-1-10000001100
χ696666-6-6-3-3-3-36-63300000000-330000000000000000000000000000002-200002-20000-1-111000000-1100
χ706666-6-6-3-3-3-36-63300000000-33000000000000000000000000000000-220000-22000011-1-10000001-100
χ716666-6-6-3-3-3-3-6633000000003-30000000000000000000000000000002-20000-22000011-1-1000000-1100
χ726666-6-6-3-3-3-3-6633000000003-3000000000000000000000000000000-2200002-20000-1-1110000001-100
χ738-88-80088-8-80000-4-4444-44-40020000002-2-20000000000000000000000000000000000000000000000
χ748-8-88008-8-880000-4-444-44-44002000000-22-20000000000000000000000000000000000000000000000
χ751212-12-1212-12-66-6600-66000000000000000000000000000000000000000000000000000000000000000000
χ761212-12-12-1212-66-66006-6000000000000000000000000000000000000000000000000000000000000000000
χ7712-1212-1200-6-666000000000000000000000000000000000000000000000000000000000023−230000000000
χ7812-1212-1200-6-6660000000000000000000000000000000000000000000000000000000000−23230000000000
χ7912-12-121200-666-600000000000000000000000000000000000000000000000000000000−2i32i3000000000000
χ8012-12-121200-666-6000000000000000000000000000000000000000000000000000000002i3−2i3000000000000

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