Finite Group Databasebeta

← Group #13140397

Character table — Group #13140397

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162
size1111222222222222222222222233334444444444444444444444444444444444444444444466666666666666666688888888888888888888888888121212121212121212121212121212121212121212121212121218181818363636363636545454547272108108
order12223344666666999181818181818181818444422366666669991212121218181818181818181818181818181818181818181836363636363622121212123636363636363636363636366666661212181818181818181818181818363636363636446612121212181818181818363636363636363636363636888844242424248888121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111111111111111-1-11111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1111111-1-1
χ911-1-1111-1-1-1-111-1111-1-1-1-1-1-111111-1-11-1111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11-111-1-1111111-1-1-1-1-1-11-111-1-11-1111111-1-1-1-1-1-1111-1-1-11-11-111-1-1111-1-1-1111111-1-1-1-1-1-1ii−i−ii−iii−i−iii−i−ii−ii−i
χ1011-1-1111-1-1-1-111-1111-1-1-1-1-1-111111-1-11-1111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11-111-1-1111111-1-1-1-1-1-11-111-1-11-1111111-1-1-1-1-1-1111-1-1-11-11-111-1-1111-1-1-1111111-1-1-1-1-1-1−i−iii−ii−i−iii−i−iii−ii−ii
χ1111-1-1111-1-1-1-111-1111-1-1-1-1-1-111111-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-11-111-1-1111111-1-1-1-1-1-1-11-1-1111-1-1-1-1-1-1-1111111111-1-1-1-111-1-1-111111-1-1-1-1-1-1-1-1-1111111ii−i−i−iiii−i−iii−i−i−ii−ii
χ1211-1-1111-1-1-1-111-1111-1-1-1-1-1-111111-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-11-111-1-1111111-1-1-1-1-1-1-11-1-1111-1-1-1-1-1-1-1111111111-1-1-1-111-1-1-111111-1-1-1-1-1-1-1-1-1111111−i−iiii−i−i−iii−i−iiii−ii−i
χ1311-1-1111-1-1-1-111-1111-1-1-1-1-1-1111-1-1111-1111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-1-111-1-1-1-1-1-11111111-111-1-11-1111111-1-1-1-1-1-1111-1-1-1-11-11-1-111-1-1-1111-1-1-1-1-1-1111111ii−i−ii−iii−i−i−i−iiii−i−ii
χ1411-1-1111-1-1-1-111-1111-1-1-1-1-1-1111-1-1111-1111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-1-111-1-1-1-1-1-11111111-111-1-11-1111111-1-1-1-1-1-1111-1-1-1-11-11-1-111-1-1-1111-1-1-1-1-1-1111111−i−iii−ii−i−iiiii−i−i−iii−i
χ1511-1-1111-1-1-1-111-1111-1-1-1-1-1-1111-1-111-111-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-11-1-111-1-1-1-1-1-1111111-11-1-1111-1-1-1-1-1-1-1111111111-1-1-11-1-1111-1-1-1-1-1111111111-1-1-1-1-1-1ii−i−i−iiii−i−i−i−iii−iii−i
χ1611-1-1111-1-1-1-111-1111-1-1-1-1-1-1111-1-111-111-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-11-1-111-1-1-1-1-1-1111111-11-1-1111-1-1-1-1-1-1-1111111111-1-1-11-1-1111-1-1-1-1-1111111111-1-1-1-1-1-1−i−iiii−i−i−iiiii−i−ii−i−ii
χ1722222222222222-1-1-1-1-1-1-1-1-1-1-1-122222222222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ1822222222222222-1-1-1-1-1-1-1-1-1-1-1-12222-2-22-2-2-2-2222-1-1-12222111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222111111111111-1-1-1-1-1-1-2-222-2-2-2-2-1-1-1-1-1-1111111111111000000000000000000
χ1922222222222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211111111111122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111111000000000000000000
χ2022222222222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-22-2-2-2-2222-1-1-12222111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2111111111111-2-2-2-2-2-222111111111111-1-1-1-1-1-122-2-22222111111-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ21222222-2-222222222222222222222220020000222222-2-2-2-2000000000000222222222-2-2-2-2-2-2-2-22222222222222222000000-2-2000000000000-2-2-2-2-2-200-2-20000-2-2-2-2-2-2000000000000000000000000000000
χ22222222-2-2222222222222222222-2-2-2-20020000222222-2-2-2-2000000000000222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000-2-2000000000000-2-2-2-2-2-200220000222222000000000000000000000000000000
χ23222222-2-2222222-1-1-1-1-1-1-1-1-1-1-1-122220020000222-1-1-1-2-2-2-2−i3−i3−i3i3i3i3−i3−i3−i3i3i3i3-1-1-1-1-1-1-1-1-1111111-2-22222-1-1-1-1-1-1-1-1-1-1-1-1000000-2-2−i3−i3−i3i3i3i3−i3−i3−i3i3i3i311111100-2-20000111111−i3−i3−i3i3i3i3−i3−i3−i3i3i3i3000000000000000000
χ24222222-2-2222222-1-1-1-1-1-1-1-1-1-1-1-122220020000222-1-1-1-2-2-2-2i3i3i3−i3−i3−i3i3i3i3−i3−i3−i3-1-1-1-1-1-1-1-1-1111111-2-22222-1-1-1-1-1-1-1-1-1-1-1-1000000-2-2i3i3i3−i3−i3−i3i3i3i3−i3−i3−i311111100-2-20000111111i3i3i3−i3−i3−i3i3i3i3−i3−i3−i3000000000000000000
χ25222222-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20020000222-1-1-1-2-2-2-2−i3−i3−i3i3i3i3−i3−i3−i3i3i3i3-1-1-1-1-1-1-1-1-111111122-2-2-2-2111111111111000000-2-2−i3−i3−i3i3i3i3−i3−i3−i3i3i3i311111100220000-1-1-1-1-1-1i3i3i3−i3−i3−i3i3i3i3−i3−i3−i3000000000000000000
χ26222222-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20020000222-1-1-1-2-2-2-2i3i3i3−i3−i3−i3i3i3i3−i3−i3−i3-1-1-1-1-1-1-1-1-111111122-2-2-2-2111111111111000000-2-2i3i3i3−i3−i3−i3i3i3i3−i3−i3−i311111100220000-1-1-1-1-1-1−i3−i3−i3i3i3i3−i3−i3−i3i3i3i3000000000000000000
χ2722222-1222-1-12-12ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68222222-1-1-1-1-1-1-1-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ682-1-12ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ6822-1-1-1-1ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ6822-1-1-1-1-1-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ6822-1-1-1-1-1-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68000000000000000000
χ2822222-1222-1-12-12ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ682222-2-2-11111-1-1-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ682-1-12−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ6822-1-1-1-1ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68-2-21111-1-1−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68-2-2-1-11111ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68000000000000000000
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χ3022222-1222-1-12-12ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68-2-2-2-2-2-2-11111-1-1-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ682-1-12−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68-2-21111−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ68-2-21111-1-1−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ682211-1-1-1-1−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68000000000000000000
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Here ζ is a primitive root of unity of order 72 (ζ72 = 1); i = ζ18.