Finite Group Databasebeta

← Group #13161847

Character table — Group #13161847

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176C177C178C179C180
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444444444444444444444444444444444444444444444444181818181818181818181818181818181818181818181818363636363636363636363636363636363636363636363636
order122222223334444666666666666666666666121212121212121233333666666666666666666666666666666666661212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212124444444412121212121212121212121212121212224444446666121212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ511111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ611111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111
χ711111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-1-1-11111
χ811111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111111111-1-1-1-1
χ911-111-1-1-111111-1-11111-1-1-1-11-1-1-1-1111-1-1-1-111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−i11-1-111-1-1ii−i−iii−i−i
χ1011-111-1-1-111111-1-11111-1-1-1-11-1-1-1-1111-1-1-1-111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i-11-11−ii−ii-1-111-1-111−i−iii−i−iii
χ1111-111-1-1-111111-1-11111-1-1-1-11-1-1-1-1111-1-1-1-111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii11-1-111-1-1−i−iii−i−iii
χ1211-111-1-1-111111-1-11111-1-1-1-11-1-1-1-1111-1-1-1-111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−i-1-111-1-111ii−i−iii−i−i
χ1311-111-1-1-1111-1-1111111-1-1-1-11-1-1-1-1111-1-1-1-11-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1-1-11−iii−i11-1-1-1-111ii−i−i−i−iii
χ1411-111-1-1-1111-1-1111111-1-1-1-11-1-1-1-1111-1-1-1-11-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-111-1i−i−ii-1-11111-1-1−i−iiiii−i−i
χ1511-111-1-1-1111-1-1111111-1-1-1-11-1-1-1-1111-1-1-1-11-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-11i−i−ii11-1-1-1-111−i−iiiii−i−i
χ1611-111-1-1-1111-1-1111111-1-1-1-11-1-1-1-1111-1-1-1-11-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-111-1−iii−i-1-11111-1-1ii−i−i−i−iii
χ172222222222-1222222222222-1-1-1-1-122-12222-1222222222-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-122-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000022220000-1-1-1-1-1-1-1-100000000
χ182222222222-1222222222222-1-1-1-1-122-12222-1222222222-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-122-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-2-2-200001111111100000000
χ192222222222-1-2-2-2-222222222-1-1-1-1-122-12222-1-2-2-2-2-2-2-2-22-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-2-211-2-211-2-2-2-21111111111111111-2-2-2-2111111111111111100000000000000000000000022-2-20000-1-1-1-1111100000000
χ202222222222-1-2-2-2-222222222-1-1-1-1-122-12222-1-2-2-2-2-2-2-2-22-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-2-211-2-211-2-2-2-21111111111111111-2-2-2-21111111111111111000000000000000000000000-2-22200001111-1-1-1-100000000
χ21222222222-12222222-1-122-1-1222222-1222-1-1222222222-12-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-122-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000222200000000-1-1-1-1-1-1-1-1
χ22222222222-12222222-1-122-1-1222222-1222-1-1222222222-12-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-122-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000-2-2-2-20000000011111111
χ23222222222-12-2-2-2-222-1-122-1-1222222-1222-1-12-2-2-2-2-2-2-2-2-12-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-111-2-211-2-21111-2-2-2-21111111111111111-2-2-2-2111111111111000000000000000000000000000022-2-2000000001111-1-1-1-1
χ24222222222-12-2-2-2-222-1-122-1-1222222-1222-1-12-2-2-2-2-2-2-2-2-12-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-111-2-211-2-21111-2-2-2-21111111111111111-2-2-2-21111111111110000000000000000000000000000-2-22200000000-1-1-1-11111
χ2522222222-1222222-1-122-1-12222222-122-1-1222-1-1-1-1-1-1-1-1-1-12-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ2622222222-1222222-1-122-1-12222222-122-1-1222-1-1-1-1-1-1-1-1-1-12-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000000000000000
χ2722222222-122-2-2-2-2-1-122-1-12222222-122-1-122211111111-1-12-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12-1-1-2-2-2-2-2-2-2-211111111-2-2-2-21111111111111111-2-2-2-2111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000000000
χ2822222222-122-2-2-2-2-1-122-1-12222222-122-1-122211111111-1-12-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12-1-1-2-2-2-2-2-2-2-211111111-2-2-2-21111111111111111-2-2-2-211111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000000000000
χ29222-2-2-2-222222i−2i2i−2i2-22-22-22-2222-2-2-2-2-22-22-2-22i2i−2i−2i2i2i−2i−2i222222-22-22-222-2-222-2-222-2-222-2-22222-2-2-2-2-2-2-2-2-22i−2i2i−2i2i−2i2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000000000000000
χ30222-2-2-2-22222−2i2i−2i2i2-22-22-22-2222-2-2-2-2-22-22-2-2−2i−2i2i2i−2i−2i2i2i222222-22-22-222-2-222-2-222-2-222-2-22222-2-2-2-2-2-2-2-2-2−2i2i−2i2i−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000000000000000
χ31222-2-2-2-2222-12i−2i2i−2i2-22-22-22-2-1-1-111-2-212-22-212i2i−2i−2i2i2i−2i−2i2-1-1-1-12-2-11-11-1-11122-2-2-1-111-1-111-1-1-1-11111-211112i−2i−ii2i−2i−ii2i2i−2i−2i−i−iii−i−iii−i−i−i−iiiii2i2i−2i−2i−i−iii−i−iii−i−i−i−iiiii00000000000000000000000000000000−i3i3−i3i33−33−300000000
χ32222-2-2-2-2222-12i−2i2i−2i2-22-22-22-2-1-1-111-2-212-22-212i2i−2i−2i2i2i−2i−2i2-1-1-1-12-2-11-11-1-11122-2-2-1-111-1-111-1-1-1-11111-211112i−2i−ii2i−2i−ii2i2i−2i−2i−i−iii−i−iii−i−i−i−iiiii2i2i−2i−2i−i−iii−i−iii−i−i−i−iiiii00000000000000000000000000000000i3−i3i3−i3−33−3300000000
χ33222-2-2-2-2222-1−2i2i−2i2i2-22-22-22-2-1-1-111-2-212-22-21−2i−2i2i2i−2i−2i2i2i2-1-1-1-12-2-11-11-1-11122-2-2-1-111-1-111-1-1-1-11111-21111−2i2ii−i−2i2ii−i−2i−2i2i2iii−i−iii−i−iiiii−i−i−i−i−2i−2i2i2iii−i−iii−i−iiiii−i−i−i−i00000000000000000000000000000000−i3i3−i3i3−33−3300000000
χ34222-2-2-2-2222-1−2i2i−2i2i2-22-22-22-2-1-1-111-2-212-22-21−2i−2i2i2i−2i−2i2i2i2-1-1-1-12-2-11-11-1-11122-2-2-1-111-1-111-1-1-1-11111-21111−2i2ii−i−2i2ii−i−2i−2i2i2iii−i−iii−i−iiiii−i−i−i−i−2i−2i2i2iii−i−iii−i−iiiii−i−i−i−i00000000000000000000000000000000i3−i3i3−i33−33−300000000
χ35222-2-2-2-222-122i−2i2i−2i2-2-112-2-11222-2-2-21-22-2-11-22i2i−2i−2i2i2i−2i−2i-12-1-1-1-112-2-11-1-111-1-11122-2-2-1-111-1-1-1-111111-2111−ii2i−2i−ii2i−2i−i−iii2i2i−2i−2i−i−iii−i−i−i−iiiii−i−iii2i2i−2i−2i−i−iii−i−i−i−iiiii0000000000000000000000000000000000000000−i3i3−i3i33−33−3
χ36222-2-2-2-222-122i−2i2i−2i2-2-112-2-11222-2-2-21-22-2-11-22i2i−2i−2i2i2i−2i−2i-12-1-1-1-112-2-11-1-111-1-11122-2-2-1-111-1-1-1-111111-2111−ii2i−2i−ii2i−2i−i−iii2i2i−2i−2i−i−iii−i−i−i−iiiii−i−iii2i2i−2i−2i−i−iii−i−i−i−iiiii0000000000000000000000000000000000000000i3−i3i3−i3−33−33
χ37222-2-2-2-222-12−2i2i−2i2i2-2-112-2-11222-2-2-21-22-2-11-2−2i−2i2i2i−2i−2i2i2i-12-1-1-1-112-2-11-1-111-1-11122-2-2-1-111-1-1-1-111111-2111i−i−2i2ii−i−2i2iii−i−i−2i−2i2i2iii−i−iiiii−i−i−i−iii−i−i−2i−2i2i2iii−i−iiiii−i−i−i−i0000000000000000000000000000000000000000−i3i3−i3i3−33−33
χ38222-2-2-2-222-12−2i2i−2i2i2-2-112-2-11222-2-2-21-22-2-11-2−2i−2i2i2i−2i−2i2i2i-12-1-1-1-112-2-11-1-111-1-11122-2-2-1-111-1-1-1-111111-2111i−i−2i2ii−i−2i2iii−i−i−2i−2i2i2iii−i−iiiii−i−i−i−iii−i−i−2i−2i2i2iii−i−iiiii−i−i−i−i0000000000000000000000000000000000000000i3−i3i3−i33−33−3
χ39222-2-2-2-22-1222i−2i2i−2i-112-2-112-2222-2-21-2-2-112-2-2−i−iii−i−iii-1-12-1-1-11-112-2-1-111-1-111-1-11122-2-2-1-1-1-1111111-2112i−2i2i−2i2i−2i2i−2i−i−iii−i−iii2i2i−2i−2i−i−i−i−iiiii−i−iii−i−iii2i2i−2i−2i−i−i−i−iiiii0000000033−3−333−3−3−i3−i3i3i3−i3−i3i3i3000000000000000000000000
χ40222-2-2-2-22-1222i−2i2i−2i-112-2-112-2222-2-21-2-2-112-2-2−i−iii−i−iii-1-12-1-1-11-112-2-1-111-1-111-1-11122-2-2-1-1-1-1111111-2112i−2i2i−2i2i−2i2i−2i−i−iii−i−iii2i2i−2i−2i−i−i−i−iiiii−i−iii−i−iii2i2i−2i−2i−i−i−i−iiiii00000000−3−333−3−333i3i3−i3−i3i3i3−i3−i3000000000000000000000000
χ41222-2-2-2-22-122−2i2i−2i2i-112-2-112-2222-2-21-2-2-112-2-2ii−i−iii−i−i-1-12-1-1-11-112-2-1-111-1-111-1-11122-2-2-1-1-1-1111111-211−2i2i−2i2i−2i2i−2i2iii−i−iii−i−i−2i−2i2i2iiiii−i−i−i−iii−i−iii−i−i−2i−2i2i2iiiii−i−i−i−i0000000033−3−333−3−3i3i3−i3−i3i3i3−i3−i3000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.