Finite Group Databasebeta

← Group #13178512

Character table — Group #13178512

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162
size112222222222222224444444444444444444444444444444444444444444444363636363636363636363636363636363636112222222222222224444444444444444444444444444444444444444444444363636363636363636363636363636363636
order12233344666661212121233333666666666666666661212121212121212121212121212121212121212121212122224666666881212242424242226664466666121212126666666666666666666666121212121212121212121212121212121212121212121212222466666688121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-1111111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111
χ511-1111-11-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111111-1-1-1-1-1-1-1-1-1-11-11-11111-1-11-1-1-111-1-111-1111-11-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111111-1-1-1-1-1-1-1-1-1-11-11-11111-1-11-1-1-111-1-1
χ611-1111-11-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-1-1111-1-11111-1111-11-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-1-1111-1-111
χ711-1111-11-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-111-111-1-111-11-1-1-1-11111-1111-11-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-111-111-1-111-11-1-1-1-111
χ811-1111-11-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1111-11111-1-111-1111-11-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1111-11111-1-1
χ9222222-2-222222-2-2-2-22222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000222222-2-222222-2-2-2-22222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000
χ1022222-122-1-12-1222222-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-1-12-1222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1220000-1-1-1-10000000022222-122-1-12-1222222-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-1-12-1222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1220000-1-1-1-100000000
χ1122222-122-1-12-1222222-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-1-12-1222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2000011110000000022222-122-1-12-1222222-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-1-12-1222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-20000111100000000
χ1222222-1-2-2-1-12-12-2-2-2-22-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-11-21-2-2-211111111-2-211111111000000−i3i3−i3i30000000022222-1-2-2-1-12-12-2-2-2-22-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-11-21-2-2-211111111-2-211111111000000−i3i3−i3i300000000
χ1322222-1-2-2-1-12-12-2-2-2-22-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-11-21-2-2-211111111-2-211111111000000i3−i3i3−i30000000022222-1-2-2-1-12-12-2-2-2-22-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-11-21-2-2-211111111-2-211111111000000i3−i3i3−i300000000
χ142222-12222222-1-1-122-12-1-1-12-1-1-122-1-1-1-1-1-1-12-1-1-1222-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-10022-1-1000000-1-100002222-12222222-1-1-122-12-1-1-12-1-1-122-1-1-1-1-1-1-12-1-1-1222-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-10022-1-1000000-1-10000
χ152222-12222222-1-1-122-12-1-1-12-1-1-122-1-1-1-1-1-1-12-1-1-1222-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-100-2-2110000001100002222-12222222-1-1-122-12-1-1-12-1-1-122-1-1-1-1-1-1-12-1-1-1222-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-100-2-211000000110000
χ162222-12-2-22222-111-2-2-12-1-1-12-1-1-122-1-1-1-1-1-1-12-1-1-1-2-2-2111-2-211111111-2-21111110000−i3i3000000−i3i300002222-12-2-22222-111-2-2-12-1-1-12-1-1-122-1-1-1-1-1-1-12-1-1-1-2-2-2111-2-211111111-2-21111110000−i3i3000000−i3i30000
χ172222-12-2-22222-111-2-2-12-1-1-12-1-1-122-1-1-1-1-1-1-12-1-1-1-2-2-2111-2-211111111-2-21111110000i3−i3000000i3−i300002222-12-2-22222-111-2-2-12-1-1-12-1-1-122-1-1-1-1-1-1-12-1-1-1-2-2-2111-2-211111111-2-21111110000i3−i3000000i3−i30000
χ18222-1222222-12222-1-1-1-12-1-1-12-1-1-1-122-1-1-1-1-1-12-1-12-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100000000002200-1-1-1-1222-1222222-12222-1-1-1-12-1-1-12-1-1-1-122-1-1-1-1-1-12-1-12-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100000000002200-1-1-1-1
χ19222-1222222-12222-1-1-1-12-1-1-12-1-1-1-122-1-1-1-1-1-12-1-12-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-10000000000-2-2001111222-1222222-12222-1-1-1-12-1-1-12-1-1-1-122-1-1-1-1-1-12-1-12-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-10000000000-2-2001111
χ20222-122-2-222-122-2-211-1-12-1-1-12-1-1-1-122-1-1-1-1-1-12-1-1-21-2-21111-2-211111111-2-21111000000000000003−33−3222-122-2-222-122-2-211-1-12-1-1-12-1-1-1-122-1-1-1-1-1-12-1-1-21-2-21111-2-211111111-2-21111000000000000003−33−3
χ21222-122-2-222-122-2-211-1-12-1-1-12-1-1-1-122-1-1-1-1-1-12-1-1-21-2-21111-2-211111111-2-2111100000000000000−33−33222-122-2-222-122-2-211-1-12-1-1-12-1-1-1-122-1-1-1-1-1-12-1-1-21-2-21111-2-211111111-2-2111100000000000000−33−33
χ2222-22222-2-2-222222-2-222222-2-2-2-2-2-2-2-2-2-2-2-222222-222-2-2-2-2-2-2-2-2-2-2-2222222222200000000000000000022-22222-2-2-222222-2-222222-2-2-2-2-2-2-2-2-2-2-2-222222-222-2-2-2-2-2-2-2-2-2-2-22222222222000000000000000000
χ2322-222-12-2112-1222-2-22-1-1-1-1-2-2-2-2111111112-1-1-1-112-1-2-2-21111111122-1-1-1-1-1-1-1-1000000−i3i3i3−i30000000022-222-12-2112-1222-2-22-1-1-1-1-2-2-2-2111111112-1-1-1-112-1-2-2-21111111122-1-1-1-1-1-1-1-1000000−i3i3i3−i300000000
χ2422-222-12-2112-1222-2-22-1-1-1-1-2-2-2-2111111112-1-1-1-112-1-2-2-21111111122-1-1-1-1-1-1-1-1000000i3−i3−i3i30000000022-222-12-2112-1222-2-22-1-1-1-1-2-2-2-2111111112-1-1-1-112-1-2-2-21111111122-1-1-1-1-1-1-1-1000000i3−i3−i3i300000000
χ2522-222-1-22112-12-2-2222-1-1-1-1-2-2-2-2111111112-1-1-1-1-1-21222-1-1-1-1-1-1-1-1-2-2111111112-20000-1-1110000000022-222-1-22112-12-2-2222-1-1-1-1-2-2-2-2111111112-1-1-1-1-1-21222-1-1-1-1-1-1-1-1-2-2111111112-20000-1-11100000000
χ2622-222-1-22112-12-2-2222-1-1-1-1-2-2-2-2111111112-1-1-1-1-1-21222-1-1-1-1-1-1-1-1-2-211111111-22000011-1-10000000022-222-1-22112-12-2-2222-1-1-1-1-2-2-2-2111111112-1-1-1-1-1-21222-1-1-1-1-1-1-1-1-2-211111111-22000011-1-100000000
χ2722-22-122-2-2-222-1-1-1-2-2-12-1-1-1-2111-2-2111111-12-1-1-1-222111-2-2111111-1-122-1-1-1-1-1-10000−i3i3000000i3−i3000022-22-122-2-2-222-1-1-1-2-2-12-1-1-1-2111-2-2111111-12-1-1-1-222111-2-2111111-1-122-1-1-1-1-1-10000−i3i3000000i3−i30000
χ2822-22-122-2-2-222-1-1-1-2-2-12-1-1-1-2111-2-2111111-12-1-1-1-222111-2-2111111-1-122-1-1-1-1-1-10000i3−i3000000−i3i3000022-22-122-2-2-222-1-1-1-2-2-12-1-1-1-2111-2-2111111-12-1-1-1-222111-2-2111111-1-122-1-1-1-1-1-10000i3−i3000000−i3i30000
χ2922-22-12-22-2-222-11122-12-1-1-1-2111-2-2111111-12-1-1-12-2-2-1-1-122-1-1-1-1-1-111-2-2111111002-2-1-100000011000022-22-12-22-2-222-11122-12-1-1-1-2111-2-2111111-12-1-1-12-2-2-1-1-122-1-1-1-1-1-111-2-2111111002-2-1-1000000110000
χ3022-22-12-22-2-222-11122-12-1-1-1-2111-2-2111111-12-1-1-12-2-2-1-1-122-1-1-1-1-1-111-2-211111100-2211000000-1-1000022-22-12-22-2-222-11122-12-1-1-1-2111-2-2111111-12-1-1-12-2-2-1-1-122-1-1-1-1-1-111-2-211111100-2211000000-1-10000
χ3122-2-1222-2-2-2-1222211-1-12-1-11-21111-2-21111-1-12-1-1-2-12-21111-2-21111-1-1-1-122-1-1-1-1000000000000003−3−3322-2-1222-2-2-2-1222211-1-12-1-11-21111-2-21111-1-12-1-1-2-12-21111-2-21111-1-1-1-122-1-1-1-1000000000000003−3−33
χ3222-2-1222-2-2-2-1222211-1-12-1-11-21111-2-21111-1-12-1-1-2-12-21111-2-21111-1-1-1-122-1-1-1-100000000000000−333−322-2-1222-2-2-2-1222211-1-12-1-11-21111-2-21111-1-12-1-1-2-12-21111-2-21111-1-1-1-122-1-1-1-100000000000000−333−3
χ3322-2-122-22-2-2-122-2-2-1-1-1-12-1-11-21111-2-21111-1-12-1-121-22-1-1-1-122-1-1-1-11111-2-2111100000000002-200-1-11122-2-122-22-2-2-122-2-2-1-1-1-12-1-11-21111-2-21111-1-12-1-121-22-1-1-1-122-1-1-1-11111-2-2111100000000002-200-1-111
χ3422-2-122-22-2-2-122-2-2-1-1-1-12-1-11-21111-2-21111-1-12-1-121-22-1-1-1-122-1-1-1-11111-2-211110000000000-220011-1-122-2-122-22-2-2-122-2-2-1-1-1-12-1-11-21111-2-21111-1-12-1-121-22-1-1-1-122-1-1-1-11111-2-211110000000000-220011-1-1
χ354444-2-244-2-24-2-2-2-244-2-21114-2-2-2-2-2111111-2-2111-24-2-2-2-2-2-2111111-2-2-2-21111110000000000000000004444-2-244-2-24-2-2-2-244-2-21114-2-2-2-2-2111111-2-2111-24-2-2-2-2-2-2111111-2-2-2-2111111000000000000000000
χ364444-2-2-4-4-2-24-2-222-4-4-2-21114-2-2-2-2-2111111-2-21112-4222222-1-1-1-1-1-12222-1-1-1-1-1-10000000000000000004444-2-2-4-4-2-24-2-222-4-4-2-21114-2-2-2-2-2111111-2-21112-4222222-1-1-1-1-1-12222-1-1-1-1-1-1000000000000000000
χ37444-24-244-2-2-2-2444-2-2-21-211-24-2-211-2-21111-21-211-2-2-24-2-211-2-21111-2-211-2-21111000000000000000000444-24-244-2-2-2-2444-2-2-21-211-24-2-211-2-21111-21-211-2-2-24-2-211-2-21111-2-211-2-21111000000000000000000
χ38444-24-2-4-4-2-2-2-24-4-422-21-211-24-2-211-2-21111-21-211222-422-1-122-1-1-1-122-1-122-1-1-1-1000000000000000000444-24-2-4-4-2-2-2-24-4-422-21-211-24-2-211-2-21111-21-211222-422-1-122-1-1-1-122-1-122-1-1-1-1000000000000000000
χ39444-2-244444-24-2-2-2-2-21-2-211-2-211-2-2-2-211111-2-2114-24-211-2-2-2-2111111-2-2-2-21111000000000000000000444-2-244444-24-2-2-2-2-21-2-211-2-211-2-2-2-211111-2-2114-24-211-2-2-2-2111111-2-2-2-21111000000000000000000
χ40444-2-24-4-444-24-222221-2-211-2-211-2-2-2-211111-2-211-42-42-1-12222-1-1-1-1-1-12222-1-1-1-1000000000000000000444-2-24-4-444-24-222221-2-211-2-211-2-2-2-211111-2-211-42-42-1-12222-1-1-1-1-1-12222-1-1-1-1000000000000000000
χ41444-2-2-244-2-2-2-2-2-2-2-2-2111−1−3i32−1+3i32-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i32-2-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111111−1−3i32−1−3i32−1+3i32−1+3i32000000000000000000444-2-2-244-2-2-2-2-2-2-2-2-2111−1−3i32−1+3i32-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i32-2-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111111−1−3i32−1−3i32−1+3i32−1+3i32000000000000000000
χ42444-2-2-244-2-2-2-2-2-2-2-2-2111−1+3i32−1−3i32-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111−1+3i32−1−3i32-2-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111111−1+3i32−1+3i32−1−3i32−1−3i32000000000000000000444-2-2-244-2-2-2-2-2-2-2-2-2111−1+3i32−1−3i32-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111−1+3i32−1−3i32-2-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111111−1+3i32−1+3i32−1−3i32−1−3i32000000000000000000
χ43444-2-2-2-4-4-2-2-2-2-22222111−1−3i32−1+3i32-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i322222-1-1-1-1-1-11+3i321+3i321−3i321−3i32-1-1-1-1-1-11+3i321+3i321−3i321−3i32000000000000000000444-2-2-2-4-4-2-2-2-2-22222111−1−3i32−1+3i32-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i322222-1-1-1-1-1-11+3i321+3i321−3i321−3i32-1-1-1-1-1-11+3i321+3i321−3i321−3i32000000000000000000
χ44444-2-2-2-4-4-2-2-2-2-22222111−1+3i32−1−3i32-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111−1+3i32−1−3i322222-1-1-1-1-1-11−3i321−3i321+3i321+3i32-1-1-1-1-1-11−3i321−3i321+3i321+3i32000000000000000000444-2-2-2-4-4-2-2-2-2-22222111−1+3i32−1−3i32-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111−1+3i32−1−3i322222-1-1-1-1-1-11−3i321−3i321+3i321+3i32-1-1-1-1-1-11−3i321−3i321+3i321+3i32000000000000000000
χ4544-44-2-24-4224-2-2-2-2-4-4-2-2111-422222-1-1-1-1-1-1-2-211124-222222-1-1-1-1-1-1-2-2-2-211111100000000000000000044-44-2-24-4224-2-2-2-2-4-4-2-2111-422222-1-1-1-1-1-1-2-211124-222222-1-1-1-1-1-1-2-2-2-2111111000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.