Finite Group Databasebeta

← Group #13164658

Character table — Group #13164658

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1122336666666666666699121212121212121212121212121212122727484848485454545496969696144144144144
order123622344446666666662212121212121212121212121212121212223366444433666666
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ31111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ411111111111111111111-1-11111111111111111-1-11111-1-1-1-11111-1-1-1-1
χ511111111111111111111-1-11111111111111111-1-1−1+i32−1−i32−1+i32−1−i32-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32
χ611111111111111111111-1-11111111111111111-1-1−1−i32−1+i32−1−i32−1+i32-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32
χ7222222-1222222-1-1-1-1-1-1-1002222-1-1-1-1-1-1-1-1-1-1-1-10022220000-1-1-1-10000
χ8222222-1222222-1-1-1-1-1-1-1002222-1-1-1-1-1-1-1-1-1-1-1-100−1+i3−1−i3−1+i3−1−i300001−i321+i321−i321+i320000
χ9222222-1222222-1-1-1-1-1-1-1002222-1-1-1-1-1-1-1-1-1-1-1-100−1−i3−1+i3−1−i3−1+i300001+i321−i321+i321−i320000
χ102-22-22-2200002-2222-2-2-2-22-200000000000000002-2-1-1110000-1-1111-11-1
χ112-22-22-2200002-2222-2-2-2-22-200000000000000002-21−i321+i32−1+i32−1−i3200001−i321+i32−1+i32−1−i32−1+i321−i32−1−i321+i32
χ122-22-22-2200002-2222-2-2-2-22-200000000000000002-21+i321−i32−1−i32−1+i3200001+i321−i32−1−i32−1+i32−1−i321+i32−1+i321−i32
χ132-22-22-2200002-2222-2-2-2-2-220000000000000000-22-1-1110000-1-111-11-11
χ142-22-22-2200002-2222-2-2-2-2-220000000000000000-221−i321+i32−1+i32−1−i3200001−i321+i32−1+i32−1−i321−i32−1+i321+i32−1−i32
χ152-22-22-2200002-2222-2-2-2-2-220000000000000000-221+i321−i32−1−i32−1+i3200001+i321−i32−1−i32−1+i321+i32−1−i321−i32−1+i32
χ163333333-1-1-1-133333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1330000-1-1-1-100000000
χ173333333-1-1-1-1333333333-3-3-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-3-30000111100000000
χ183333-1-133-1-1-1-1-1-1-1-1-1-1-13333-1-1-1333-1-1-1-1-1-1-1-1-1-1-100003-1-1-100000000
χ193333-1-133-1-1-1-1-1-1-1-1-1-1-13-3-33-1-1-1333-1-1-1-1-1-1-1-1-1110000-311100000000
χ203333-1-13-13-1-1-1-1-1-1-1-1-1-1333-13-1-1-1-1-1333-1-1-1-1-1-1-1-10000-13-1-100000000
χ213333-1-13-13-1-1-1-1-1-1-1-1-1-13-3-3-13-1-1-1-1-1333-1-1-1-1-1-11100001-31100000000
χ223333-1-13-1-13-1-1-1-1-1-1-1-1-1333-1-13-1-1-1-1-1-1-1333-1-1-1-1-10000-1-13-100000000
χ233333-1-13-1-13-1-1-1-1-1-1-1-1-13-3-3-1-13-1-1-1-1-1-1-1333-1-1-111000011-3100000000
χ243333-1-13-1-1-13-1-1-1-1-1-1-1-1333-1-1-13-1-1-1-1-1-1-1-1-1333-1-10000-1-1-1300000000
χ253333-1-13-1-1-13-1-1-1-1-1-1-1-13-3-3-1-1-13-1-1-1-1-1-1-1-1-1333110000111-300000000
χ264-44-44-4-200004-4-2-2-2222200000000000000000000-2-222000011-1-10000
χ274-44-44-4-200004-4-2-2-22222000000000000000000001−i31+i3−1+i3−1−i30000−1+i32−1−i321−i321+i320000
χ284-44-44-4-200004-4-2-2-22222000000000000000000001+i31−i3−1−i3−1+i30000−1−i32−1+i321+i321−i320000
χ29666666-3-2-2-2-266-3-3-3-3-3-3-300-2-2-2-2111111111111000000000000000000
χ306666-2-2-36-2-2-2-2-2111111-3006-2-2-2-3-3-3111111111000000000000000000
χ316666-2-2-3-26-2-2-2-2111111-300-26-2-2111-3-3-3111111000000000000000000
χ326666-2-2-3-2-26-2-2-2111111-300-2-26-2111111-3-3-3111000000000000000000
χ336666-2-2-3-2-2-26-2-2111111-300-2-2-26111111111-3-3-3000000000000000000
χ3466-3-36606666-3-3000000000-3-3-3-3000000000000000000000000000000
χ3566-3-3660-2-2-2-2-3-300000000011114-2-24-2-24-2-24-2-2000000000000000000
χ3666-3-3660-2-2-2-2-3-30000000001111-24-2-24-2-24-2-24-2000000000000000000
χ3766-3-3660-2-2-2-2-3-30000000001111-2-24-2-24-2-24-2-24000000000000000000
χ3866-3-3-2-206-2-2-2114-2-24-2-2000-31110004-2-2-24-2-2-24000000000000000000
χ3966-3-3-2-206-2-2-211-24-2-24-2000-3111000-24-2-2-244-2-2000000000000000000
χ4066-3-3-2-206-2-2-211-2-24-2-24000-3111000-2-244-2-2-24-2000000000000000000
χ4166-3-3-2-20-26-2-2114-2-24-2-20001-3114-2-2000-2-24-24-2000000000000000000
χ4266-3-3-2-20-26-2-211-24-2-24-20001-311-24-20004-2-2-2-24000000000000000000
χ4366-3-3-2-20-26-2-211-2-24-2-240001-311-2-24000-24-24-2-2000000000000000000
χ4466-3-3-2-20-2-26-2114-2-24-2-200011-31-24-2-2-240004-2-2000000000000000000
χ4566-3-3-2-20-2-26-211-24-2-24-200011-31-2-244-2-2000-24-2000000000000000000
χ4666-3-3-2-20-2-26-211-2-24-2-2400011-314-2-2-24-2000-2-24000000000000000000
χ4766-3-3-2-20-2-2-26114-2-24-2-2000111-3-2-24-24-24-2-2000000000000000000000
χ4866-3-3-2-20-2-2-2611-24-2-24-2000111-34-2-2-2-24-24-2000000000000000000000
χ4966-3-3-2-20-2-2-2611-2-24-2-24000111-3-24-24-2-2-2-24000000000000000000000
χ506-66-6-2260000-22-2-2-2222-66-60000000000000000-220000000000000000
χ516-66-6-2260000-22-2-2-2222-6-6600000000000000002-20000000000000000
χ5212-1212-12-44-60000-44222-2-2-26000000000000000000000000000000000000
χ5312-12-6612-1200000-660000000000000000000000000000000000000000000
χ5412-12-66-44000002-28-4-4-8440000000000000000000000000000000000000
χ5512-12-66-44000002-2-48-44-840000000000000000000000000000000000000
χ5612-12-66-44000002-2-4-4844-80000000000000000000000000000000000000

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