Finite Group Databasebeta

← Group #13156658

Character table — Group #13156658

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size11112222222222222244444444444444444488888888888888181818181818181818181818242424242424242424242424242424242424242424242424242424363636363636363636363636216
order1222333446666666663336666666661212121212123666121212121212121212124444888888884441212121212121212121212121212121212121212121212121212121224242424242424244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1
χ3111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1111-1-111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-11-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11
χ511111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-111111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11
χ711111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ811111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1111111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1
χ92222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-222-2-20000000000000000000000000000000000022-2-2000000000
χ102222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22200000000000000000000000000000000000-2-222000000000
χ11222222-122222-1222-1-12-1-12-1-12-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-122220000000020222002200-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1000000000
χ12222222-122222-1222-1-12-1-12-1-12-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-1222200000000-20-2-2-200-2-2001111111111110000-1-1-1-1000000000
χ13222222-122222-1222-1-12-1-12-1-12-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-20000000020-2-2-2002200-1-111-1-1-1-1111100001111000000000
χ14222222-122222-1222-1-12-1-12-1-12-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-200000000-2022200-2-20011-1-11111-1-1-1-100001111000000000
χ15222222-1-2-2222-1222-1-12-1-12-1-12-1-12-1-1-2-211-2-2-1-1-1-1-2-21111111122-2-20000000000000000000−i3i3−i3i3−i3−i3i3i3−i3−i3i3i30000-1-111000000000
χ16222222-1-2-2222-1222-1-12-1-12-1-12-1-12-1-1-2-211-2-2-1-1-1-1-2-21111111122-2-20000000000000000000i3−i3i3−i3i3i3−i3−i3i3i3−i3−i30000-1-111000000000
χ17222222-1-2-2222-1222-1-12-1-12-1-12-1-12-1-1-2-211-2-2-1-1-1-1-2-211111111-2-2220000000000000000000−i3i3i3−i3−i3−i3i3i3i3i3−i3−i3000011-1-1000000000
χ18222222-1-2-2222-1222-1-12-1-12-1-12-1-12-1-1-2-211-2-2-1-1-1-1-2-211111111-2-2220000000000000000000i3−i3−i3i3i3i3−i3−i3−i3−i3i3i3000011-1-1000000000
χ1922222-122222-12-1-1222-12-1-12-1-12-1-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-1000000002222022-1-1-1-1002200220000-1-1-1-1-1-1-1-100000000-1-1-1-10
χ2022222-122222-12-1-1222-12-1-12-1-12-1-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-10000000022220-2-2111100-2-200-2-200001111111100000000-1-1-1-10
χ2122222-122222-12-1-1222-12-1-12-1-12-1-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-100000000-2-2-2-202-211-1-1002200-2-200001111-1-1-1-10000000011110
χ2222222-122222-12-1-1222-12-1-12-1-12-1-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-100000000-2-2-2-20-22-1-11100-2-200220000-1-1-1-111110000000011110
χ232222-12222-1-12222-122-1-12-1-12-1-12-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-10000222200002200022-1-1-1-12200-1-1-1-10000-1-1-1-10000-1-1-1-100000
χ242222-12222-1-12222-122-1-12-1-12-1-12-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-1000022220000-2-2000-2-21111-2-2001111000011110000-1-1-1-100000
χ252222-12222-1-12222-122-1-12-1-12-1-12-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-10000-2-2-2-200002-2000-2-2-1-1112200-1-1-1-1000011110000111100000
χ262222-12222-1-12222-122-1-12-1-12-1-12-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-10000-2-2-2-20000-220002211-1-1-2-20011110000-1-1-1-10000111100000
χ2722-2-22222-2-2222-2-2-2-2-2222-2-2-2222-2-2-22-22-2-222-2-222-22-22-222-2-20000000022-2-20000000000000000000000000000000000022-2-20
χ2822-2-22222-2-2222-2-2-2-2-2222-2-2-2222-2-2-22-22-2-222-2-222-22-22-222-2-200000000-2-22200000000000000000000000000000000000-2-2220
χ2922-2-2222-22-2222-2-2-2-2-2222-2-2-2222-2-2-2-22-222-22-2-22-22-22-22-2-222000022-2-20000000000000000000000000000000000022-2-200000
χ3022-2-2222-22-2222-2-2-2-2-2222-2-2-2222-2-2-2-22-222-22-2-22-22-22-22-2-2220000-2-22200000000000000000000000000000000000-2-22200000
χ3122-2-22-122-2-22-1211-2-2-2-12-11-21-12-11-21212-2-2-1-111-1-112-2-11-1-1110000000022-2-20003−33−30000000000003−33−333−3−300000000-1-1110
χ3222-2-22-122-2-22-1211-2-2-2-12-11-21-12-11-21212-2-2-1-111-1-112-2-11-1-1110000000022-2-2000−33−33000000000000−33−33−3−33300000000-1-1110
χ3322-2-22-122-2-22-1211-2-2-2-12-11-21-12-11-21212-2-2-1-111-1-112-2-11-1-11100000000-2-2220003−3−330000000000003−33−3−3−3330000000011-1-10
χ3422-2-22-122-2-22-1211-2-2-2-12-11-21-12-11-21212-2-2-1-111-1-112-2-11-1-11100000000-2-222000−333−3000000000000−33−3333−3−30000000011-1-10
χ3522-2-2-122-221-122-2-21-2-2-1-1211-2-1-1211-212-22-1-2-111-11-11-1-2211-1-1000022-2-2000000000003−33−300003−33−300003−33−30000-1-11100000
χ3622-2-2-122-221-122-2-21-2-2-1-1211-2-1-1211-212-22-1-2-111-11-11-1-2211-1-1000022-2-200000000000−33−330000−33−330000−33−330000-1-11100000
χ3722-2-2-122-221-122-2-21-2-2-1-1211-2-1-1211-212-22-1-2-111-11-11-1-2211-1-10000-2-222000000000003−3−3300003−33−30000−33−33000011-1-100000
χ3822-2-2-122-221-122-2-21-2-2-1-1211-2-1-1211-212-22-1-2-111-11-11-1-2211-1-10000-2-22200000000000−333−30000−33−3300003−33−3000011-1-100000
χ392-22-222200-2-2-2-22-222-2222-2-22-2-2-222-200000022-2-20000000000002i−2i2−22−2−i2i2−i2i2000000000000000000000000000002i−2i2−22−2−i2i2−i2i20
χ402-22-222200-2-2-2-22-222-2222-2-22-2-2-222-200000022-2-20000000000002i−2i−22−22i2−i2i2−i2000000000000000000000000000002i−2i−22−22i2−i2i2−i20
χ412-22-222200-2-2-2-22-222-2222-2-22-2-2-222-200000022-2-2000000000000−2i2i2−22−2i2−i2i2−i200000000000000000000000000000−2i2i2−22−2i2−i2i2−i20
χ422-22-222200-2-2-2-22-222-2222-2-22-2-2-222-200000022-2-2000000000000−2i2i−22−22−i2i2−i2i200000000000000000000000000000−2i2i−22−22−i2i2−i2i20
χ432-2-22222002-2-2-2-22-2-2222222-2-2-2-2-2-220000002-22-200000000002i−2i002−2−22−i2i2i2−i20000000000000000000000000002i−2i002−2−22−i2i2i2−i20
χ442-2-22222002-2-2-2-22-2-2222222-2-2-2-2-2-220000002-22-200000000002i−2i00−222−2i2−i2−i2i20000000000000000000000000002i−2i00−222−2i2−i2−i2i20
χ452-2-22222002-2-2-2-22-2-2222222-2-2-2-2-2-220000002-22-20000000000−2i2i002−2−22i2−i2−i2i2000000000000000000000000000−2i2i002−2−22i2−i2−i2i20
χ462-2-22222002-2-2-2-22-2-2222222-2-2-2-2-2-220000002-22-20000000000−2i2i00−222−2−i2i2i2−i2000000000000000000000000000−2i2i00−222−2−i2i2i2−i20
χ4744444-24-4-444-24-2-2444-24-2-24-2-24-2-24-2-42-4-4-42-2-2-2-222-4-42222220000000000000000000000000000000000000000000000000000
χ4844444-2-24444-2-2-2-24-2-2-2-21-2-21-2-21-2-214-2-2-24-21111-2-2-2-2111111000000000000004-2-200000000-2-20000111100000000000000000
χ4944444-2-24444-2-2-2-24-2-2-2-21-2-21-2-21-2-214-2-2-24-21111-2-2-2-211111100000000000000-42200000000220000-1-1-1-100000000000000000
χ5044444-2-2-4-444-2-2-2-24-2-2-2-21-2-21-2-21-2-21-4222-4211112222-1-1-1-1-1-10000000000000000000000000−2i32i30000i3i3−i3−i300000000000000000
χ5144444-2-2-4-444-2-2-2-24-2-2-2-21-2-21-2-21-2-21-4222-4211112222-1-1-1-1-1-100000000000000000000000002i3−2i30000−i3−i3i3i300000000000000000
χ524444-244-4-4-2-24444-244-2-24-2-24-2-24-2-242-4-4-42-4-2-2-2-22222-4-422220000000000000000000000000000000000000000000000000000
χ534444-24-244-2-24-244-2-2-2-21-2-21-2-21-2-21-2-24-2-2-241111-2-211-2-211110000000000004000000-2-200-2-2001111000000000000000000000
χ544444-24-244-2-24-244-2-2-2-21-2-21-2-21-2-21-2-24-2-2-241111-2-211-2-21111000000000000-400000022002200-1-1-1-1000000000000000000000
χ554444-24-2-4-4-2-24-244-2-2-2-21-2-21-2-21-2-21-22-4222-4111122-1-122-1-1-1-100000000000000000000000−2i32i300i3i3−i3−i3000000000000000000000
χ564444-24-2-4-4-2-24-244-2-2-2-21-2-21-2-21-2-21-22-4222-4111122-1-122-1-1-1-1000000000000000000000002i3−2i300−i3−i3i3i3000000000000000000000
χ574444-2-2444-2-2-24-2-2-2441-2-21-2-21-2-21-2-2-2-244-2-2111111-2-2-2-2111100000000000004000-2-200-2-200000000000011110000000000000
χ584444-2-2444-2-2-24-2-2-2441-2-21-2-21-2-21-2-2-2-244-2-2111111-2-2-2-211110000000000000-4000220022000000000000-1-1-1-10000000000000
χ594444-2-24-4-4-2-2-24-2-2-2441-2-21-2-21-2-21-2-222-4-4221111-1-12222-1-1-1-1000000000000000000000000000000000003-3-330000000000000
χ604444-2-24-4-4-2-2-24-2-2-2441-2-21-2-21-2-21-2-222-4-4221111-1-12222-1-1-1-100000000000000000000000000000000000-333-30000000000000
χ6144-4-444-24-4-444-2-4-4-4224-2-2-4224-2-2-4224-4-22-44-222-24-4-22-22-2-2220000000000000000000000000000000000000000000000000000
χ6244-4-444-2-44-444-2-4-4-4224-2-2-4224-2-2-422-442-24-4-222-2-442-22-222-2-20000000000000000000000000000000000000000000000000000
χ6344-4-44-24-44-44-2422-4-4-4-24-22-42-24-22-42-4-2-4442-222-22-2-442-222-2-20000000000000000000000000000000000000000000000000000
χ6444-4-44-2-24-4-44-2-222-422-2-2122-1-2-2122-142-22-4-21-1-11-22-221-111-1-100000000000000023−2300000000000000−33−3300000000000000000
χ6544-4-44-2-24-4-44-2-222-422-2-2122-1-2-2122-142-22-4-21-1-11-22-221-111-1-1000000000000000−2323000000000000003−33−300000000000000000
χ6644-4-44-2-2-44-44-2-222-422-2-2122-1-2-2122-1-4-22-2421-1-112-22-2-11-1-11100000000000000000000000000000003i−3i−3i3i00000000000000000
χ6744-4-44-2-2-44-44-2-222-422-2-2122-1-2-2122-1-4-22-2421-1-112-22-2-11-1-1110000000000000000000000000000000−3i3i3i−3i00000000000000000
χ6844-4-4-2444-42-244-4-42-4-4-2-2422-4-2-2422-4-2-44-424-222-2-22-224-4-2-2220000000000000000000000000000000000000000000000000000
χ6944-4-4-24-24-42-24-2-4-4222-21-22-12-21-22-12-2-4-22241-1-11-221-1-2211-1-10000000000000000000000000003i−3i−3i3i000000000000000000000
χ7044-4-4-24-24-42-24-2-4-4222-21-22-12-21-22-12-2-4-22241-1-11-221-1-2211-1-1000000000000000000000000000−3i3i3i−3i000000000000000000000
χ7144-4-4-24-2-442-24-2-4-4222-21-22-12-21-22-12242-2-2-41-1-112-2-112-2-1-111000000000000000000023−23000000−33−33000000000000000000000
χ7244-4-4-24-2-442-24-2-4-4222-21-22-12-21-22-12242-2-2-41-1-112-2-112-2-1-1110000000000000000000−23230000003−33−3000000000000000000000
χ7344-4-4-2-244-42-2-24222-4-41-2-2-1221-2-2-122-224-42-21-1-111-1-22-2211-1-10000000000000000023−230000000000000000−3−3330000000000000
χ7444-4-4-2-244-42-2-24222-4-41-2-2-1221-2-2-122-224-42-21-1-111-1-22-2211-1-100000000000000000−2323000000000000000033−3−30000000000000
χ7544-4-4-2-24-442-2-24222-4-41-2-2-1221-2-2-1222-2-44-221-1-11-112-22-2-1-11100000000000000000000023−23000000000000−33−330000000000000
χ7644-4-4-2-24-442-2-24222-4-41-2-2-1221-2-2-1222-2-44-221-1-11-112-22-2-1-111000000000000000000000−23230000000000003−33−30000000000000
χ774-44-444-200-4-4-424-44-224-2-2-42-2-4224-22000000-2-2220000000000004i−4i0000000000000000000000000000000000000−2i2i000000000
χ784-44-444-200-4-4-424-44-224-2-2-42-2-4224-22000000-2-222000000000000−4i4i00000000000000000000000000000000000002i−2i000000000
χ794-44-44-2400-4-42-4-2244-4-24-22-4-22-42-242000000-2-222000000000000000000−2i22i2−2i22i200000000000000000000000000000000000i2−i2i2−i20
χ804-44-44-2400-4-42-4-2244-4-24-22-4-22-42-242000000-2-2220000000000000000002i2−2i22i2−2i200000000000000000000000000000000000−i2i2−i2i20
χ814-44-4-2440022-4-44-4-24-4-2-2422422-4-2-2-4000000-2-2220000000000000022−2222−2200000000000000000000000000000000000−22−2200000
χ824-44-4-2440022-4-44-4-24-4-2-2422422-4-2-2-4000000-2-22200000000000000−2222−2222000000000000000000000000000000000002−22−200000
χ834-4-4444-2004-4-42-44-42-24-2-24-22-422-42-2000000-22-2200000000004i−4i0000000000000000000000000000000000000−2i2i00000000000
χ844-4-4444-2004-4-42-44-42-24-2-24-22-422-42-2000000-22-220000000000−4i4i00000000000000000000000000000000000002i−2i00000000000
χ854-4-444-24004-42-42-2-4-44-24-2-2422-422-4-2000000-22-22000000000000000000−2i22i22i2−2i200000000000000000000000000000000000i2−i2−i2i20
χ864-4-444-24004-42-42-2-4-44-24-2-2422-422-4-2000000-22-220000000000000000002i2−2i2−2i22i200000000000000000000000000000000000−i2i2i2−i20
χ874-4-44-24400-22-4-4-442-44-2-24-2-2-422-4224000000-22-220000000000000022−22−222200000000000000000000000000000000000−222−200000
χ884-4-44-24400-22-4-4-442-44-2-24-2-2-422-4224000000-22-2200000000000000−222222−22000000000000000000000000000000000002−2−2200000
χ898888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-4-4-4-1-1-1-1222222-1-1-1-10000000000000000000000000000000000000000000000000000
χ908888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444444-1-1-1-1-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000
χ9188-8-8-4-4-48-84-4-4-444444222-2-2-2222-2-2-2-44-444-4-111-12-22-22-2-1-1110000000000000000000000000000000000000000000000000000
χ9288-8-8-4-4-4-884-4-4-444444222-2-2-2222-2-2-24-44-4-44-111-1-22-22-2211-1-10000000000000000000000000000000000000000000000000000
χ938-88-88-4-400-8-844-448-44-4-4244244-2-4-4-200000022-2-200000000000000000000000000000000000000000000000000000000000000
χ948-88-8-48-40044-848-8-4-44-42-44-2-44-24-42400000022-2-200000000000000000000000000000000000000000000000000000000000000
χ958-88-8-4-4800444-8-44-48-82-4-4-24-4-2442-4400000022-2-200000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-4-4004444-44-4-44222-2-22-2-2-222-2000000-1-11100000033−3333−330000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-4004444-44-4-44222-2-22-2-2-222-2000000-1-111000000−3333−33330000000000000000000000000000000000000000000000000000
χ988-8-888-4-4008-8444-4-84-4-4-42-4-4-244-24420000002-22-200000000000000000000000000000000000000000000000000000000000000
χ998-8-88-48-400-44-84-8844-4-42-4-4244-244-2-40000002-22-200000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-4800-444-84-44-882-4-42-44-244-24-40000002-22-200000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-400-44444-444-422222-2-2-2-2-2-22000000-11-1100000033−33−33330000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-400-44444-444-422222-2-2-2-2-2-22000000-11-11000000−333333−330000000000000000000000000000000000000000000000000000

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