Finite Group Databasebeta

← Group #13156571

Character table — Group #13156571

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222244444444444444444488888888888888242424242424242424242424242424242424242424242424242424363636363636363636363636363636363636216
order1222333446666666663336666666661212121212123666121212121212121212124441212121212121212121212121212121212121212121212124488881212121224242424242424244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-11111-1-1-1-1111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111-1111-1-1111111-1-11111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111
χ511111111111111111111111111111111111111111111111111-111-1-1111111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1
χ611111111111111111111111111111111111111111111111111-11-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11
χ711111111111111111111111111111111111111111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11
χ811111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1
χ92222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-20000000000000000000000000002-2000022-2-2000000000
χ102222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2000000000000000000000000000-220000-2-222000000000
χ11222222-12222-12222-1-12-1-122-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-122022220000-1-1-1-1-1-1-1-1-1-1-1-10000220000-1-1-1-1000000000
χ12222222-12222-12222-1-12-1-122-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-12-2022-2-20000-1-111-1-1-1-111110000-2-200001111000000000
χ13222222-12222-12222-1-12-1-122-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-220-2-222000011-1-11111-1-1-1-10000-2-200001111000000000
χ14222222-12222-12222-1-12-1-122-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-2-20-2-2-2-200001111111111110000220000-1-1-1-1000000000
χ15222222-1-2-222-12222-1-12-1-122-1-1-1-1-1-1211-2-2-2-2-1-1-1-11111-2-2111100000000000−i3i3−i3i3−i3−i3i3i3−i3−i3i3i300002-20000-1-111000000000
χ16222222-1-2-222-12222-1-12-1-122-1-1-1-1-1-1211-2-2-2-2-1-1-1-11111-2-2111100000000000−i3i3i3−i3−i3−i3i3i3i3i3−i3−i30000-22000011-1-1000000000
χ17222222-1-2-222-12222-1-12-1-122-1-1-1-1-1-1211-2-2-2-2-1-1-1-11111-2-2111100000000000i3−i3−i3i3i3i3−i3−i3−i3−i3i3i30000-22000011-1-1000000000
χ18222222-1-2-222-12222-1-12-1-122-1-1-1-1-1-1211-2-2-2-2-1-1-1-11111-2-2111100000000000i3−i3i3−i3i3i3−i3−i3i3i3−i3−i300002-20000-1-111000000000
χ1922222-12222-122-12-122-12-1-1-12-12-12-1-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-102200-1-122-1-100220000-1-1-1-1-1-1-1-100002200000000-1-1-1-10
χ2022222-12222-122-12-122-12-1-1-12-12-12-1-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-102-200-1-1-2-21100220000-1-1-1-111110000-2-20000000011110
χ2122222-12222-122-12-122-12-1-1-12-12-12-1-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-10-22001122-1-100-2-200001111-1-1-1-10000-2-20000000011110
χ2222222-12222-122-12-122-12-1-1-12-12-12-1-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-10-2-20011-2-21100-2-200001111111100002200000000-1-1-1-10
χ232222-12222-122-12-1222-1-12-1-1-12-12-12-122-12-12-1-1-1-1-1-122-1-1-1-1-1-1202-1-100-1-1222200-1-1-1-10000-1-1-1-10022000000-1-1-1-100000
χ242222-12222-122-12-1222-1-12-1-1-12-12-12-122-12-12-1-1-1-1-1-122-1-1-1-1-1-120-2-1-10011-2-22200-1-1-1-10000111100-2-2000000111100000
χ252222-12222-122-12-1222-1-12-1-1-12-12-12-122-12-12-1-1-1-1-1-122-1-1-1-1-1-1-2021100-1-122-2-20011110000-1-1-1-100-2-2000000111100000
χ262222-12222-122-12-1222-1-12-1-1-12-12-12-122-12-12-1-1-1-1-1-122-1-1-1-1-1-1-20-2110011-2-2-2-2001111000011110022000000-1-1-1-100000
χ272-2-222222-2-2-22-2-222-2-2222-2-2-2-222-2-222-22-2-222-2-222-22-22-222-2-2000000000000000000000000000002i−2i0000002i2i−2i−2i00000
χ282-2-222222-2-2-22-2-222-2-2222-2-2-2-222-2-222-22-2-222-2-222-22-22-222-2-200000000000000000000000000000−2i2i000000−2i−2i2i2i00000
χ292-2-22222-22-2-22-2-222-2-2222-2-2-2-222-2-22-22-222-22-2-22-22-22-22-2-22200000000000000000000000000000002i−2i000000002i2i−2i−2i0
χ302-2-22222-22-2-22-2-222-2-2222-2-2-2-222-2-22-22-222-22-2-22-22-22-22-2-2220000000000000000000000000000000−2i2i00000000−2i−2i2i2i0
χ312-2-222-12-22-212-212-1-2-2-12-111-212-1-21-1-22-2-121-111-1-221-11-111-1-1000003−300−i3i3000000003−33−3−i3−i3i3i300002i−2i00000000−i−iii0
χ322-2-222-12-22-212-212-1-2-2-12-111-212-1-21-1-22-2-121-111-1-221-11-111-1-1000003−300i3−i3000000003−33−3i3i3−i3−i30000−2i2i00000000ii−i−i0
χ332-2-222-12-22-212-212-1-2-2-12-111-212-1-21-1-22-2-121-111-1-221-11-111-1-100000−3300−i3i300000000−33−33−i3−i3i3i30000−2i2i00000000ii−i−i0
χ342-2-222-12-22-212-212-1-2-2-12-111-212-1-21-1-22-2-121-111-1-221-11-111-1-100000−3300i3−i300000000−33−33i3i3−i3−i300002i−2i00000000−i−iii0
χ352-2-22-1222-21-221-2-12-2-2-1-12111-2-121-2-12-2-1-212-111-1-112-2-11-1-1110003−300−i3i30000003−33−30000−i3i3−i3i3002i−2i000000−i−iii00000
χ362-2-22-1222-21-221-2-12-2-2-1-12111-2-121-2-12-2-1-212-111-1-112-2-11-1-1110003−300i3−i30000003−33−30000i3−i3i3−i300−2i2i000000ii−i−i00000
χ372-2-22-1222-21-221-2-12-2-2-1-12111-2-121-2-12-2-1-212-111-1-112-2-11-1-111000−3300−i3i3000000−33−330000−i3i3−i3i300−2i2i000000ii−i−i00000
χ382-2-22-1222-21-221-2-12-2-2-1-12111-2-121-2-12-2-1-212-111-1-112-2-11-1-111000−3300i3−i3000000−33−330000i3−i3i3−i3002i−2i000000−i−iii00000
χ3944444-24-4-44-244-24-244-24-2-2-24-24-24-2-2-4-4-42-42-2-2-2-2-4-4222222220000000000000000000000000000000000000000000000
χ4044444-2-2444-2-24-24-2-2-2-2-21-2-2-21-21-21-2-2-24-24-21111-2-211-2-2111104000-2-2000000-2-20000111100000000000000000000000
χ4144444-2-2444-2-24-24-2-2-2-2-21-2-2-21-21-21-2-2-24-24-21111-2-211-2-211110-400022000000220000-1-1-1-100000000000000000000000
χ4244444-2-2-4-44-2-24-24-2-2-2-2-21-2-2-21-21-21-222-42-42111122-1-122-1-1-1-10000000000000−2i32i30000i3i3−i3−i300000000000000000000000
χ4344444-2-2-4-44-2-24-24-2-2-2-2-21-2-2-21-21-21-222-42-42111122-1-122-1-1-1-100000000000002i3−2i30000−i3−i3i3i300000000000000000000000
χ444444-244-4-4-244-24-2444-2-24-2-2-24-24-24-2-4-42-42-4-2-2-2-222-4-42222220000000000000000000000000000000000000000000000
χ454444-24-244-24-2-24-24-2-2-21-2-2-21-21-21-2-2-2-2-24-24111111-2-2-2-21111400-2-2000000-2-2001111000000000000000000000000000
χ464444-24-244-24-2-24-24-2-2-21-2-2-21-21-21-2-2-2-2-24-24111111-2-2-2-21111-400220000002200-1-1-1-1000000000000000000000000000
χ474444-24-2-4-4-24-2-24-24-2-2-21-2-2-21-21-21-2-2222-42-41111-1-12222-1-1-1-100000000000−2i32i300i3i3−i3−i3000000000000000000000000000
χ484444-24-2-4-4-24-2-24-24-2-2-21-2-2-21-21-21-2-2222-42-41111-1-12222-1-1-1-1000000000002i3−2i300−i3−i3i3i3000000000000000000000000000
χ494444-2-2444-2-24-2-2-2-2441-2-211-2-2-2-2-2-2144-2-2-2-21111-2-2-2-21111110040000-2-2-2-200000000000011110000000000000000000
χ504444-2-2444-2-24-2-2-2-2441-2-211-2-2-2-2-2-2144-2-2-2-21111-2-2-2-211111100-400002222000000000000-1-1-1-10000000000000000000
χ514444-2-24-4-4-2-24-2-2-2-2441-2-211-2-2-2-2-2-21-4-4222211112222-1-1-1-1-1-1000000000000000000000003-3-330000000000000000000
χ524444-2-24-4-4-2-24-2-2-2-2441-2-211-2-2-2-2-2-21-4-4222211112222-1-1-1-1-1-100000000000000000000000-333-30000000000000000000
χ5344-4-4444004-4-4-44-4-44-44444-44-4-4-4-44-400000044-4-400000000000000000000000000000000000000000000000000000000
χ5444-4-444-2004-42-44-4-4-224-2-24-4-22222-2-4000000-2-22200000000000000000000000000000000000000000000023−23000000000
χ5544-4-444-2004-42-44-4-4-224-2-24-4-22222-2-4000000-2-222000000000000000000000000000000000000000000000−2323000000000
χ5644-4-44-240042-4-4-2-424-4-24-2-2242-42-4-22000000-2-2220000000000000000000000000000000000000000000000000006−66−60
χ5744-4-44-240042-4-4-2-424-4-24-2-2242-42-4-22000000-2-222000000000000000000000000000000000000000000000000000−66−660
χ5844-4-4-24400-2-4-4242-44-4-2-24-22-2-42-4242000000-2-22200000000000000000000000000000000000000000000000i6−i6i6−i600000
χ5944-4-4-24400-2-4-4242-44-4-2-24-22-2-42-4242000000-2-22200000000000000000000000000000000000000000000000−i6i6−i6i600000
χ604-44-444400-44-44-4-4-4-44444-44-44-4-44-4-40000004-44-400000000000000000000000000000000000000000000000000000000
χ614-44-444-200-4424-4-4-42-24-2-2-442-222-22-4000000-22-22000000000000000000000000000000000000000000023−2300000000000
χ624-44-444-200-4424-4-4-42-24-2-2-442-222-22-4000000-22-220000000000000000000000000000000000000000000−232300000000000
χ634-44-44-2400-4-2-442-42-44-24-22-2-4-2-42422000000-22-22000000000000000000000000000000000000000000000000000i6−i6−i6i60
χ644-44-44-2400-4-2-442-42-44-24-22-2-4-2-42422000000-22-22000000000000000000000000000000000000000000000000000−i6i6i6−i60
χ654-44-4-2440024-4-2-42-4-44-2-242-2242-4-2-42000000-22-22000000000000000000000000000000000000000000000006−6−6600000
χ664-44-4-2440024-4-2-42-4-44-2-242-2242-4-2-42000000-22-2200000000000000000000000000000000000000000000000−666−600000
χ674-4-4444-24-4-4-4-2-4-444224-2-2-4-422-2-2224-224-4-44-222-2-22-224-4-2-2220000000000000000000000000000000000000000000000
χ684-4-4444-2-44-4-4-2-4-444224-2-2-4-422-2-22242-2-444-4-222-22-22-2-4422-2-20000000000000000000000000000000000000000000000
χ694-4-444-244-4-424-424-2-4-4-24-222-424-2-42-24-442-4-2-222-24-4-22-22-2-2220000000000000000000000000000000000000000000000
χ704-4-444-2-24-4-42-2-424-222-2-21222-1-212-1-2-2242-4-21-1-11-221-1-2211-1-100000000000000000003i−3i−3i3i00000000000000000000000
χ714-4-444-2-24-4-42-2-424-222-2-21222-1-212-1-2-2242-4-21-1-11-221-1-2211-1-10000000000000000000−3i3i3i−3i00000000000000000000000
χ724-4-444-2-2-44-42-2-424-222-2-21222-1-212-1-22-2-4-2421-1-112-2-112-2-1-1110000023−23000000000000−33−3300000000000000000000000
χ734-4-444-2-2-44-42-2-424-222-2-21222-1-212-1-22-2-4-2421-1-112-2-112-2-1-11100000−23230000000000003−33−300000000000000000000000
χ744-4-44-244-442-442-4-24-4-4-2-24222-4-242-4-2-4424-2-4-222-22-2-442-222-2-20000000000000000000000000000000000000000000000
χ754-4-44-24-24-42-4-22-4-2422-21-222-121-2-12-2-22-2-4241-1-111-1-22-2211-1-100023−230000000000−33−33000000000000000000000000000
χ764-4-44-24-24-42-4-22-4-2422-21-222-121-2-12-2-22-2-4241-1-111-1-22-2211-1-1000−232300000000003−33−3000000000000000000000000000
χ774-4-44-24-2-442-4-22-4-2422-21-222-121-2-12-22-224-2-41-1-11-112-22-2-1-1110000000000000003i−3i−3i3i000000000000000000000000000
χ784-4-44-24-2-442-4-22-4-2422-21-222-121-2-12-22-224-2-41-1-11-112-22-2-1-111000000000000000−3i3i3i−3i000000000000000000000000000
χ794-4-44-2-244-422422-2-2-4-41-2-2-1-122-2-22214-4-222-21-1-11-22-221-111-1-10000000−2i32i300000000000000i3−i3i3−i30000000000000000000
χ804-4-44-2-244-422422-2-2-4-41-2-2-1-122-2-22214-4-222-21-1-11-22-221-111-1-100000002i3−2i300000000000000−i3i3−i3i30000000000000000000
χ814-4-44-2-24-4422422-2-2-4-41-2-2-1-122-2-2221-442-2-221-1-112-22-2-11-1-111000000000−2i32i3000000000000i3i3−i3−i30000000000000000000
χ824-4-44-2-24-4422422-2-2-4-41-2-2-1-122-2-2221-442-2-221-1-112-22-2-11-1-1110000000002i3−2i3000000000000−i3−i3i3i30000000000000000000
χ838888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-4-4-4-1-1-1-1222222-1-1-1-10000000000000000000000000000000000000000000000
χ848888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444444-1-1-1-1-2-2-2-2-2-211110000000000000000000000000000000000000000000000
χ8588-8-88-4-400844-8-4-84-44-4-42-44-4-24-242400000022-2-200000000000000000000000000000000000000000000000000000000
χ8688-8-8-48-400-4-84484-8-44-42-4-4424-24-2-4400000022-2-200000000000000000000000000000000000000000000000000000000
χ8788-8-8-4-4800-44-84-4448-82-4-42-2-44444-4-200000022-2-200000000000000000000000000000000000000000000000000000000
χ8888-8-8-4-4-400-4444-444-442222-22-2-2-2-22-2000000-1-11100000033−3333−330000000000000000000000000000000000000000000000
χ8988-8-8-4-4-400-4444-444-442222-22-2-2-2-22-2000000-1-111000000−3333−33330000000000000000000000000000000000000000000000
χ908-88-88-4-400-8-4484-844-4-4-424-4424-2-4-240000002-22-200000000000000000000000000000000000000000000000000000000
χ918-88-8-48-400484-4-84-84-4-42-44-4-2-4-242440000002-22-200000000000000000000000000000000000000000000000000000000
χ928-88-8-4-48004-4-8-4444-882-4-4-224-444-44-20000002-22-200000000000000000000000000000000000000000000000000000000
χ938-88-8-4-4-4004-44-44444-4222-22-22-2-22-2-2000000-11-1100000033−33−33330000000000000000000000000000000000000000000000
χ948-88-8-4-4-4004-44-44444-4222-22-22-2-22-2-2000000-11-11000000−333333−330000000000000000000000000000000000000000000000
χ958-8-88-4-4-48-844-444-4-444222-2-2-2-222-2-22-44-444-4-111-12-22-22-2-1-1110000000000000000000000000000000000000000000000
χ968-8-88-4-4-4-8844-444-4-444222-2-2-2-222-2-224-44-4-44-111-1-22-22-2211-1-10000000000000000000000000000000000000000000000

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