Finite Group Databasebeta

← Group #13161789

Character table — Group #13161789

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176C177C178C179C180
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444444444444444444444444444444444444444444444444181818181818181818181818181818181818181818181818363636363636363636363636363636363636363636363636
order1222222233344446666666666666666666661212121212121212333336666666666666666666666666666666666612121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121244444444121212121212121212121212121212124444444412121212121212121212121212121212
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
χ511111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ611111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111
χ711111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ811111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ9111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-111-1-1-111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−ii−ii−i1-11-1ii−i−iii−i−i11-1-111-1-1
χ10111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-111-1-1-111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i−ii−ii-11-11−i−iii−i−iii-1-111-1-111
χ11111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-111-1-1-111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiiii−ii−i-11-11ii−i−iii−i−i-1-111-1-111
χ12111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-111-1-1-111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii−ii−ii1-11-1−i−iii−i−iii11-1-111-1-1
χ13111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-111-1-1-11-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiiii−i−ii1-1-11ii−i−i−i−iii11-1-1-1-111
χ14111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-111-1-1-11-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii−iii−i-111-1−i−iiiii−i−i-1-11111-1-1
χ15111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-111-1-1-11-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−ii−i−ii-111-1ii−i−i−i−iii-1-11111-1-1
χ16111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-111-1-1-11-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i−iii−i1-1-11−i−iiiii−i−i11-1-1-1-111
χ172222222222-122222222-1-12222222-1-12-1-1-122-1-1-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ182222222222-122222222-1-12222222-1-12-1-1-122-1-1-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000000000000000
χ192222222222-1-2-2-2-22222-1-12222222-1-12-1-1-122111111112-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-21111111111111111-2-2-2-211111111111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000000000
χ202222222222-1-2-2-2-22222-1-12222222-1-12-1-1-122111111112-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-21111111111111111-2-2-2-21111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000000000000
χ21222222222-12222222-1-1222222-1-1-122-1222-1222222222-12-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000022220000-1-1-1-1-1-1-1-100000000
χ22222222222-12222222-1-1222222-1-1-122-1222-1222222222-12-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-2-2-200001111111100000000
χ23222222222-12-2-2-2-222-1-1222222-1-1-122-1222-12-2-2-2-2-2-2-2-2-12-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-11111-2-2-2-21111-2-2-2-21111111111111111-2-2-2-211111111111100000000000000000000000022-2-20000-1-1-1-1111100000000
χ24222222222-12-2-2-2-222-1-1222222-1-1-122-1222-12-2-2-2-2-2-2-2-2-12-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-11111-2-2-2-21111-2-2-2-21111111111111111-2-2-2-2111111111111000000000000000000000000-2-22200001111-1-1-1-100000000
χ2522222222-1222222-1-12222-1-1-1-12222222222-122222222-1-12-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000000000000000222200000000-1-1-1-1-1-1-1-1
χ2622222222-1222222-1-12222-1-1-1-12222222222-122222222-1-12-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000000000000000-2-2-2-20000000011111111
χ2722222222-122-2-2-2-2-1-12222-1-1-1-12222222222-1-2-2-2-2-2-2-2-2-1-12-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12-1-1-2-2-2-2111111111111-2-2-2-21111111111111111-2-2-2-211111111000000000000000000000000000022-2-200000000-1-1-1-11111
χ2822222222-122-2-2-2-2-1-12222-1-1-1-12222222222-1-2-2-2-2-2-2-2-2-1-12-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12-1-1-2-2-2-2111111111111-2-2-2-21111111111111111-2-2-2-2111111110000000000000000000000000000-2-222000000001111-1-1-1-1
χ29222-2-2-2-2222-122-2-22222-1-1-2-2-2-2-2-2-2112-111-22-1-1-1-111112-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-211111111111111112-1-1-1-122-2-222-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111111111112i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii000000000000000000000000
χ30222-2-2-2-2222-122-2-22222-1-1-2-2-2-2-2-2-2112-111-22-1-1-1-111112-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-211111111111111112-1-1-1-122-2-222-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111111111−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i000000000000000000000000
χ31222-2-2-2-2222-1-2-2222222-1-1-2-2-2-2-2-2-2112-111-221111-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-211111111111111112-1-1-1-1-2-222-2-222-2-2-2-211111111111111112222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i000000000000000000000000
χ32222-2-2-2-2222-1-2-2222222-1-1-2-2-2-2-2-2-2112-111-221111-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-211111111111111112-1-1-1-1-2-222-2-222-2-2-2-211111111111111112222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii000000000000000000000000
χ33222-2-2-2-222-1222-2-222-1-122-2-2-2-2111-2-2-12-2-2122222-2-2-2-2-12-1-1-1-1-122-1-1-1-1-1-11111-2-2-2-2111111111111-12-1-1-1-1-11122-2-2-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-21111111111110000000000000000000000002i−2i2i−2i0000−i−iii−i−iii00000000
χ34222-2-2-2-222-1222-2-222-1-122-2-2-2-2111-2-2-12-2-2122222-2-2-2-2-12-1-1-1-1-122-1-1-1-1-1-11111-2-2-2-2111111111111-12-1-1-1-1-11122-2-2-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-2111111111111000000000000000000000000−2i2i−2i2i0000ii−i−iii−i−i00000000
χ35222-2-2-2-222-12-2-22222-1-122-2-2-2-2111-2-2-12-2-212-2-2-2-22222-12-1-1-1-1-122-1-1-1-1-1-11111-2-2-2-2111111111111-12-1-1-111-1-1-2-2221111-2-2-2-2111111111111-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000002i−2i−2i2i0000−i−iiiii−i−i00000000
χ36222-2-2-2-222-12-2-22222-1-122-2-2-2-2111-2-2-12-2-212-2-2-2-22222-12-1-1-1-1-122-1-1-1-1-1-11111-2-2-2-2111111111111-12-1-1-111-1-1-2-2221111-2-2-2-2111111111111-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000−2i2i2i−2i0000ii−i−i−i−iii00000000
χ37222-2-2-2-22-12222-2-2-1-122221111-2-2-2-2-222-2-2-2-12222-2-2-2-2-1-12-1-1-1-1-1-122-1-1-1-111111111-2-2-2-211111111-1-12-1-122-2-2-1-111-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-111111111-2-2-2-21111111100000000000000000000000000002-22-200000000-1-111-1-111
χ38222-2-2-2-22-12222-2-2-1-122221111-2-2-2-2-222-2-2-2-12222-2-2-2-2-1-12-1-1-1-1-1-122-1-1-1-111111111-2-2-2-211111111-1-12-1-122-2-2-1-111-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-111111111-2-2-2-2111111110000000000000000000000000000-22-220000000011-1-111-1-1
χ39222-2-2-2-22-122-2-222-1-122221111-2-2-2-2-222-2-2-2-1-2-2-2-22222-1-12-1-1-1-1-1-122-1-1-1-111111111-2-2-2-211111111-1-12-1-1-2-22211-1-111111111-2-2-2-211111111-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000000000000000002-2-2200000000-1-11111-1-1
χ40222-2-2-2-22-122-2-222-1-122221111-2-2-2-2-222-2-2-2-1-2-2-2-22222-1-12-1-1-1-1-1-122-1-1-1-111111111-2-2-2-211111111-1-12-1-1-2-22211-1-111111111-2-2-2-211111111-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000000000000000-222-20000000011-1-1-1-111
χ4122-222-2-2-222200002-22-22-222-2-222-22-2-2-22-2-2-200000000222222-22-22-222-2-222-2-222-2-222-2-22222-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000000000002-22-20000000022-2-222-2-2000000000000000000000000
χ4222-222-2-2-222200002-22-22-222-2-222-22-2-2-22-2-2-200000000222222-22-22-222-2-222-2-222-2-222-2-22222-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000000000-22-2200000000-2-222-2-222000000000000000000000000
χ4322-222-2-2-222-100002-22-2-1122-2-222-2-11-21-11-2-233−3−333−3−32-1-1-1-12-2-11-11-1-11122-2-2-1-111-1-111-1-1-1-11111-2111100000000000033−3−333−3−33333−3−3−3−3000033−3−333−3−33333−3−3−3−300002-22-233−3−333−3−3-1-111-1-111000000000000000000000000
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χ1784-4-4-444-44-2-2-24-4-442222222-2-222-2-222-2-2-2-22-2-222-22-2-22111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32-111-1-111-1-111-11−3i321+3i32−1+3i32−1−3i32−1+3i32−1−3i321−3i321+3i32111−1+3i32−1−3i32-222-2-222-211-1-11-1-111-1-11−1+3i32−1−3i321−3i321+3i321−3i321+3i32−1+3i32−1−3i32-1-111-111-1-111-11−3i321+3i32−1+3i32−1−3i32−1+3i32−1−3i321−3i321+3i32000000000000000000000000000000000000000000000000
χ1794-4-4-444-44-2-2-2-444-42222222-2-222-2-222-2-2-2-22-22-2-22-222-2111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32-111-1-111-1-111-11+3i321−3i32−1−3i32−1+3i32−1−3i32−1+3i321+3i321−3i32111−1−3i32−1+3i322-2-222-2-22-1-111-111-1-111-11+3i321−3i32−1−3i32−1+3i32−1−3i32−1+3i321+3i321−3i3211-1-11-1-111-1-11−1−3i32−1+3i321+3i321−3i321+3i321−3i32−1−3i32−1+3i32000000000000000000000000000000000000000000000000
χ1804-4-4-444-44-2-2-2-444-42222222-2-222-2-222-2-2-2-22-22-2-22-222-2111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32-111-1-111-1-111-11−3i321+3i32−1+3i32−1−3i32−1+3i32−1−3i321−3i321+3i32111−1+3i32−1−3i322-2-222-2-22-1-111-111-1-111-11−3i321+3i32−1+3i32−1−3i32−1+3i32−1−3i321−3i321+3i3211-1-11-1-111-1-11−1+3i32−1−3i321−3i321+3i321−3i321+3i32−1+3i32−1−3i32000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.