Finite Group Databasebeta

← Group #13181525

Character table — Group #13181525

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size112222222222244444444444444444444444444444488888888888888888888888888888888888899181818181818181818181836363636363654545454545454545454545454545454
order1222234444612123333336666666661212121212121212121212121212126666666666666666661212121212121212121212121212121212122222244446612126661212124444444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iiiiiii−i−i−i−i−i−i
χ41111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−i−i−i−i−iiiiiii
χ51111-111-1-1-11-1-111111111-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-111-1-111-11-1-11-11-1111-1-1-1111-1-1-1
χ61111-111-1-1-11-1-111111111-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-111-1-111-11-1-1-11-11-1-1-1111-1-1-1111
χ71111-111-1-1-11-1-111111111-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-111-1-11-111i−i−iiiii−i−i−i−i−i−iiii
χ81111-111-1-1-11-1-111111111-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-111-1-11-111−iii−i−i−i−iiiiiii−i−i−i
χ9111-111-11-1-11-1-11111111-11111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1111-11-11-1-111-1-11-11-11-11-11-11-1-111-11-1-111-1
χ10111-111-11-1-11-1-11111111-11111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1111-11-11-1-111-1-11-11-11-1-11-11-111-1-11-111-1-11
χ11111-111-11-1-11-1-11111111-11111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-11-111-1-111-11-11-11i−i−iii−i−iii−i−iii−i−ii
χ12111-111-11-1-11-1-11111111-11111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-11-111-1-111-11-11-11−iii−i−iii−i−iii−i−iii−i
χ13111-1-11-1-1111111111111-1-1111111-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11111111-1-1-1-1111111-1-1-1-111-1-1-1-11
χ14111-1-11-1-1111111111111-1-1111111-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11111111-1-1-1-11-1-1-1-1-11111-1-11111-1
χ15111-1-11-1-1111111111111-1-1111111-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-1-1-1-11111-1ii−i−ii−i−i−i−ii−iiiii−i
χ16111-1-11-1-1111111111111-1-1111111-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-1-1-1-11111-1−i−iii−iiiii−ii−i−i−i−ii
χ1711-1111-1-11-11-1-1111111-111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-11-111-1-1-111-1-111-11-1-11-11-11-11-11-11
χ1811-1111-1-11-11-1-1111111-111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-11-111-1-1-111-1-11-11-111-11-11-11-11-11-1
χ1911-1111-1-11-11-1-1111111-111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-111-11-1-1111-1-111-1i−i−ii−ii−ii−iii−ii−ii−i
χ2011-1111-1-11-11-1-1111111-111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-111-11-1-1111-1-111-1−iii−ii−ii−ii−i−ii−ii−ii
χ2111-11-11-11-11111111111-11-1111111-11-1111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-11-1-11-111111-11-1-11-11111-11-1-11-1-11-1-11-1
χ2211-11-11-11-11111111111-11-1111111-11-1111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-11-1-11-111111-11-1-11-1-1-1-1-11-111-111-111-11
χ2311-11-11-11-11111111111-11-1111111-11-1111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-111-11-1-1-1-1-11-111-11ii−i−i−ii−i−ii−ii−iii−ii
χ2411-11-11-11-11111111111-11-1111111-11-1111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-111-11-1-1-1-1-11-111-11−i−iiii−iii−ii−ii−i−ii−i
χ2511-1-1111-1-11111111111-1-111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111-1-111-1-11111-1-111-1-1-1-111-1-1
χ2611-1-1111-1-11111111111-1-111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111-1-111-1-1-1-1-1-111-1-11111-1-111
χ2711-1-1111-1-11111111111-1-111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-111-1-111ii−i−i−i−iii−i−iii−i−iii
χ2811-1-1111-1-11111111111-1-111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-111-1-111−i−iiiii−i−iii−i−iii−i−i
χ2911-1-1-11111-11-1-1111111-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1111-111-1-1-1-1-11111-11-1-1-11-111-1-11-111
χ3011-1-1-11111-11-1-1111111-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1111-111-1-1-1-1-1111-11-1111-11-1-111-11-1-1
χ3111-1-1-11111-11-1-1111111-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1111-1-1-11-1-111111-1-1-1i−i−ii−i−ii−iiiii−ii−i−i
χ3211-1-1-11111-11-1-1111111-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1111-1-1-11-1-111111-1-1-1−iii−iii−ii−i−i−i−ii−iii
χ3322222-12222-1-1-122-1-1-1-1-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-10000000000000000
χ3422222-12222-1-1-122-1-1-1-1-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-2-211111111110000000000000000
χ352222-2-12-2-2-2-11122-1-1-1-1-1-1122-1-1-1-1-111-2-2-2-21111111122-1-1-1-122-1-1-1-1-2-2111122-1-1-1-1-2-21111-2-211112222-22-2-2-2-1-111-1-11-1110000000000000000
χ362222-2-12-2-2-2-11122-1-1-1-1-1-1122-1-1-1-1-111-2-2-2-21111111122-1-1-1-122-1-1-1-1-2-2111122-1-1-1-1-2-21111-2-21111-2-2-2-22-222211-1-111-11-1-10000000000000000
χ37222-22-1-22-2-2-11122-1-1-1-1-11-122-1-1-1-11-11-2-2-2-21111111122-1-1-1-1-2-2111122-1-1-1-1-2-2111122-1-1-1-1-2-21111222-22-22-2-2-1-111-11-11-110000000000000000
χ38222-22-1-22-2-2-11122-1-1-1-1-11-122-1-1-1-11-11-2-2-2-21111111122-1-1-1-1-2-2111122-1-1-1-1-2-2111122-1-1-1-1-2-21111-2-2-22-22-22211-1-11-11-11-10000000000000000
χ39222-2-2-1-2-222-1-1-122-1-1-1-1-11122-1-1-1-111-12222-1-1-1-1-1-1-1-122-1-1-1-1-2-21111-2-21111-2-21111-2-2111122-1-1-1-1222-2-2-2-222-1-1-1-1-11111-10000000000000000
χ40222-2-2-1-2-222-1-1-122-1-1-1-1-11122-1-1-1-111-12222-1-1-1-1-1-1-1-122-1-1-1-1-2-21111-2-21111-2-21111-2-2111122-1-1-1-1-2-2-22222-2-211111-1-1-1-110000000000000000
χ4122-222-1-2-22-2-11122-1-1-1-11-1-122-1-1-1-111-1-2-2-2-211111111-2-2111122-1-1-1-122-1-1-1-1-2-21111-2-2111122-1-1-1-122-222-2-22-2-1-1111-1-111-10000000000000000
χ4222-222-1-2-22-2-11122-1-1-1-11-1-122-1-1-1-111-1-2-2-2-211111111-2-2111122-1-1-1-122-1-1-1-1-2-21111-2-2111122-1-1-1-1-2-22-2-222-2211-1-1-111-1-110000000000000000
χ4322-22-2-1-22-22-1-1-122-1-1-1-11-1122-1-1-1-11-112222-1-1-1-1-1-1-1-1-2-2111122-1-1-1-1-2-21111-2-2111122-1-1-1-1-2-2111122-22-2-22-22-1-1-1-11-111-110000000000000000
χ4422-22-2-1-22-22-1-1-122-1-1-1-11-1122-1-1-1-11-112222-1-1-1-1-1-1-1-1-2-2111122-1-1-1-1-2-21111-2-2111122-1-1-1-1-2-21111-2-22-222-22-21111-11-1-11-10000000000000000
χ4522-2-22-12-2-22-1-1-122-1-1-1-111-122-1-1-1-1-1112222-1-1-1-1-1-1-1-1-2-21111-2-2111122-1-1-1-122-1-1-1-1-2-21111-2-2111122-2-222-2-22-1-1-1-111-1-1110000000000000000
χ4622-2-22-12-2-22-1-1-122-1-1-1-111-122-1-1-1-1-1112222-1-1-1-1-1-1-1-1-2-21111-2-2111122-1-1-1-122-1-1-1-1-2-21111-2-21111-2-222-2-222-21111-1-111-1-10000000000000000
χ4722-2-2-2-1222-2-11122-1-1-1-111122-1-1-1-1-1-1-1-2-2-2-211111111-2-21111-2-21111-2-2111122-1-1-1-122-1-1-1-122-1-1-1-122-2-2-2222-2-1-111111-1-1-10000000000000000
χ4822-2-2-2-1222-2-11122-1-1-1-111122-1-1-1-1-1-1-1-2-2-2-211111111-2-21111-2-21111-2-2111122-1-1-1-122-1-1-1-122-1-1-1-1-2-2222-2-2-2211-1-1-1-1-11110000000000000000
χ4944444444444441-211-2-24441-211-2-244411-2-21111-2-2-2-21-211-2-21-211-2-21-211-2-21-211-2-21-211-2-21-211-2-200000000000000000000000000000000000
χ504444444444444-21-2-211444-21-2-211444-2-211-2-2-2-21111-21-2-211-21-2-211-21-2-211-21-2-211-21-2-211-21-2-21100000000000000000000000000000000000
χ5144444-24444-2-2-21-2−1−3i32−1+3i3211-2-2-21-2−1−3i32−1+3i3211-2-2-211-2-2−1−3i32−1−3i32−1+3i32−1+3i3211111-2−1−3i32−1+3i32111-2−1−3i32−1+3i32111-2−1−3i32−1+3i32111-2−1−3i32−1+3i32111-2−1−3i32−1+3i32111-2−1−3i32−1+3i321100000000000000000000000000000000000
χ5244444-24444-2-2-21-2−1+3i32−1−3i3211-2-2-21-2−1+3i32−1−3i3211-2-2-211-2-2−1+3i32−1+3i32−1−3i32−1−3i3211111-2−1+3i32−1−3i32111-2−1+3i32−1−3i32111-2−1+3i32−1−3i32111-2−1+3i32−1−3i32111-2−1+3i32−1−3i32111-2−1+3i32−1−3i321100000000000000000000000000000000000
χ5344444-24444-2-2-2-2111−1−3i32−1+3i32-2-2-2-2111−1−3i32−1+3i32-2-2-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2111−1−3i32−1+3i32-2111−1−3i32−1+3i32-2111−1−3i32−1+3i32-2111−1−3i32−1+3i32-2111−1−3i32−1+3i32-2111−1−3i32−1+3i3200000000000000000000000000000000000
χ5444444-24444-2-2-2-2111−1+3i32−1−3i32-2-2-2-2111−1+3i32−1−3i32-2-2-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2111−1+3i32−1−3i32-2111−1+3i32−1−3i32-2111−1+3i32−1−3i32-2111−1+3i32−1−3i32-2111−1+3i32−1−3i32-2111−1+3i32−1−3i3200000000000000000000000000000000000
χ554444-444-4-4-44-4-41-211-2-244-41-211-2-24-4-4-1-122-1-1-1-122221-211-2-21-211-2-2-12-1-1221-211-2-2-12-1-122-12-1-12200000000000000000000000000000000000
χ564444-444-4-4-44-4-4-21-2-21144-4-21-2-2114-4-422-1-12222-1-1-1-1-21-2-211-21-2-2112-122-1-1-21-2-2112-122-1-12-122-1-100000000000000000000000000000000000
χ574444-4-24-4-4-4-2221-2−1−3i32−1+3i3211-2-221-2−1−3i32−1+3i3211-222-1-1221+3i321+3i321−3i321−3i32-1-1-1-11-2−1−3i32−1+3i32111-2−1−3i32−1+3i3211-121+3i321−3i32-1-11-2−1−3i32−1+3i3211-121+3i321−3i32-1-1-121+3i321−3i32-1-100000000000000000000000000000000000
χ584444-4-24-4-4-4-2221-2−1+3i32−1−3i3211-2-221-2−1+3i32−1−3i3211-222-1-1221−3i321−3i321+3i321+3i32-1-1-1-11-2−1+3i32−1−3i32111-2−1+3i32−1−3i3211-121−3i321+3i32-1-11-2−1+3i32−1−3i3211-121−3i321+3i32-1-1-121−3i321+3i32-1-100000000000000000000000000000000000
χ594444-4-24-4-4-4-222-2111−1−3i32−1+3i32-2-22-2111−1−3i32−1+3i32-22222-1-1-1-1-1-11+3i321+3i321−3i321−3i32-2111−1−3i32−1+3i32-2111−1−3i32−1+3i322-1-1-11+3i321−3i32-2111−1−3i32−1+3i322-1-1-11+3i321−3i322-1-1-11+3i321−3i3200000000000000000000000000000000000
χ604444-4-24-4-4-4-222-2111−1+3i32−1−3i32-2-22-2111−1+3i32−1−3i32-22222-1-1-1-1-1-11−3i321−3i321+3i321+3i32-2111−1+3i32−1−3i32-2111−1+3i32−1−3i322-1-1-11−3i321+3i32-2111−1+3i32−1−3i322-1-1-11−3i321+3i322-1-1-11−3i321+3i3200000000000000000000000000000000000
χ61444-444-44-4-44-4-41-211-2-24-441-211-2-2-44-4-1-122-1-1-1-122221-211-2-2-12-1-1221-211-2-2-12-1-1221-211-2-2-12-1-12200000000000000000000000000000000000
χ62444-444-44-4-44-4-4-21-2-2114-44-21-2-211-44-422-1-12222-1-1-1-1-21-2-2112-122-1-1-21-2-2112-122-1-1-21-2-2112-122-1-100000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.