Finite Group Databasebeta

← Group #13156373

Character table — Group #13156373

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size111122222222222222444444444444444444888888888888881212181824242424242424242424242424242424242424242424242424243636363636363636363636363636363636108108
order1222333446666666663336666666661212121212123666121212121212121212124444441212121212121212121212121212121212121212121212124888812121212242424242424242444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-111
χ31111111111111111111111111111111111111111111111111111-1-11-111-1-1111111-1-11111-1-1-1-11111-111-1-1-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-11-1-1111111-1-111-1-1-1-111111111-1-1-111-1-1-1-1-1-1-1-11111-1-1
χ511111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1
χ711111111111111111111111111111111111111111111111111-1-1-1-11-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ811111111111111111111111111111111111111111111111111-1-1-1-1-11-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111
χ92222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2002200000000000000000000000000-2000022-2-20000000000
χ102222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-200-2-20000000000000000000000000020000-2-2220000000000
χ11222222-12222-12222-1-12-1-122-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-100222222220000-1-1-1-1-1-1-1-1-1-1-1-1000020000-1-1-1-10000000000
χ12222222-12222-12222-1-12-1-122-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-10022-2-2-2-2-2-20000111111111111000020000-1-1-1-10000000000
χ13222222-12222-12222-1-12-1-122-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-100-2-22-222-2-20000-1-111-1-1-1-111110000-2000011110000000000
χ14222222-12222-12222-1-12-1-122-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-100-2-2-22-2-222000011-1-11111-1-1-1-10000-2000011110000000000
χ15222222-1-2-222-12222-1-12-1-122-1-1-1-1-1-1211-2-2-2-2-1-1-1-11111-2-2111100220000000000−i3i3−i3i3−i3−i3i3i3−i3−i3i3i30000-20000-1-1110000000000
χ16222222-1-2-222-12222-1-12-1-122-1-1-1-1-1-1211-2-2-2-2-1-1-1-11111-2-2111100220000000000i3−i3i3−i3i3i3−i3−i3i3i3−i3−i30000-20000-1-1110000000000
χ17222222-1-2-222-12222-1-12-1-122-1-1-1-1-1-1211-2-2-2-2-1-1-1-11111-2-2111100-2-20000000000−i3i3i3−i3−i3−i3i3i3i3i3−i3−i300002000011-1-10000000000
χ18222222-1-2-222-12222-1-12-1-122-1-1-1-1-1-1211-2-2-2-2-1-1-1-11111-2-2111100-2-20000000000i3−i3−i3i3i3i3−i3−i3−i3−i3i3i300002000011-1-10000000000
χ1922222-12222-122-12-122-12-1-1-12-12-12-1-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-122000200-1-122-1-100220000-1-1-1-1-1-1-1-10002200000000-1-1-1-100
χ2022222-12222-122-12-122-12-1-1-12-12-12-1-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-122000-2001122-1-100-2-200001111-1-1-1-1000-2-200000000111100
χ2122222-12222-122-12-122-12-1-1-12-12-12-1-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2000200-1-1-2-21100220000-1-1-1-11111000-2-200000000111100
χ2222222-12222-122-12-122-12-1-1-12-12-12-1-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2000-20011-2-21100-2-20000111111110002200000000-1-1-1-100
χ232222-12222-122-12-1222-1-12-1-1-12-12-12-122-12-12-1-1-1-1-1-122-1-1-1-1-1-1220020-1-100-1-1222200-1-1-1-10000-1-1-1-1022000000-1-1-1-1000000
χ242222-12222-122-12-1222-1-12-1-1-12-12-12-122-12-12-1-1-1-1-1-122-1-1-1-1-1-12200-201100-1-122-2-20011110000-1-1-1-10-2-20000001111000000
χ252222-12222-122-12-1222-1-12-1-1-12-12-12-122-12-12-1-1-1-1-1-122-1-1-1-1-1-1-2-20020-1-10011-2-22200-1-1-1-1000011110-2-20000001111000000
χ262222-12222-122-12-1222-1-12-1-1-12-12-12-122-12-12-1-1-1-1-1-122-1-1-1-1-1-1-2-200-20110011-2-2-2-200111100001111022000000-1-1-1-1000000
χ2722-2-22222-2-2-22-2-222-2-2222-2-2-2-222-2-222-222-2-22-2-222-22-22-222-2-22-2000000002-22-200000000000022-2-20000000000000000000
χ2822-2-22222-2-2-22-2-222-2-2222-2-2-2-222-2-222-222-2-22-2-222-22-22-222-2-2-2200000000-22-22000000000000-2-2220000000000000000000
χ2922-2-2222-22-2-22-2-222-2-2222-2-2-2-222-2-22-22-2-2222-2-22-22-22-22-2-222000000000000000000000000000000000000000000000002i−2i
χ3022-2-2222-22-2-22-2-222-2-2222-2-2-2-222-2-22-22-2-2222-2-22-22-22-22-2-22200000000000000000000000000000000000000000000000−2i2i
χ3122-2-22-122-2-212-212-1-2-2-12-111-212-1-21-12-22-1-21-111-12-2-11-11-1-1112-20000003−32-2-11000000003−33−3-1-111000000000000033−3−300
χ3222-2-22-122-2-212-212-1-2-2-12-111-212-1-21-12-22-1-21-111-12-2-11-11-1-1112-2000000−332-2-1100000000−33−33-1-1110000000000000−3−33300
χ3322-2-22-122-2-212-212-1-2-2-12-111-212-1-21-12-22-1-21-111-12-2-11-11-1-111-220000003−3-221-1000000003−33−311-1-10000000000000−3−33300
χ3422-2-22-122-2-212-212-1-2-2-12-111-212-1-21-12-22-1-21-111-12-2-11-11-1-111-22000000−33-221-100000000−33−3311-1-1000000000000033−3−300
χ3522-2-2-1222-21-221-2-12-2-2-1-12111-2-121-2-12-2-121-2-111-1-112-2-11-1-1112-200003−300-112-200003−33−30000-1-11100000000033−3−3000000
χ3622-2-2-1222-21-221-2-12-2-2-1-12111-2-121-2-12-2-121-2-111-1-112-2-11-1-1112-20000−3300-112-20000−33−330000-1-111000000000−3−333000000
χ3722-2-2-1222-21-221-2-12-2-2-1-12111-2-121-2-12-2-121-2-111-1-112-2-11-1-111-2200003−3001-1-2200003−33−3000011-1-1000000000−3−333000000
χ3822-2-2-1222-21-221-2-12-2-2-1-12111-2-121-2-12-2-121-2-111-1-112-2-11-1-111-220000−33001-1-220000−33−33000011-1-100000000033−3−3000000
χ392-2-22222002-2-2-22-2-22-22222-22-2-2-2-22-200000022-2-20000000000002i−2i0000000000000000000000000002−2−i2i22i−2i002−22−2−i2i2−i2i200
χ402-2-22222002-2-2-22-2-22-22222-22-2-2-2-22-200000022-2-20000000000002i−2i000000000000000000000000000−22i2−i22i−2i00−22−22i2−i2i2−i200
χ412-2-22222002-2-2-22-2-22-22222-22-2-2-2-22-200000022-2-2000000000000−2i2i0000000000000000000000000002−2i2−i2−2i2i002−22−2i2−i2i2−i200
χ422-2-22222002-2-2-22-2-22-22222-22-2-2-2-22-200000022-2-2000000000000−2i2i000000000000000000000000000−22−i2i2−2i2i00−22−22−i2i2−i2i200
χ4344444-24-4-44-244-24-244-24-2-2-24-24-24-2-2-4-4-42-42-2-2-2-2-4-4222222220000000000000000000000000000000000000000000000000
χ4444444-2-2444-2-24-24-2-2-2-2-21-2-2-21-21-21-2-2-24-24-21111-2-211-2-2111100000400-2-2000000-2-20000111100000000000000000000000
χ4544444-2-2444-2-24-24-2-2-2-2-21-2-2-21-21-21-2-2-24-24-21111-2-211-2-2111100000-40022000000220000-1-1-1-100000000000000000000000
χ4644444-2-2-4-44-2-24-24-2-2-2-2-21-2-2-21-21-21-222-42-42111122-1-122-1-1-1-10000000000000000−2i32i30000i3i3−i3−i300000000000000000000000
χ4744444-2-2-4-44-2-24-24-2-2-2-2-21-2-2-21-21-21-222-42-42111122-1-122-1-1-1-100000000000000002i3−2i30000−i3−i3i3i300000000000000000000000
χ484444-244-4-4-244-24-2444-2-24-2-2-24-24-24-2-4-42-42-4-2-2-2-222-4-42222220000000000000000000000000000000000000000000000000
χ494444-24-244-24-2-24-24-2-2-21-2-2-21-21-21-2-2-2-2-24-24111111-2-2-2-21111000040-2-2000000-2-2001111000000000000000000000000000
χ504444-24-244-24-2-24-24-2-2-21-2-2-21-21-21-2-2-2-2-24-24111111-2-2-2-211110000-40220000002200-1-1-1-1000000000000000000000000000
χ514444-24-2-4-4-24-2-24-24-2-2-21-2-2-21-21-21-2-2222-42-41111-1-12222-1-1-1-100000000000000−2i32i300i3i3−i3−i3000000000000000000000000000
χ524444-24-2-4-4-24-2-24-24-2-2-21-2-2-21-21-21-2-2222-42-41111-1-12222-1-1-1-1000000000000002i3−2i300−i3−i3i3i3000000000000000000000000000
χ534444-2-2444-2-24-2-2-2-2441-2-211-2-2-2-2-2-2144-2-2-2-21111-2-2-2-21111114400000000-2-2-2-200000000000011110000000000000000000
χ544444-2-2444-2-24-2-2-2-2441-2-211-2-2-2-2-2-2144-2-2-2-21111-2-2-2-2111111-4-4000000002222000000000000-1-1-1-10000000000000000000
χ554444-2-24-4-4-2-24-2-2-2-2441-2-211-2-2-2-2-2-21-4-4222211112222-1-1-1-1-1-1000000000000000000000000003-33-30000000000000000000
χ564444-2-24-4-4-2-24-2-2-2-2441-2-211-2-2-2-2-2-21-4-4222211112222-1-1-1-1-1-100000000000000000000000000-33-330000000000000000000
χ5744-4-444-24-4-4-4-2-4-444224-2-2-4-422-2-2224-2244-4-4-222-2-22-224-4-2-2220000000000000000000000000000000000000000000000000
χ5844-4-444-2-44-4-4-2-4-444224-2-2-4-422-2-22242-2-4-444-222-22-22-2-4422-2-20000000000000000000000000000000000000000000000000
χ5944-4-44-24-44-424-424-2-4-4-24-222-424-2-42-2-44-424-2-222-2-442-22-222-2-20000000000000000000000000000000000000000000000000
χ6044-4-44-2-24-4-42-2-424-222-2-21222-1-212-1-2-224-2-421-1-11-221-1-2211-1-10000000023−23000000000000−33−3300000000000000000000000
χ6144-4-44-2-24-4-42-2-424-222-2-21222-1-212-1-2-224-2-421-1-11-221-1-2211-1-100000000−23230000000000003−33−300000000000000000000000
χ6244-4-44-2-2-44-42-2-424-222-2-21222-1-212-1-22-2-424-21-1-112-2-112-2-1-11100000000000000000000003i−3i−3i3i00000000000000000000000
χ6344-4-44-2-2-44-42-2-424-222-2-21222-1-212-1-22-2-424-21-1-112-2-112-2-1-1110000000000000000000000−3i3i3i−3i00000000000000000000000
χ6444-4-4-244-442-442-4-24-4-4-2-24222-4-242-4-2-442-4-24-222-22-2-442-222-2-20000000000000000000000000000000000000000000000000
χ6544-4-4-24-24-42-4-22-4-2422-21-222-121-2-12-2-22-242-41-1-111-1-22-2211-1-100000023−230000000000−33−33000000000000000000000000000
χ6644-4-4-24-24-42-4-22-4-2422-21-222-121-2-12-2-22-242-41-1-111-1-22-2211-1-1000000−232300000000003−33−3000000000000000000000000000
χ6744-4-4-24-2-442-4-22-4-2422-21-222-121-2-12-22-22-4-241-1-11-112-22-2-1-1110000000000000000003i−3i−3i3i000000000000000000000000000
χ6844-4-4-24-2-442-4-22-4-2422-21-222-121-2-12-22-22-4-241-1-11-112-22-2-1-111000000000000000000−3i3i3i−3i000000000000000000000000000
χ6944-4-4-2-244-422422-2-2-4-41-2-2-1-122-2-22214-4-2-2221-1-11-22-221-111-1-14-400000000-22-2200000000000011-1-10000000000000000000
χ7044-4-4-2-244-422422-2-2-4-41-2-2-1-122-2-22214-4-2-2221-1-11-22-221-111-1-1-44000000002-22-2000000000000-1-1110000000000000000000
χ7144-4-4-2-24-4422422-2-2-4-41-2-2-1-122-2-2221-4422-2-21-1-112-22-2-11-1-111000000000000000000000000003-3-330000000000000000000
χ7244-4-4-2-24-4422422-2-2-4-41-2-2-1-122-2-2221-4422-2-21-1-112-22-2-11-1-11100000000000000000000000000-333-30000000000000000000
χ734-44-444400-44-44-4-4-4-44444-44-44-4-44-4-40000004-44-400000000000000000000000000000000000000000000000000000000000
χ744-44-444-200-4424-4-4-42-24-2-2-442-222-22-4000000-22-220000000000000000000000000000000000000000000000023−230000000000
χ754-44-444-200-4424-4-4-42-24-2-2-442-222-22-4000000-22-2200000000000000000000000000000000000000000000000−23230000000000
χ764-44-44-2400-4-2-442-42-44-24-22-2-4-2-42422000000-22-2200000000000000000000000000000000000000000000000000000i6−i6−i6i600
χ774-44-44-2400-4-2-442-42-44-24-22-2-4-2-42422000000-22-2200000000000000000000000000000000000000000000000000000−i6i6i6−i600
χ784-44-4-2440024-4-2-42-4-44-2-242-2242-4-2-42000000-22-2200000000000000000000000000000000000000000000000006−6−66000000
χ794-44-4-2440024-4-2-42-4-44-2-242-2242-4-2-42000000-22-220000000000000000000000000000000000000000000000000−666−6000000
χ804-4-4444-2004-42-44-4-4-224-2-24-4-22222-2-4000000-2-2220000000000004i−4i0000000000000000000000000000000−2i2i000000000000
χ814-4-4444-2004-42-44-4-4-224-2-24-4-22222-2-4000000-2-222000000000000−4i4i00000000000000000000000000000002i−2i000000000000
χ824-4-444-240042-4-4-2-424-4-24-2-2242-42-4-22000000-2-2220000000000000000000000000000000000000000000−2i22i200000000i2−i2i2−i200
χ834-4-444-240042-4-4-2-424-4-24-2-2242-42-4-22000000-2-22200000000000000000000000000000000000000000002i2−2i200000000−i2i2−i2i200
χ844-4-44-24400-2-4-4242-44-4-2-24-22-2-42-4242000000-2-2220000000000000000000000000000000000000000022−22000000−22−22000000
χ854-4-44-24400-2-4-4242-44-4-2-24-22-2-42-4242000000-2-22200000000000000000000000000000000000000000−22220000002−22−2000000
χ868888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-4-4-4-1-1-1-1222222-1-1-1-10000000000000000000000000000000000000000000000000
χ878888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444444-1-1-1-1-2-2-2-2-2-211110000000000000000000000000000000000000000000000000
χ8888-8-8-4-4-48-844-444-4-444222-2-2-2-222-2-22-44-4-444-111-12-22-22-2-1-1110000000000000000000000000000000000000000000000000
χ8988-8-8-4-4-4-8844-444-4-444222-2-2-2-222-2-224-444-4-4-111-1-22-22-2211-1-10000000000000000000000000000000000000000000000000
χ908-88-88-4-400-8-4484-844-4-4-424-4424-2-4-240000002-22-200000000000000000000000000000000000000000000000000000000000
χ918-88-8-48-400484-4-84-84-4-42-44-4-2-4-242440000002-22-200000000000000000000000000000000000000000000000000000000000
χ928-88-8-4-48004-4-8-4444-882-4-4-224-444-44-20000002-22-200000000000000000000000000000000000000000000000000000000000
χ938-88-8-4-4-4004-44-44444-4222-22-22-2-22-2-2000000-11-1100000033−3333−330000000000000000000000000000000000000000000000000
χ948-88-8-4-4-4004-44-44444-4222-22-22-2-22-2-2000000-11-11000000−3333−33330000000000000000000000000000000000000000000000000
χ958-8-888-4-400844-8-4-84-44-4-42-44-4-24-242400000022-2-200000000000000000000000000000000000000000000000000000000000
χ968-8-88-48-400-4-84484-8-44-42-4-4424-24-2-4400000022-2-200000000000000000000000000000000000000000000000000000000000
χ978-8-88-4-4800-44-84-4448-82-4-42-2-44444-4-200000022-2-200000000000000000000000000000000000000000000000000000000000
χ988-8-88-4-4-400-4444-444-442222-22-2-2-2-22-2000000-1-11100000033−33−33330000000000000000000000000000000000000000000000000
χ998-8-88-4-4-400-4444-444-442222-22-2-2-2-22-2000000-1-111000000−333333−330000000000000000000000000000000000000000000000000

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