Finite Group Databasebeta

← Group #13151495

Character table — Group #13151495

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444466666666881212121212121212121212121818181818181818242424242424242436363636363636363636363636363636363636363636363672727272
order1222223666246633666666612366666666612124444121212126666612121222244444446666121212121212121212126121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-111-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-1-11
χ51111111111-1-11111111111-1-1111-1-111111-1-111111111-111-1-1-1-1-111-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1
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
χ71111111111-1-11111111111-1-1111-1-111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1111-1-11
χ81111111111-1-11111111111-1-1111-1-111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-111-111-1
χ91111-1-111111-1-1-1111111111-11-1-111-1-1111-1-111-1-111111-1-111-1-1-11-11-11-11-11-111-1-1-1-111-1-1-1-11111-1-1
χ101111-1-111111-1-1-1111111111-11-1-111-1-1111-1-111-1-111111-1-111-1-1-1-11-111-1-11-11-1-111-1-1-1-111-1-111-1-111
χ111111-1-111111-1-1-1111111111-11-1-111-1-1111-1-1-1-111-1-1-1-11-1-111-1-1-11-1-11-111-1-1111-1-111-1-11111-1-1-11-11
χ121111-1-111111-1-1-1111111111-11-1-111-1-1111-1-1-1-111-1-1-1-11-1-111-1-1-1-111-1-11-111-1-1-1111111-1-111-1-11-11-1
χ131111-1-11111-11-1-111111111-111-1-1-1-1-1-11111111-1-11111-1-1-1-1-11111-1-11-11-111-111-1-11111-1-1-1-1-1-1-1-111
χ141111-1-11111-11-1-111111111-111-1-1-1-1-1-11111111-1-11111-1-1-1-1-1111-111-1-111-1-11-1-11111-1-111-1-1-1-111-1-1
χ151111-1-11111-11-1-111111111-111-1-1-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-11111-11-11-1-11-1111-1-1-1-1-1-11111111-11-1
χ161111-1-11111-11-1-111111111-111-1-1-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-1111-11-111-11-11-1-1-111-1-111-1-11111-11-11
χ17222222222222222-1-122-1-1222-12222-1-1-1-1-12200000000-1-1-1-1-1-1-1-10022000022000000-1-1-1-10000-100-1
χ18222222222222222-1-122-1-1222-12222-1-1-1-1-12200000000-1-1-1-1-1-1-1-100-2-20000-2-2000000111100001001
χ1922222222222222-122-1-122-122-1-1-1-1-122-1-1-1-1-12222-1-1-1-12-1-1-1-12-1-100002200000000-1-10000-1-1-1-10000
χ2022222222222222-122-1-122-122-1-1-1-1-122-1-1-1-1-1-2-2-2-211112-1-1-1-12-1-10000-2-20000000011000011110000
χ212222222222-2-2222-1-122-1-12-2-2-122-2-2-1-1-1-1-1-2-2000000001-1-11111100220000-2-200000011110000-100-1
χ222222222222-2-2222-1-122-1-12-2-2-122-2-2-1-1-1-1-1-2-2000000001-1-11111100-2-2000022000000-1-1-1-100001001
χ232222222222-2-222-122-1-122-1-2-2-1-1-11122-1-1-1112222-1-1-1-1-2-1-111-2110000-2-200000000110000-1-1110000
χ242222222222-2-222-122-1-122-1-2-2-1-1-11122-1-1-111-2-2-2-21111-2-1-111-21100002200000000-1-1000011-1-10000
χ252222-2-222222-2-2-22-1-122-1-122-2-1-2-22211-1-1-1-2-200000000-111-1-1111002-200002-2000000-1-1110000-1001
χ262222-2-222222-2-2-22-1-122-1-122-2-1-2-22211-1-1-1-2-200000000-111-1-111100-220000-2200000011-1-10000100-1
χ272222-2-222222-2-2-2-122-1-122-12-2-111-1-1-2-2-1-1-11122-2-2-1-1-1-1211-1-1-21100002-20000000011000011-1-10000
χ282222-2-222222-2-2-2-122-1-122-12-2-111-1-1-2-2-1-1-111-2-2221111211-1-1-2110000-2200000000-1-10000-1-1110000
χ292222-2-22222-22-2-22-1-122-1-12-22-1-2-2-2-211-1-1-1220000000011111-1-1-1002-20000-2200000011-1-10000-1001
χ302222-2-22222-22-2-22-1-122-1-12-22-1-2-2-2-211-1-1-1220000000011111-1-1-100-2200002-2000000-1-1110000100-1
χ312222-2-22222-22-2-2-122-1-122-1-22-11111-2-2-1-1-1-1-122-2-2-1-1-1-1-211112-1-10000-2200000000-1-1000011110000
χ322222-2-22222-22-2-2-122-1-122-1-22-11111-2-2-1-1-1-1-1-2-2221111-211112-1-100002-200000000110000-1-1-1-10000
χ3322-2-22-222-2-2002-222-22-22-2-20022-2002-2-2-22002i−2i2i−2i2i2i−2i−2i02-200000000000000000000000002i−2i000000
χ3422-2-22-222-2-2002-222-22-22-2-20022-2002-2-2-2200−2i2i−2i2i−2i−2i2i2i02-20000000000000000000000000−2i2i000000
χ3522-2-22-222-2-2002-2-12-2-112-2100-1-11−i3i32-211-1−i3i32i−2i2i−2i−i−iii0-11−i3i30−i3i3000000000000003−30000−ii3−30000
χ3622-2-22-222-2-2002-2-12-2-112-2100-1-11−i3i32-211-1−i3i3−2i2i−2i2iii−i−i0-11−i3i30−i3i300000000000000−330000i−i−330000
χ3722-2-22-222-2-2002-2-12-2-112-2100-1-11i3−i32-211-1i3−i32i−2i2i−2i−i−iii0-11i3−i30i3−i300000000000000−330000−ii−330000
χ3822-2-22-222-2-2002-2-12-2-112-2100-1-11i3−i32-211-1i3−i3−2i2i−2i2iii−i−i0-11i3−i30i3−i3000000000000003−30000i−i3−30000
χ3922-2-2-2222-2-200-2222-22-22-2-2002-2200-22-2-22002i−2i−2i2i2i2i−2i−2i0-220000000000000000000000000−2i2i000000
χ4022-2-2-2222-2-200-2222-22-22-2-2002-2200-22-2-2200−2i2i2i−2i−2i−2i2i2i0-2200000000000000000000000002i−2i000000
χ4122-2-2-2222-2-200-22-12-2-112-2100-11-1−i3i3-2211-1i3−i32i−2i−2i2i−i−iii01-1−i3i30i3−i300000000000000−330000i−i3−30000
χ4222-2-2-2222-2-200-22-12-2-112-2100-11-1−i3i3-2211-1i3−i3−2i2i2i−2iii−i−i01-1−i3i30i3−i3000000000000003−30000−ii−330000
χ4322-2-2-2222-2-200-22-12-2-112-2100-11-1i3−i3-2211-1−i3i32i−2i−2i2i−i−iii01-1i3−i30−i3i3000000000000003−30000i−i−330000
χ4422-2-2-2222-2-200-22-12-2-112-2100-11-1i3−i3-2211-1−i3i3−2i2i2i−2iii−i−i01-1i3−i30−i3i300000000000000−330000−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
χ4944-4-44-444-4-4004-44-224-4-22-400-24-400-2222-200000000000-22000000000000000000000000000000000
χ5044-4-44-444-4-4004-4-2-22-22-222001-22−2i32i3-22-1-11−2i32i30000000001-1i3−i30i3−i30000000000000000000000000000
χ5144-4-44-444-4-4004-4-2-22-22-222001-222i3−2i3-22-1-112i3−2i30000000001-1−i3i30−i3i30000000000000000000000000000
χ5244-4-4-4444-4-400-444-224-4-22-400-2-44002-222-2000000000002-2000000000000000000000000000000000
χ5344-4-4-4444-4-400-44-2-22-22-2220012-2−2i32i32-2-1-112i3−2i3000000000-11i3−i30−i3i30000000000000000000000000000
χ5444-4-4-4444-4-400-44-2-22-22-2220012-22i3−2i32-2-1-11−2i32i3000000000-11−i3i30i3−i30000000000000000000000000000
χ554-44-4004-44-40000444-4-4-4-440040000004-4-40000000000000000000000000000000000000000000000
χ564-44-4004-44-400004-2-2-4-422400-2000000-22200000000000000000000000000000000000023−2300000000
χ574-44-4004-44-400004-2-2-4-422400-2000000-222000000000000000000000000000000000000−232300000000
χ584-44-4004-44-40000-24422-4-4-200-2000000-222000000−2i32i3−2i32i3000000000000000000000000000000000000
χ594-44-4004-44-40000-24422-4-4-200-2000000-2220000002i3−2i32i3−2i3000000000000000000000000000000000000
χ604-4-44004-4-44000044-4-44-44-4004000000-44-40000000000000000000000000000000000000000000000
χ614-4-44004-4-4400004-22-442-2-400-20000002-220000000000000000000000000000000000−2i32i30000000000
χ624-4-44004-4-4400004-22-442-2-400-20000002-2200000000000000000000000000000000002i3−2i30000000000
χ634-4-44004-4-440000-24-42-2-44200-20000002-2200000023−23−2323000000000000000000000000000000000000
χ644-4-44004-4-440000-24-42-2-44200-20000002-22000000−232323−23000000000000000000000000000000000000
χ65666666-3-3-3-366-3-300000000-3-300000000000000000000000000002200002200-1-1-1-100000000000-1-10
χ66666666-3-3-3-366-3-300000000-3-30000000000000000000000000000-2-20000-2-200111100000000000110
χ67666666-3-3-3-3-6-6-3-300000000330000000000000000000000000000220000-2-200-1-1-1-100000000000110
χ68666666-3-3-3-3-6-6-3-300000000330000000000000000000000000000-2-200002200111100000000000-1-10
χ696666-6-6-3-3-3-36-63300000000-3300000000000000000000000000002-200002-200-1-11100000000000-110
χ706666-6-6-3-3-3-36-63300000000-330000000000000000000000000000-220000-220011-1-1000000000001-10
χ716666-6-6-3-3-3-3-6633000000003-300000000000000000000000000002-20000-2200-1-111000000000001-10
χ726666-6-6-3-3-3-3-6633000000003-30000000000000000000000000000-2200002-20011-1-100000000000-110
χ738-88-8008-88-80000-4-4-44444-40020000002-2-20000000000000000000000000000000000000000000000
χ748-8-88008-8-880000-4-444-44-44002000000-22-20000000000000000000000000000000000000000000000
χ751212-12-1212-12-6-66600-66000000000000000000000000000000000000000000000000000000000000000000
χ761212-12-12-1212-6-666006-6000000000000000000000000000000000000000000000000000000000000000000
χ7712-1212-1200-66-66000000000000000000000000000000000000000000000000000000−2i32i300000000000000
χ7812-1212-1200-66-660000000000000000000000000000000000000000000000000000002i3−2i300000000000000
χ7912-12-121200-666-60000000000000000000000000000000000000000000000000000−2i32i30000000000000000
χ8012-12-121200-666-600000000000000000000000000000000000000000000000000002i3−2i30000000000000000

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