Finite Group Databasebeta

← Group #13162027

Character table — Group #13162027

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size112222222222244444444444444444444444444444444448888888888888888888888888888888888363636363636363636363636363636363636727272727272727272
order12233344666663333344666666666666666661212121212121212121212121212121212121212121212121212121212121212121212121212121212121212224444666612121212121212122668824242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111-1-1111111111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1111111-1-1-1-1-11-111-1-1
χ6111111111111111111-1-1111111111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-111-1-1-1-1-1-111-1-1111-11-1-111
χ7111111111111111111-1-1111111111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1111111-1-111-1-1-1-11-1-111
χ8111111111111111111-1-1111111111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-1-1-1-1-1111111-111-1-1
χ9222222-2-222222222222-222222222222222222-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2000000000000000000000000000
χ10222222-2-22222222222-2222222222222222222-2-2-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222000000000000000000000000000
χ1122222-1222222-12-1-1-1-1222-122-1-1-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1222200-1-1-1-10000-1-1-1-1000000000
χ1222222-1222222-12-1-1-1-1222-122-1-1-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-200111100001111000000000
χ1322222-1222222-12-1-1-1-1-2-22-122-1-1-1-1-1-1-1-12-1-1-1-122-1-1111122-2-2-2-222-1-1-1-1-1-1-1-1-2-211111111-2-2111111112-22-200-1-1110000-1-111000000000
χ1422222-1222222-12-1-1-1-1-2-22-122-1-1-1-1-1-1-1-12-1-1-1-122-1-1111122-2-2-2-222-1-1-1-1-1-1-1-1-2-211111111-2-211111111-22-220011-1-1000011-1-1000000000
χ1522222-1-2-22222-12-1-1-1-12-22-122-1-1-1-1-1-1-1-12-1-1-1-1-2-211-1-111-2-222-2-2-2-21111111122-1-1-1-1-1-1-1-1-2-211111111000000−i3i3−i3i30000−i3i3−i3i3000000000
χ1622222-1-2-22222-12-1-1-1-12-22-122-1-1-1-1-1-1-1-12-1-1-1-1-2-211-1-111-2-222-2-2-2-21111111122-1-1-1-1-1-1-1-1-2-211111111000000i3−i3i3−i30000i3−i3i3−i3000000000
χ1722222-1-2-22222-12-1-1-1-1-222-122-1-1-1-1-1-1-1-12-1-1-1-1-2-21111-1-1-2-2-2-222-2-211111111-2-21111111122-1-1-1-1-1-1-1-1000000−i3i3i3−i30000−i3i3i3−i3000000000
χ1822222-1-2-22222-12-1-1-1-1-222-122-1-1-1-1-1-1-1-12-1-1-1-1-2-21111-1-1-2-2-2-222-2-211111111-2-21111111122-1-1-1-1-1-1-1-1000000i3−i3−i3i30000i3−i3−i3i3000000000
χ192222-12222-1-1-12-12-1-1-12222-1-122-1-1-1-1-1-1-12-1-1-1-1-1222222222-12-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-10000220000-1-1-1-100002-1-1000000
χ202222-12222-1-1-12-12-1-1-12222-1-122-1-1-1-1-1-1-12-1-1-1-1-1222222222-12-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-10000-2-2000011110000-211000000
χ212222-12222-1-1-12-12-1-1-1-2-222-1-122-1-1-1-1-1-1-12-1-1-1-1-122-2-2-2-222-21-21-1-122-1-1-1-1-1-111-2-211111111-2-21111110000220000-1-1-1-10000-211000000
χ222222-12222-1-1-12-12-1-1-1-2-222-1-122-1-1-1-1-1-1-12-1-1-1-1-122-2-2-2-222-21-21-1-122-1-1-1-1-1-111-2-211111111-2-21111110000-2-20000111100002-1-1000000
χ232222-12-2-22-1-1-12-12-1-1-12-222-1-122-1-1-1-1-1-1-12-1-1-111-2-222-2-2-2-22-1-2111-2-2111111-1-122-1-1-1-1-1-111-2-21111110000000000−i3−i3i3i300000−i3i3000000
χ242222-12-2-22-1-1-12-12-1-1-12-222-1-122-1-1-1-1-1-1-12-1-1-111-2-222-2-2-2-22-1-2111-2-2111111-1-122-1-1-1-1-1-111-2-21111110000000000i3i3−i3−i300000i3−i3000000
χ252222-12-2-22-1-1-12-12-1-1-1-2222-1-122-1-1-1-1-1-1-12-1-1-111-2-2-2-222-2-2-212-111-2-211111111-2-2111111-1-122-1-1-1-1-1-10000000000−i3−i3i3i300000i3−i3000000
χ262222-12-2-22-1-1-12-12-1-1-1-2222-1-122-1-1-1-1-1-1-12-1-1-111-2-2-2-222-2-2-212-111-2-211111111-2-2111111-1-122-1-1-1-1-1-10000000000i3i3−i3−i300000−i3i3000000
χ27222-12222-12222-1-12-1-122-12-1-1-1-122-1-1-1-1-1-12-1-122222222-1-1-12-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100000000000000000000022-1-1-1-1
χ28222-12222-12222-1-12-1-122-12-1-1-1-122-1-1-1-1-1-12-1-122222222-1-1-12-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1000000000000000000000-2-21111
χ29222-12222-12222-1-12-1-1-2-2-12-1-1-1-122-1-1-1-1-1-12-1-12222-2-2-2-2-1-11-21-2-1-1-1-122-1-1-1-11111-2-211111111-2-211110000000000000000000002-2-1-111
χ30222-12222-12222-1-12-1-1-2-2-12-1-1-1-122-1-1-1-1-1-12-1-12222-2-2-2-2-1-11-21-2-1-1-1-122-1-1-1-11111-2-211111111-2-21111000000000000000000000-2211-1-1
χ31222-122-2-2-12222-1-12-1-12-2-12-1-1-1-122-1-1-1-1-1-12-1-1-2-2-2-222-2-211-121-21111-2-21111-1-1-1-122-1-1-1-11111-2-21111000000000000000000000003−33−3
χ32222-122-2-2-12222-1-12-1-12-2-12-1-1-1-122-1-1-1-1-1-12-1-1-2-2-2-222-2-211-121-21111-2-21111-1-1-1-122-1-1-1-11111-2-2111100000000000000000000000−33−33
χ33222-122-2-2-12222-1-12-1-1-22-12-1-1-1-122-1-1-1-1-1-12-1-1-2-2-2-2-2-222111-2-121111-2-211111111-2-21111-1-1-1-122-1-1-1-1000000000000000000000003−3−33
χ34222-122-2-2-12222-1-12-1-1-22-12-1-1-1-122-1-1-1-1-1-12-1-1-2-2-2-2-2-222111-2-121111-2-211111111-2-21111-1-1-1-122-1-1-1-100000000000000000000000−333−3
χ3522-22222-222-2-222222200-2-2-2-2-2-2-2-2-2-2-2-2222222-22-200002-200002-22-22-222-2-200000000000000000000020-2000022000000-2-2000000000
χ3622-22222-222-2-222222200-2-2-2-2-2-2-2-2-2-2-2-2222222-22-200002-200002-22-22-222-2-2000000000000000000000-2020000-2-200000022000000000
χ3722-2222-2222-2-222222200-2-2-2-2-2-2-2-2-2-2-2-222222-22-220000-220000-22-22-22-2-2220000000000000000000020-200022000000-2-200000000000
χ3822-2222-2222-2-222222200-2-2-2-2-2-2-2-2-2-2-2-222222-22-220000-220000-22-22-22-2-22200000000000000000000-202000-2-20000002200000000000
χ3922-222-12-222-2-2-12-1-1-1-100-21-2-2111111112-1-1-1-12-2-11−i3i3−i3i32-200002-2-11-11-1-11100−i3i3−i3i3−i3−i3i3i300−i3i3−i3i3−i3−i3i3i3020-200−i3i3-1-10000i3−i311000000000
χ4022-222-12-222-2-2-12-1-1-1-100-21-2-2111111112-1-1-1-12-2-11−i3i3−i3i32-200002-2-11-11-1-11100−i3i3−i3i3−i3−i3i3i300−i3i3−i3i3−i3−i3i3i30-20200i3−i3110000−i3i3-1-1000000000
χ4122-222-12-222-2-2-12-1-1-1-100-21-2-2111111112-1-1-1-12-2-11i3−i3i3−i32-200002-2-11-11-1-11100i3−i3i3−i3i3i3−i3−i300i3−i3i3−i3i3i3−i3−i3020-200i3−i3-1-10000−i3i311000000000
χ4222-222-12-222-2-2-12-1-1-1-100-21-2-2111111112-1-1-1-12-2-11i3−i3i3−i32-200002-2-11-11-1-11100i3−i3i3−i3i3i3−i3−i300i3−i3i3−i3i3i3−i3−i30-20200−i3i3110000i3−i3-1-1000000000
χ4322-222-1-2222-2-2-12-1-1-1-100-21-2-2111111112-1-1-1-1-221-1−i3i3i3−i3-220000-221-11-111-1-100−i3i3−i3i3−i3−i3i3i300i3−i3i3−i3i3i3−i3−i320-2000-1-1−i3i3000011i3−i3000000000
χ4422-222-1-2222-2-2-12-1-1-1-100-21-2-2111111112-1-1-1-1-221-1−i3i3i3−i3-220000-221-11-111-1-100−i3i3−i3i3−i3−i3i3i300i3−i3i3−i3i3i3−i3−i3-20200011i3−i30000-1-1−i3i3000000000
χ4522-222-1-2222-2-2-12-1-1-1-100-21-2-2111111112-1-1-1-1-221-1i3−i3−i3i3-220000-221-11-111-1-100i3−i3i3−i3i3i3−i3−i300−i3i3−i3i3−i3−i3i3i320-2000-1-1i3−i3000011−i3i3000000000
χ4622-222-1-2222-2-2-12-1-1-1-100-21-2-2111111112-1-1-1-1-221-1i3−i3−i3i3-220000-221-11-111-1-100i3−i3i3−i3i3i3−i3−i300−i3i3−i3i3−i3−i3i3i3-20200011−i3i30000-1-1i3−i3000000000
χ474444-2-2444-2-2-2-2-2-2111444-2-2-2-2-2111111-2-2111-2-2-2-2-2-2-2-2444-24-2-2-2-2-2111111-2-2-2-2111111-2-2-2-2111111000000000000000000000000000
χ484444-2-2444-2-2-2-2-2-2111-4-44-2-2-2-2-2111111-2-2111-2-2-2-2222244-42-42-2-2-2-21111112222-1-1-1-1-1-12222-1-1-1-1-1-1000000000000000000000000000
χ494444-2-2-4-44-2-2-2-2-2-21114-44-2-2-2-2-2111111-2-21112222-2-222-4-44-2-422222-1-1-1-1-1-1-2-2-2-21111112222-1-1-1-1-1-1000000000000000000000000000
χ504444-2-2-4-44-2-2-2-2-2-2111-444-2-2-2-2-2111111-2-2111222222-2-2-4-4-424-22222-1-1-1-1-1-12222-1-1-1-1-1-1-2-2-2-2111111000000000000000000000000000
χ51444-24-244-2444-2-21-21144-2-2-2-211-2-21111-21-21144-2-2-2-2-2-2-2-2-24-24-2-211-2-21111-2-211-2-21111-2-211-2-21111000000000000000000000000000
χ52444-24-244-2444-2-21-211-4-4-2-2-2-211-2-21111-21-21144-2-22222-2-22-42-4-2-211-2-2111122-1-122-1-1-1-122-1-122-1-1-1-1000000000000000000000000000
χ53444-24-2-4-4-2444-2-21-2114-4-2-2-2-211-2-21111-21-211-4-422-2-22222-242-422-1-122-1-1-1-1-2-211-2-2111122-1-122-1-1-1-1000000000000000000000000000
χ54444-24-2-4-4-2444-2-21-211-44-2-2-2-211-2-21111-21-211-4-42222-2-2222-4-2422-1-122-1-1-1-122-1-122-1-1-1-1-2-211-2-21111000000000000000000000000000
χ55444-2-2444-2-2-2-241-2-21144-2411-2-2-2-211111-2-211-2-2444444-2-2-2-2-2-211-2-2-2-2111111-2-2-2-2111111-2-2-2-21111000000000000000000000000000
χ56444-2-2444-2-2-2-241-2-211-4-4-2411-2-2-2-211111-2-211-2-244-4-4-4-4-2-2222211-2-2-2-21111-1-12222-1-1-1-1-1-12222-1-1-1-1000000000000000000000000000
χ57444-2-24-4-4-2-2-2-241-2-2114-4-2411-2-2-2-211111-2-21122-4-444-4-422-2-222-1-12222-1-1-1-111-2-2-2-21111-1-12222-1-1-1-1000000000000000000000000000
χ58444-2-24-4-4-2-2-2-241-2-211-44-2411-2-2-2-211111-2-21122-4-4-4-4442222-2-2-1-12222-1-1-1-1-1-12222-1-1-1-111-2-2-2-21111000000000000000000000000000
χ59444-2-2-244-2-2-2-2-2111−1−3i32−1+3i3244-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i32-2-2-2-2-2-2-2-2-2-2-2-2-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i32000000000000000000000000000
χ60444-2-2-244-2-2-2-2-2111−1−3i32−1+3i32-4-4-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i32-2-2-2-22222-2-22222111111−1−3i32−1+3i32−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000000000000000000000000
χ61444-2-2-244-2-2-2-2-2111−1+3i32−1−3i3244-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111−1+3i32−1−3i32-2-2-2-2-2-2-2-2-2-2-2-2-2-2111111−1+3i32−1−3i32−1+3i32−1−3i32111111−1+3i32−1−3i32−1+3i32−1−3i32111111−1+3i32−1−3i32−1+3i32−1−3i32000000000000000000000000000
χ62444-2-2-244-2-2-2-2-2111−1+3i32−1−3i32-4-4-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111−1+3i32−1−3i32-2-2-2-22222-2-22222111111−1+3i32−1−3i32−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32000000000000000000000000000
χ63444-2-2-2-4-4-2-2-2-2-2111−1−3i32−1+3i324-4-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i322222-2-22222-2-222-1-1-1-1-1-11+3i321−3i321+3i321−3i32111111−1−3i32−1+3i32−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000000000000000000000000
χ64444-2-2-2-4-4-2-2-2-2-2111−1−3i32−1+3i32-44-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i32222222-2-22222-2-2-1-1-1-1-1-11+3i321−3i321+3i321−3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32111111−1−3i32−1+3i32−1−3i32−1+3i32000000000000000000000000000
χ65444-2-2-2-4-4-2-2-2-2-2111−1+3i32−1−3i324-4-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111−1+3i32−1−3i322222-2-22222-2-222-1-1-1-1-1-11−3i321+3i321−3i321+3i32111111−1+3i32−1−3i32−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32000000000000000000000000000
χ66444-2-2-2-4-4-2-2-2-2-2111−1+3i32−1−3i32-44-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111−1+3i32−1−3i32222222-2-22222-2-2-1-1-1-1-1-11−3i321+3i321−3i321+3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32111111−1+3i32−1−3i32−1+3i32−1−3i32000000000000000000000000000
χ6744-44-244-44-2224-24-2-2-200-4-422-4-4222222-24-2-2-2-224-400004-40000-224-4-22-2-22200000000000000000000000000000000000000000000000
χ6844-44-24-444-2224-24-2-2-200-4-422-4-4222222-24-2-2-22-2-440000-4400002-2-442-222-2-200000000000000000000000000000000000000000000000
χ6944-44-2-24-44-222-2-2-211100-422222-1-1-1-1-1-1-2-2111-22-22−2i32i3−2i32i34-40000-22-221-111-1-100−2i32i3i3−i3i3i3−i3−i300−2i32i3i3−i3i3i3−i3−i3000000000000000000000000000
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χ1088-80-4-4-400444i3−4i34222−1+3i3−1−3i30000−2i32i36-6−2i32i3−3+i33−i33+i3−3−i3-2-2-21−3i31+3i300000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.