Finite Group Databasebeta

← Group #13161761

Character table — Group #13161761

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size112222222222244444444444444444444444444444444448888888888888888888888888888888888181818181818363636363636363636727272727272727272727272
order122333446661212333336666666688121212121212121212121212121212242424246666612121212122424242424242424242424242424242424242424242424248824242424246681212242444881212121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ511111111111111111111111111-1-1111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-1-11111-1-11111-1-1-1-1
χ611111111111111111111111111-1-1111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-1-111-1-111-1-1-1-11111
χ711111111111111111111111111-1-1111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-11-1-1111-1-1-1-111
χ811111111111111111111111111-1-1111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-111-1-1-11111-1-1
χ9222222-2-2222-2-222222222222222i−2i-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22i2i−2i−2i22222-2-2-2-2-22i2i2i2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i000000000000000000000000000
χ10222222-2-2222-2-22222222222222−2i2i-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2−2i−2i2i2i22222-2-2-2-2-2−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i2i2i2i2i000000000000000000000000000
χ1122222-122-122-1-12-1-1-1-122-12-1-1-1-122-12222-1-1-1-1-1-1-1-122-1-1-1-12-1-1-1-12-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-122-1-12-1-1-1-1000000000000
χ1222222-122-122-1-12-1-1-1-122-12-1-1-1-122-12222-1-1-1-1-1-1-1-122-1-1-1-12-1-1-1-12-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-21111-2-211-21111000000000000
χ1322222-122-122-1-12-1-1-1-122-12-1-1-1-1-2-2-12222-1-1-1-1-1-1-1-12211112-1-1-1-12-1-1-1-1-2-2-2-211111111-2-2-2-21111111122-1-1-1-1-2-211211-1-1000000000000
χ1422222-122-122-1-12-1-1-1-122-12-1-1-1-1-2-2-12222-1-1-1-1-1-1-1-12211112-1-1-1-12-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2111122-1-1-2-1-111000000000000
χ1522222-1-2-2-122112-1-1-1-122-12-1-1-1-12i−2i1-2-2-2-211111111-2-2−i−iii2-1-1-1-1-211112i2i2i2i−i−i−i−i−i−i−i−i−2i−2i−2i−2iiiiiiiii0033−3−300−i3i30−i3i33−3000000000000
χ1622222-1-2-2-122112-1-1-1-122-12-1-1-1-12i−2i1-2-2-2-211111111-2-2−i−iii2-1-1-1-1-211112i2i2i2i−i−i−i−i−i−i−i−i−2i−2i−2i−2iiiiiiiii00−3−33300i3−i30i3−i3−33000000000000
χ1722222-1-2-2-122112-1-1-1-122-12-1-1-1-1−2i2i1-2-2-2-211111111-2-2ii−i−i2-1-1-1-1-21111−2i−2i−2i−2iiiiiiiii2i2i2i2i−i−i−i−i−i−i−i−i0033−3−300i3−i30i3−i33−3000000000000
χ1822222-1-2-2-122112-1-1-1-122-12-1-1-1-1−2i2i1-2-2-2-211111111-2-2ii−i−i2-1-1-1-1-21111−2i−2i−2i−2iiiiiiiii2i2i2i2i−i−i−i−i−i−i−i−i00−3−33300−i3i30−i3i3−33000000000000
χ192222-122222-122-12-1-1-12-12-12-1-1-12222-1-1-122-1-1-1-1-1-12-12222-12-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-12-1-1-122-1-1-1-1-1-1000000000000000020200-1-100-1-1
χ202222-122222-122-12-1-1-12-12-12-1-1-12222-1-1-122-1-1-1-1-1-12-12222-12-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-12-1-1-122-1-1-1-1-1-10000000000000000-20-200110011
χ212222-122222-122-12-1-1-12-12-12-1-1-1-2-222-1-1-122-1-1-1-1-1-12-1-2-2-2-2-12-1-1-1-12-1-1-1-2111-2-2111111-2111-2-2111111000000000000000020-200-1-10011
χ222222-122222-122-12-1-1-12-12-12-1-1-1-2-222-1-1-122-1-1-1-1-1-12-1-2-2-2-2-12-1-1-1-12-1-1-1-2111-2-2111111-2111-2-21111110000000000000000-202001100-1-1
χ232222-12-2-222-1-2-2-12-1-1-12-12-12-1-1-12i−2i-2-2111-2-2111111-212i2i−2i−2i-12-1-1-11-21112i−i−i−i2i2i−i−i−i−i−i−i−2iiii−2i−2iiiiiii000000000000000000000−i3i3003−3
χ242222-12-2-222-1-2-2-12-1-1-12-12-12-1-1-12i−2i-2-2111-2-2111111-212i2i−2i−2i-12-1-1-11-21112i−i−i−i2i2i−i−i−i−i−i−i−2iiii−2i−2iiiiiii000000000000000000000i3−i300−33
χ252222-12-2-222-1-2-2-12-1-1-12-12-12-1-1-1−2i2i-2-2111-2-2111111-21−2i−2i2i2i-12-1-1-11-2111−2iiii−2i−2iiiiiii2i−i−i−i2i2i−i−i−i−i−i−i000000000000000000000−i3i300−33
χ262222-12-2-222-1-2-2-12-1-1-12-12-12-1-1-1−2i2i-2-2111-2-2111111-21−2i−2i2i2i-12-1-1-11-2111−2iiii−2i−2iiiiiii2i−i−i−i2i2i−i−i−i−i−i−i000000000000000000000i3−i3003−3
χ27222-122222-1222-1-12-1-1-122-1-12-1-1222-12-1-1-1-122-1-1-1-1-122222-1-12-1-1-1-12-1-1-12-1-1-1-122-1-1-1-1-12-1-1-1-122-1-1-1-10000000000000002020-1-100-1-100
χ28222-122222-1222-1-12-1-1-122-1-12-1-1222-12-1-1-1-122-1-1-1-1-122222-1-12-1-1-1-12-1-1-12-1-1-1-122-1-1-1-1-12-1-1-1-122-1-1-1-1000000000000000-20-2011001100
χ29222-122222-1222-1-12-1-1-122-1-12-1-1-2-22-12-1-1-1-122-1-1-1-1-12-2-2-2-2-1-12-1-1-1-12-1-11-21111-2-211111-21111-2-2111100000000000000020-20-1-1001100
χ30222-122222-1222-1-12-1-1-122-1-12-1-1-2-22-12-1-1-1-122-1-1-1-1-12-2-2-2-2-1-12-1-1-1-12-1-11-21111-2-211111-21111-2-21111000000000000000-20201100-1-100
χ31222-122-2-22-12-2-2-1-12-1-1-122-1-12-1-12i−2i-21-21111-2-211111-22i2i−2i−2i-1-12-1-111-211−i2i−i−i−i−i2i2i−i−i−i−ii−2iiiii−2i−2iiiii0000000000000000000−i3i3003−300
χ32222-122-2-22-12-2-2-1-12-1-1-122-1-12-1-12i−2i-21-21111-2-211111-22i2i−2i−2i-1-12-1-111-211−i2i−i−i−i−i2i2i−i−i−i−ii−2iiiii−2i−2iiiii0000000000000000000i3−i300−3300
χ33222-122-2-22-12-2-2-1-12-1-1-122-1-12-1-1−2i2i-21-21111-2-211111-2−2i−2i2i2i-1-12-1-111-211i−2iiiii−2i−2iiiii−i2i−i−i−i−i2i2i−i−i−i−i0000000000000000000−i3i300−3300
χ34222-122-2-22-12-2-2-1-12-1-1-122-1-12-1-1−2i2i-21-21111-2-211111-2−2i−2i2i2i-1-12-1-111-211i−2iiiii−2i−2iiiii−i2i−i−i−i−i2i2i−i−i−i−i0000000000000000000i3−i3003−300
χ3522-22222-22222222222-2-2-22222200-2222222222222-2-20000-2-2-2-2-2-2-2-2-2-20000000000000000000000002222220000-200-2-2000000000000
χ3622-22222-22222222222-2-2-22222200-2222222222222-2-20000-2-2-2-2-2-2-2-2-2-2000000000000000000000000-2-2-2-2-2-2000020022000000000000
χ3722-2222-22222-2-222222-2-2-222222002-2-2-2-2-2-2-2-2-2-2-2-2220000-2-2-2-2-2222220000000000000000000000000000002-2220-2-200000000000000
χ3822-2222-22222-2-222222-2-2-222222002-2-2-2-2-2-2-2-2-2-2-2-2220000-2-2-2-2-222222000000000000000000000000000000-22-2-202200000000000000
χ3922-222-12-2-122-1-12-1-1-1-1-2-212-1-1-1-10012222-1-1-1-1-1-1-1-1-2-2−i3i3−i3i3-21111-211110000−i3i3−i3i3−i3−i3i3i30000−i3i3−i3i3−i3−i3i3i322-1-1-1-100−i3i3-2i3−i311000000000000
χ4022-222-12-2-122-1-12-1-1-1-1-2-212-1-1-1-10012222-1-1-1-1-1-1-1-1-2-2−i3i3−i3i3-21111-211110000−i3i3−i3i3−i3−i3i3i30000−i3i3−i3i3−i3−i3i3i3-2-2111100i3−i32−i3i3-1-1000000000000
χ4122-222-12-2-122-1-12-1-1-1-1-2-212-1-1-1-10012222-1-1-1-1-1-1-1-1-2-2i3−i3i3−i3-21111-211110000i3−i3i3−i3i3i3−i3−i30000i3−i3i3−i3i3i3−i3−i322-1-1-1-100i3−i3-2−i3i311000000000000
χ4222-222-12-2-122-1-12-1-1-1-1-2-212-1-1-1-10012222-1-1-1-1-1-1-1-1-2-2i3−i3i3−i3-21111-211110000i3−i3i3−i3i3i3−i3−i30000i3−i3i3−i3i3i3−i3−i3-2-2111100−i3i32i3−i3-1-1000000000000
χ4322-222-1-22-122112-1-1-1-1-2-212-1-1-1-100-1-2-2-2-211111111223−3−33-211112-1-1-1-100003−33−333−3−30000−33−33−3−3330033−3−32-2-1-1011−33000000000000
χ4422-222-1-22-122112-1-1-1-1-2-212-1-1-1-100-1-2-2-2-211111111223−3−33-211112-1-1-1-100003−33−333−3−30000−33−33−3−33300−3−333-22110-1-13−3000000000000
χ4522-222-1-22-122112-1-1-1-1-2-212-1-1-1-100-1-2-2-2-21111111122−333−3-211112-1-1-1-10000−33−33−3−33300003−33−333−3−30033−3−3-22110-1-1−33000000000000
χ4622-222-1-22-122112-1-1-1-1-2-212-1-1-1-100-1-2-2-2-21111111122−333−3-211112-1-1-1-10000−33−33−3−33300003−33−333−3−300−3−3332-2-1-10113−3000000000000
χ474444-2-244-24-2-2-2-2-21114-2-2-2-211144-24-2-2-2-2-21111114-2-2-2-2-2-2-2111-2-21114-2-2-2-2-21111114-2-2-2-2-2111111000000000000000000000000000
χ484444-2-244-24-2-2-2-2-21114-2-2-2-2111-4-4-24-2-2-2-2-21111114-22222-2-2111-2-2111-422222-1-1-1-1-1-1-422222-1-1-1-1-1-1000000000000000000000000000
χ494444-2-2-4-4-24-222-2-21114-2-2-2-21114i−4i2-422222-1-1-1-1-1-1-42−2i−2i2i2i-2-211122-1-1-14i−2i−2i−2i−2i−2iiiiiii−4i2i2i2i2i2i−i−i−i−i−i−i000000000000000000000000000
χ504444-2-2-4-4-24-222-2-21114-2-2-2-2111−4i4i2-422222-1-1-1-1-1-1-422i2i−2i−2i-2-211122-1-1-1−4i2i2i2i2i2i−i−i−i−i−i−i4i−2i−2i−2i−2i−2iiiiiii000000000000000000000000000
χ51444-24-244-2-24-2-2-21-211-24-2-21-21144-2-24-2-211-2-21111-24-2-2-2-2-21-211-21-211-24-2-211-2-21111-24-2-211-2-21111000000000000000000000000000
χ52444-24-244-2-24-2-2-21-211-24-2-21-211-4-4-2-24-2-211-2-21111-242222-21-211-21-2112-422-1-122-1-1-1-12-422-1-122-1-1-1-1000000000000000000000000000
χ53444-24-2-4-4-2-2422-21-211-24-2-21-2114i−4i22-422-1-122-1-1-1-12-4−2i−2i2i2i-21-2112-12-1-1−2i4i−2i−2iii−2i−2iiiii2i−4i2i2i−i−i2i2i−i−i−i−i000000000000000000000000000
χ54444-24-2-4-4-2-2422-21-211-24-2-21-211−4i4i22-422-1-122-1-1-1-12-42i2i−2i−2i-21-2112-12-1-12i−4i2i2i−i−i2i2i−i−i−i−i−2i4i−2i−2iii−2i−2iiiii000000000000000000000000000
χ55444-2-24444-2-2441-2-211-2-241-2-211444-2-211-2-2-2-21111-2-244441-2-2111-2-211-2-211-2-2-2-21111-2-211-2-2-2-21111000000000000000000000000000
χ56444-2-24444-2-2441-2-211-2-241-2-211-4-44-2-211-2-2-2-21111-2-2-4-4-4-41-2-2111-2-21122-1-12222-1-1-1-122-1-12222-1-1-1-1000000000000000000000000000
χ57444-2-24-4-44-2-2-4-41-2-211-2-241-2-2114i−4i-422-1-12222-1-1-1-1224i4i−4i−4i1-2-211-122-1-1−2i−2iii−2i−2i−2i−2iiiii2i2i−i−i2i2i2i2i−i−i−i−i000000000000000000000000000
χ58444-2-24-4-44-2-2-4-41-2-211-2-241-2-211−4i4i-422-1-12222-1-1-1-122−4i−4i4i4i1-2-211-122-1-12i2i−i−i2i2i2i2i−i−i−i−i−2i−2iii−2i−2i−2i−2iiiii000000000000000000000000000
χ59444-2-2-244-2-2-2-2-2111−1−3i32−1+3i32-2-2-2111−1−3i32−1+3i3244-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2-2-2-2-2-2111−1−3i32−1+3i32111−1−3i32−1+3i32-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32000000000000000000000000000
χ60444-2-2-244-2-2-2-2-2111−1−3i32−1+3i32-2-2-2111−1−3i32−1+3i32-4-4-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2-22222111−1−3i32−1+3i32111−1−3i32−1+3i3222-1-1-1-1-1-11+3i321−3i321+3i321−3i3222-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000000000000000000000000
χ61444-2-2-244-2-2-2-2-2111−1+3i32−1−3i32-2-2-2111−1+3i32−1−3i3244-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2-2-2-2-2-2111−1+3i32−1−3i32111−1+3i32−1−3i32-2-2111111−1+3i32−1−3i32−1+3i32−1−3i32-2-2111111−1+3i32−1−3i32−1+3i32−1−3i32000000000000000000000000000
χ62444-2-2-244-2-2-2-2-2111−1+3i32−1−3i32-2-2-2111−1+3i32−1−3i32-4-4-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2-22222111−1+3i32−1−3i32111−1+3i32−1−3i3222-1-1-1-1-1-11−3i321+3i321−3i321+3i3222-1-1-1-1-1-11−3i321+3i321−3i321+3i32000000000000000000000000000
χ63444-2-2-2-4-4-2-2-222111−1−3i32−1+3i32-2-2-2111−1−3i32−1+3i324i−4i222-1-1-1-1-1-11+3i321+3i321−3i321−3i3222−2i−2i2i2i111−1−3i32−1+3i32-1-1-11+3i321−3i32−2i−2iiiiiii−ζ14+2ζ222ζ14−ζ22−ζ14+2ζ222ζ14−ζ222i2i−i−i−i−i−i−iζ14−2ζ22−2ζ14+ζ22ζ14−2ζ22−2ζ14+ζ22000000000000000000000000000
χ64444-2-2-2-4-4-2-2-222111−1−3i32−1+3i32-2-2-2111−1−3i32−1+3i32−4i4i222-1-1-1-1-1-11+3i321+3i321−3i321−3i32222i2i−2i−2i111−1−3i32−1+3i32-1-1-11+3i321−3i322i2i−i−i−i−i−i−iζ14−2ζ22−2ζ14+ζ22ζ14−2ζ22−2ζ14+ζ22−2i−2iiiiiii−ζ14+2ζ222ζ14−ζ22−ζ14+2ζ222ζ14−ζ22000000000000000000000000000
χ65444-2-2-2-4-4-2-2-222111−1+3i32−1−3i32-2-2-2111−1+3i32−1−3i324i−4i222-1-1-1-1-1-11−3i321−3i321+3i321+3i3222−2i−2i2i2i111−1+3i32−1−3i32-1-1-11−3i321+3i32−2i−2iiiiiii2ζ14−ζ22−ζ14+2ζ222ζ14−ζ22−ζ14+2ζ222i2i−i−i−i−i−i−i−2ζ14+ζ22ζ14−2ζ22−2ζ14+ζ22ζ14−2ζ22000000000000000000000000000
χ66444-2-2-2-4-4-2-2-222111−1+3i32−1−3i32-2-2-2111−1+3i32−1−3i32−4i4i222-1-1-1-1-1-11−3i321−3i321+3i321+3i32222i2i−2i−2i111−1+3i32−1−3i32-1-1-11−3i321+3i322i2i−i−i−i−i−i−i−2ζ14+ζ22ζ14−2ζ22−2ζ14+ζ22ζ14−2ζ22−2i−2iiiiiii2ζ14−ζ22−ζ14+2ζ222ζ14−ζ22−ζ14+2ζ22000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.