Finite Group Databasebeta

← Group #13138024

Character table — Group #13138024

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222224466666666888121212121212121224242424242424242424363636363636363636363636363636363636727272727272727272
order12223446661212336666664121236661212121212121212121212121212448888121212122424242424242424444121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-111
χ311111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-11-111-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11-1-111-1-1
χ511111111111111111111-1-1-111111111-1-1-1-111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1111111-1-1
χ711111111111111111111-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-11-1-11111
χ811111111111111111111-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-111-1-111
χ92222222222222-12-12-12-1222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1220000-1-1-1-1000000002000000-1-1
χ102222222222222-12-12-12-1222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-20000111100000000-200000011
χ112222222222222-12-12-12-1-2-2-2-1-1-1-1-1-122-2-211-1-11111220000-1-1-1-100000000-200000011
χ122222222222222-12-12-12-1-2-2-2-1-1-1-1-1-122-2-211-1-11111-2-200001111000000002000000-1-1
χ13222222222222-12-12-12-12222-1-1-1-122-1-1-1-122-1-1-1-1-1-100002200000000-1-1-1-100200-1-100
χ14222222222222-12-12-12-12222-1-1-1-122-1-1-1-122-1-1-1-1-1-10000-2-200000000111100-2001100
χ15222222222222-12-12-12-12-2-2-2-1-1-1-122-1-111-2-2-1-1111100002200000000-1-1-1-100-2001100
χ16222222222222-12-12-12-12-2-2-2-1-1-1-122-1-111-2-2-1-111110000-2-200000000111100200-1-100
χ1722222-2-2222-2-2222222220002222-2-2-2-20000-2-200002-2000022-2-200000000000000000
χ1822222-2-2222-2-2222222220002222-2-2-2-20000-2-20000-220000-2-22200000000000000000
χ1922222-2-2222-2-22-12-12-12-1000-1-1-1-111-2-200−i3i311−i3−i3i3i32-20000-1-111000000000000000−i3i3
χ2022222-2-2222-2-22-12-12-12-1000-1-1-1-111-2-200−i3i311−i3−i3i3i3-22000011-1-1000000000000000i3−i3
χ2122222-2-2222-2-22-12-12-12-1000-1-1-1-111-2-200i3−i311i3i3−i3−i32-20000-1-111000000000000000i3−i3
χ2222222-2-2222-2-22-12-12-12-1000-1-1-1-111-2-200i3−i311i3i3−i3−i3-22000011-1-1000000000000000−i3i3
χ232-2-2222-2-2-222-222-22-2-22-20002-22-22-2-2200002-20000002i−2i0000002i2i−2i−2i0000000000000
χ242-2-2222-2-2-222-222-22-2-22-20002-22-22-2-2200002-2000000−2i2i000000−2i−2i2i2i0000000000000
χ252-2-222-22-2-22-2222-22-2-22-20002-22-2-222-20000-22000000002i−2i000000002i2i−2i−2i000000000
χ262-2-222-22-2-22-2222-22-2-22-20002-22-2-222-20000-2200000000−2i2i00000000−2i−2i2i2i000000000
χ272-2-222-22-2-22-22-12121-2-1-2000-11-11-22-113−3001-13−33−300002i−2i00000000−i−iii00000−i3i300
χ282-2-222-22-2-22-22-12121-2-1-2000-11-11-22-113−3001-13−33−30000−2i2i00000000ii−i−i00000i3−i300
χ292-2-222-22-2-22-22-12121-2-1-2000-11-11-22-11−33001-1−33−3300002i−2i00000000−i−iii00000i3−i300
χ302-2-222-22-2-22-22-12121-2-1-2000-11-11-22-11−33001-1−33−330000−2i2i00000000ii−i−i00000−i3i300
χ31444444444444-2-2-2-2-2-2-2-24441111-2-2-2-2-2-2-2-2111111000000000000000000000000000
χ32444444444444-2-2-2-2-2-2-2-2-4-4-41111-2-2-2-2222211-1-1-1-1000000000000000000000000000
χ3344444-4-4444-4-4-24-24-24-24000-2-2-2-2-4-4220000220000000000000000000000000000000
χ3444444-4-4444-4-4-2-2-2-2-2-2-2-20001111222200−2i32i3-1-1i3i3−i3−i3000000000000000000000000000
χ3544444-4-4444-4-4-2-2-2-2-2-2-2-200011112222002i3−2i3-1-1−i3−i3i3i3000000000000000000000000000
χ3644-4-4400-44-40044-4-444-4-40004-4-4400000000000000000000000000000000000000000
χ3744-4-4400-44-4004-2-424-2-42000-222-2000000000000000000000023−2300000000000000000
χ3844-4-4400-44-4004-2-424-2-42000-222-20000000000000000000000−232300000000000000000
χ3944-4-4400-44-400-242-4-242-4000-222-200000000000000000000000000006−66−6000000000
χ4044-4-4400-44-400-242-4-242-4000-222-20000000000000000000000000000−66−66000000000
χ414-44-44004-4-400444-4-4-4-4400044-4-400000000000000000000000000000000000000000
χ424-44-44004-4-4004-242-42-4-2000-2-2220000000000000000000023−230000000000000000000
χ434-44-44004-4-4004-242-42-4-2000-2-22200000000000000000000−23230000000000000000000
χ444-44-44004-4-400-24-2-42-424000-2-2220000000000000000000000000000i6−i6−i6i6000000000
χ454-44-44004-4-400-24-2-42-424000-2-2220000000000000000000000000000−i6i6i6−i6000000000
χ464-4-4444-4-4-444-44-2-4-2-4242000-22-22-22-440000-220000000000000000000000000000000
χ474-4-4444-4-4-444-4-24242-4-2-4000-22-224-42-20000-220000000000000000000000000000000
χ484-4-4444-4-4-444-4-2-22-222-220001-11-1-222-200001-13i−3i−3i3i000000000000000000000000000
χ494-4-4444-4-4-444-4-2-22-222-220001-11-1-222-200001-1−3i3i3i−3i000000000000000000000000000
χ504-4-444-44-4-44-444-2-4-2-4242000-22-222-24-400002-20000000000000000000000000000000
χ514-4-444-44-4-44-44-2-22-222-220001-11-12-2-2223−2300-11−33−33000000000000000000000000000
χ524-4-444-44-4-44-44-2-22-222-220001-11-12-2-22−232300-113−33−3000000000000000000000000000
χ536666-366-3-3-3-3-3000000006-3-30000000000000000000022000000-1-1-1-10000020-1-10000
χ546666-366-3-3-3-3-3000000006-3-300000000000000000000-2-2000000111100000-20110000
χ556666-366-3-3-3-3-300000000-6330000000000000000000022000000-1-1-1-100000-20110000
χ566666-366-3-3-3-3-300000000-63300000000000000000000-2-200000011110000020-1-10000
χ576-6-66-36-633-3-3300000000033−33000000000000000000002i−2i000000−i−iii0000000−i3i30000
χ586-6-66-36-633-3-3300000000033−3300000000000000000000−2i2i000000ii−i−i0000000i3−i30000
χ596-6-66-36-633-3-33000000000−3333000000000000000000002i−2i000000−i−iii0000000i3−i30000
χ606-6-66-36-633-3-33000000000−333300000000000000000000−2i2i000000ii−i−i0000000−i3i30000
χ6188-8-8800-88-800-4-444-4-4440002-2-2200000000000000000000000000000000000000000
χ628-88-88008-8-800-4-4-44444-400022-2-200000000000000000000000000000000000000000
χ6312121212-6-12-12-6-6-66600000000000000000000000000000000000000000000000000000000
χ641212-12-12-6006-66000000000000000000000000000000000000000006−66−60000000000000
χ651212-12-12-6006-6600000000000000000000000000000000000000000−66−660000000000000
χ6612-1212-12-600-66600000000000000000000000000000000000000000i6−i6−i6i60000000000000
χ6712-1212-12-600-66600000000000000000000000000000000000000000−i6i6i6−i60000000000000
χ6812-12-1212-6-121266-66-600000000000000000000000000000000000000000000000000000000

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