Finite Group Databasebeta

← Group #72255544

Character table — Group #72255544

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168
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order1222444422222222223444444444466666661212121212121212222222222244444444446666666666666666666666666666121212121212121212121212121212121212121212121212121212128888888824242424242424242424242424242424222244444444444424444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
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χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
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χ51111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
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χ81111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111
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χ1511111111111-1-1-1-111111111-1-1-1-111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-111111-1-11-1-111
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χ1534-4-4444-4-44-4-400004-44-24-44-400004-422-2-222-2-2-222-2-222000000-4-444000000-4-444-22-22000000000000000022-2-222-2-2-22-22000000000000000022-2-222-2-2000000000000000000000000000000000000000000000000
χ1544-4-4444-4-4-44400004-4-44-444-40000-44-4-4-4-444444-4-4-4-44400000000000000000000-444-4000000000000000000000000-444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ1554-4-4444-4-4-44400004-4-4-2-444-40000-442222-2-2-2-2-22222-2-2000000000000000000002-2-2200000000−2i3−2i32i32i32i32i3−2i3−2i3000000002-2-2200000000−2i3−2i32i32i32i32i3−2i3−2i300000000000000000000000000000000000000000000000000000000
χ1564-4-4444-4-4-44400004-4-4-2-444-40000-442222-2-2-2-2-22222-2-2000000000000000000002-2-22000000002i32i3−2i3−2i3−2i3−2i32i32i3000000002-2-22000000002i32i3−2i3−2i3−2i3−2i32i32i300000000000000000000000000000000000000000000000000000000
χ1574-4-4444-4-4-44-40000-444-24-4-440000-442222-2-2-2-2-22222-2-20044-4-400000044-4-40000-222-200000000-2-222-2-22200000000-222-200000000-2-222-2-22200000000000000000000000000000000000000000000000000000000
χ1584-4-4444-4-4-44-40000-444-24-4-440000-442222-2-2-2-2-22222-2-200-4-444000000-4-4440000-222-20000000022-2-222-2-200000000-222-20000000022-2-222-2-200000000000000000000000000000000000000000000000000000000
χ1594-4-44-4-4444-440000-44-444-44-40000-44-4-444-4-44-4-444-4-44400000000000000000000-44-440000000000000000000000004-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ1604-4-44-4-4444-440000-44-4-24-44-40000-4422-2-222-222-2-222-2-2000000000000000000002-22-20000000000000000−2i3−2i32i32i32i32i3−2i3−2i3-22-2200000000000000002i32i3−2i3−2i3−2i3−2i32i32i3000000000000000000000000000000000000000000000000
χ1614-4-44-4-4444-440000-44-4-24-44-40000-4422-2-222-222-2-222-2-2000000000000000000002-22-200000000000000002i32i3−2i3−2i3−2i3−2i32i32i3-22-220000000000000000−2i3−2i32i32i32i32i3−2i3−2i3000000000000000000000000000000000000000000000000
χ1624-4-44-4-4444-4-400004-44-2-44-440000-4422-2-222-222-2-222-2-200000044-4-4000000-4-444-22-220000000000000000-2-222-2-2222-22-2000000000000000022-2-222-2-2000000000000000000000000000000000000000000000000
χ1634-4-44-4-4444-4-400004-44-2-44-440000-4422-2-222-222-2-222-2-2000000-4-44400000044-4-4-22-22000000000000000022-2-222-2-22-22-20000000000000000-2-222-2-222000000000000000000000000000000000000000000000000
χ1644-4-44-4-444-44400004-4-444-4-4400004-4-4-4-4-4444-4-44444-4-400000000000000000000-444-40000000000000000000000004-4-44000000000000000000000000000000000000000000000000000000000000000000000000
χ1654-4-44-4-444-44400004-4-4-24-4-4400004-42222-2-2-222-2-2-2-222000000000000000000002-2-2200000000−2i3−2i32i32i32i32i3−2i3−2i300000000-222-2000000002i32i3−2i3−2i3−2i3−2i32i32i300000000000000000000000000000000000000000000000000000000
χ1664-4-44-4-444-44400004-4-4-24-4-4400004-42222-2-2-222-2-2-2-222000000000000000000002-2-22000000002i32i3−2i3−2i3−2i3−2i32i32i300000000-222-200000000−2i3−2i32i32i32i32i3−2i3−2i300000000000000000000000000000000000000000000000000000000
χ1674-4-44-4-444-44-40000-444-2-444-400004-42222-2-2-222-2-2-2-2220044-4-4000000-4-4440000-222-200000000-2-222-2-222000000002-2-220000000022-2-222-2-200000000000000000000000000000000000000000000000000000000
χ1684-4-44-4-444-44-40000-444-2-444-400004-42222-2-2-222-2-2-2-22200-4-44400000044-4-40000-222-20000000022-2-222-2-2000000002-2-2200000000-2-222-2-22200000000000000000000000000000000000000000000000000000000

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