Finite Group Databasebeta

← Group #13153863

Character table — Group #13153863

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155
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χ711111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-11-1-11-1-1-1-111-1-1-1-111
χ811111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-11111-1-11111-1-1
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χ13866-6-6−3−3i3−3+3i3−3−3i3−3+3i33+3i33−3i33+3i33−3i3006-66i−6i6i−6i0000−3−3i3−3+3i33+3i33−3i36ζ116ζ7−6ζ11−6ζ76ζ116ζ7−6ζ11−6ζ700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ13966-6-6−3−3i3−3+3i3−3−3i3−3+3i33+3i33−3i33+3i33−3i3006-6−6i6i−6i6i0000−3−3i3−3+3i33+3i33−3i3−6ζ11−6ζ76ζ116ζ7−6ζ11−6ζ76ζ116ζ700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ14066-6-6−3−3i3−3+3i3−3−3i3−3+3i33+3i33−3i33+3i33−3i300-666i−6i−6i6i00003+3i33−3i3−3−3i3−3+3i36ζ116ζ7−6ζ11−6ζ7−6ζ11−6ζ76ζ116ζ700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ14166-6-6−3−3i3−3+3i3−3−3i3−3+3i33+3i33−3i33+3i33−3i300-66−6i6i6i−6i00003+3i33−3i3−3−3i3−3+3i3−6ζ11−6ζ76ζ116ζ76ζ116ζ7−6ζ11−6ζ700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ14266-6-6−3+3i3−3−3i3−3+3i3−3−3i33−3i33+3i33−3i33+3i3006-66i−6i6i−6i0000−3+3i3−3−3i33−3i33+3i36ζ76ζ11−6ζ7−6ζ116ζ76ζ11−6ζ7−6ζ1100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ14366-6-6−3+3i3−3−3i3−3+3i3−3−3i33−3i33+3i33−3i33+3i3006-6−6i6i−6i6i0000−3+3i3−3−3i33−3i33+3i3−6ζ7−6ζ116ζ76ζ11−6ζ7−6ζ116ζ76ζ1100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ14466-6-6−3+3i3−3−3i3−3+3i3−3−3i33−3i33+3i33−3i33+3i300-666i−6i−6i6i00003−3i33+3i3−3+3i3−3−3i36ζ76ζ11−6ζ7−6ζ11−6ζ7−6ζ116ζ76ζ1100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ14566-6-6−3+3i3−3−3i3−3+3i3−3−3i33−3i33+3i33−3i33+3i300-66−6i6i6i−6i00003−3i33+3i3−3+3i3−3−3i3−6ζ7−6ζ116ζ76ζ116ζ76ζ11−6ζ7−6ζ1100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1466-6-66−3−3i3−3+3i33+3i33−3i33+3i33−3i3−3−3i3−3+3i36-6000000−3−3i3−3+3i33+3i33−3i3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002i−2i2i−2i2ζ112ζ7−2ζ11−2ζ72ζ112ζ7−2ζ11−2ζ7000000000000000000
χ1476-6-66−3−3i3−3+3i33+3i33−3i33+3i33−3i3−3−3i3−3+3i36-6000000−3−3i3−3+3i33+3i33−3i300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000−2i2i−2i2i−2ζ11−2ζ72ζ112ζ7−2ζ11−2ζ72ζ112ζ7000000000000000000
χ1486-6-66−3−3i3−3+3i33+3i33−3i33+3i33−3i3−3−3i3−3+3i3-660000003+3i33−3i3−3−3i3−3+3i3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002i−2i−2i2i2ζ112ζ7−2ζ11−2ζ7−2ζ11−2ζ72ζ112ζ7000000000000000000
χ1496-6-66−3−3i3−3+3i33+3i33−3i33+3i33−3i3−3−3i3−3+3i3-660000003+3i33−3i3−3−3i3−3+3i300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000−2i2i2i−2i−2ζ11−2ζ72ζ112ζ72ζ112ζ7−2ζ11−2ζ7000000000000000000
χ1506-6-66−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i36-6000000−3+3i3−3−3i33−3i33+3i3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002i−2i2i−2i2ζ72ζ11−2ζ7−2ζ112ζ72ζ11−2ζ7−2ζ11000000000000000000
χ1516-6-66−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i36-6000000−3+3i3−3−3i33−3i33+3i300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000−2i2i−2i2i−2ζ7−2ζ112ζ72ζ11−2ζ7−2ζ112ζ72ζ11000000000000000000
χ1526-6-66−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i3-660000003−3i33+3i3−3+3i3−3−3i3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002i−2i−2i2i2ζ72ζ11−2ζ7−2ζ11−2ζ7−2ζ112ζ72ζ11000000000000000000
χ1536-6-66−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i3-660000003−3i33+3i3−3+3i3−3−3i300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000−2i2i2i−2i−2ζ7−2ζ112ζ72ζ112ζ72ζ11−2ζ7−2ζ11000000000000000000
χ15412-1212-12−6−6i3−6+6i36+6i36−6i3−6−6i3−6+6i36+6i36−6i300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ15512-1212-12−6+6i3−6−6i36−6i36+6i3−6+6i3−6−6i36−6i36+6i300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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