Finite Group Databasebeta

← Group #13141249

Character table — Group #13141249

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size111111333333333333333333333344444412121212121212121212121212121212121212121212121212121212121212121212121212121212484848484848484848484848484848484848484848484848
order1233662233666666666666666666226666444466661212121212121212121212121212121212121212121212121212121212121212333333666666666666666666
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ311111111111111111111111111111111111111111111111111111111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ41111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1111-1-1-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32
χ61111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32
χ711111111−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i321111111111−1−i32−1−i32−1+i32−1+i3211111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32
χ811111111−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i321111111111−1−i32−1−i32−1+i32−1+i3211111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i321−1−i32−1−i32−1+i32−1+i3211−1+i321−1−i32−1+i32−1+i3211−1−i32−1−i32
χ911111111−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i321111111111−1−i32−1−i32−1+i32−1+i3211111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−1−i32−1−i32−1+i321−1+i321−1−i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1+i321−1−i32−1−i32−1+i32−1+i3211
χ1011111111−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i32-1-1-1-1-1-1-1-1111+i321+i321−i321−i32-1-1-1-11111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i32
χ1111111111−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i32-1-1-1-1-1-1-1-1111+i321+i321−i321−i32-1-1-1-11111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i3211+i321+i321−i321−i32-1-1−1+i321−1−i321−i321−i32-1-11+i321+i32
χ1211111111−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i32-1-1-1-1-1-1-1-1111+i321+i321−i321−i32-1-1-1-11111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i32−1+i321−1−i32−1−i32−1+i321−1+i321−1−i321−i321−i32-1-11+i321+i32−1−i32−1+i3211+i321+i321−i321−i32-1-1
χ1311111111−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i321111111111−1+i32−1+i32−1−i32−1−i3211111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32
χ1411111111−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i321111111111−1+i32−1+i32−1−i32−1−i3211111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321−1+i32−1+i32−1−i321−1−i321−1+i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1−i321−1+i32−1+i32−1−i32−1−i3211
χ1511111111−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i321111111111−1+i32−1+i32−1−i32−1−i3211111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i321−1+i32−1+i32−1−i32−1−i3211−1−i321−1+i32−1−i32−1−i3211−1+i32−1+i32
χ1611111111−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i32-1-1-1-1-1-1-1-1111−i321−i321+i321+i32-1-1-1-11111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i32
χ1711111111−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i32-1-1-1-1-1-1-1-1111−i321−i321+i321+i32-1-1-1-11111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i32−1−i321−1+i32−1+i32−1−i321−1−i321−1+i321+i321+i32-1-11−i321−i32−1+i32−1−i3211−i321−i321+i321+i32-1-1
χ1811111111−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i32-1-1-1-1-1-1-1-1111−i321−i321+i321+i32-1-1-1-11111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i3211−i321−i321+i321+i32-1-1−1−i321−1+i321+i321+i32-1-11−i321−i32
χ192-222-2-22-22222222222-2-2-2-2-2-2-2-2-2-22-222-2-200002-22-200000000000000000000000000000000-1-1-1-1-1-11111-11-11-11111-11-11-1
χ202-222-2-22-22222222222-2-2-2-2-2-2-2-2-2-22-222-2-200002-22-2000000000000000000000000000000001+i321+i321+i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i32
χ212-222-2-22-22222222222-2-2-2-2-2-2-2-2-2-22-222-2-200002-22-2000000000000000000000000000000001−i321−i321−i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i32
χ222-222-2-22-22222222222-2-2-2-2-2-2-2-2-2-2-22-2-2220000-22-2200000000000000000000000000000000-1-1-1-1-1-1111-11-11-11111-11-11-11
χ232-222-2-22-22222222222-2-2-2-2-2-2-2-2-2-2-22-2-2220000-22-22000000000000000000000000000000001+i321+i321+i321−i321−i321−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i32
χ242-222-2-22-22222222222-2-2-2-2-2-2-2-2-2-2-22-2-2220000-22-22000000000000000000000000000000001−i321−i321−i321+i321+i321+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i32
χ252-222-2-22-2−1−i3−1+i322−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-2-21+i31+i31+i31−i31−i31−i31+i31−i32-222-2-20000−1−i31+i3−1+i31−i300000000000000000000000000000000-11+i321−i32-11+i321−i321−1−i32−1+i321-1−1−i321+i32−1+i321−i321−1−i32−1+i321-1−1−i321+i32−1+i321−i32
χ262-222-2-22-2−1−i3−1+i322−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-2-21+i31+i31+i31−i31−i31−i31+i31−i32-222-2-20000−1−i31+i3−1+i31−i3000000000000000000000000000000001+i321−i32-11−i32-11+i32−1−i32−1+i321−1−i321+i32−1+i321−i321-1−1+i321−1−i32−1+i321−i321-1−1−i321+i32
χ272-222-2-22-2−1−i3−1+i322−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-2-21+i31+i31+i31−i31−i31−i31+i31−i32-222-2-20000−1−i31+i3−1+i31−i3000000000000000000000000000000001−i32-11+i321+i321−i32-1−1+i321−1−i32−1+i321−i321-1−1−i321+i32−1−i32−1+i321−1−i321+i32−1+i321−i321-1
χ282-222-2-22-2−1−i3−1+i322−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-2-21+i31+i31+i31−i31−i31−i31+i31−i3-22-2-22200001+i3−1−i31−i3−1+i300000000000000000000000000000000-11+i321−i32-11+i321−i321−1−i32−1+i32-111+i32−1−i321−i32−1+i321−1−i32−1+i32-111+i32−1−i321−i32−1+i32
χ292-222-2-22-2−1−i3−1+i322−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-2-21+i31+i31+i31−i31−i31−i31+i31−i3-22-2-22200001+i3−1−i31−i3−1+i3000000000000000000000000000000001+i321−i32-11−i32-11+i32−1−i32−1+i3211+i32−1−i321−i32−1+i32-11−1+i321−1−i321−i32−1+i32-111+i32−1−i32
χ302-222-2-22-2−1−i3−1+i322−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-2-21+i31+i31+i31−i31−i31−i31+i31−i3-22-2-22200001+i3−1−i31−i3−1+i3000000000000000000000000000000001−i32-11+i321+i321−i32-1−1+i321−1−i321−i32−1+i32-111+i32−1−i32−1−i32−1+i3211+i32−1−i321−i32−1+i32-11
χ312-222-2-22-2−1+i3−1−i322−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-2-21−i31−i31−i31+i31+i31+i31−i31+i32-222-2-20000−1+i31−i3−1−i31+i300000000000000000000000000000000-11−i321+i32-11−i321+i321−1+i32−1−i321-1−1+i321−i32−1−i321+i321−1+i32−1−i321-1−1+i321−i32−1−i321+i32
χ322-222-2-22-2−1+i3−1−i322−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-2-21−i31−i31−i31+i31+i31+i31−i31+i32-222-2-20000−1+i31−i3−1−i31+i3000000000000000000000000000000001+i32-11−i321−i321+i32-1−1−i321−1+i32−1−i321+i321-1−1+i321−i32−1+i32−1−i321−1+i321−i32−1−i321+i321-1
χ332-222-2-22-2−1+i3−1−i322−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-2-21−i31−i31−i31+i31+i31+i31−i31+i32-222-2-20000−1+i31−i3−1−i31+i3000000000000000000000000000000001−i321+i32-11+i32-11−i32−1+i32−1−i321−1+i321−i32−1−i321+i321-1−1−i321−1+i32−1−i321+i321-1−1+i321−i32
χ342-222-2-22-2−1+i3−1−i322−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-2-21−i31−i31−i31+i31+i31+i31−i31+i3-22-2-22200001−i3−1+i31+i3−1−i300000000000000000000000000000000-11−i321+i32-11−i321+i321−1+i32−1−i32-111−i32−1+i321+i32−1−i321−1+i32−1−i32-111−i32−1+i321+i32−1−i32
χ352-222-2-22-2−1+i3−1−i322−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-2-21−i31−i31−i31+i31+i31+i31−i31+i3-22-2-22200001−i3−1+i31+i3−1−i3000000000000000000000000000000001+i32-11−i321−i321+i32-1−1−i321−1+i321+i32−1−i32-111−i32−1+i32−1+i32−1−i3211−i32−1+i321+i32−1−i32-11
χ362-222-2-22-2−1+i3−1−i322−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-2-21−i31−i31−i31+i31+i31+i31−i31+i3-22-2-22200001−i3−1+i31+i3−1−i3000000000000000000000000000000001−i321+i32-11+i32-11−i32−1+i32−1−i3211−i32−1+i321+i32−1−i32-11−1−i321−1+i321+i32−1−i32-111−i32−1+i32
χ373333333333333333333333333333333333-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ383333333333333333333333333333-3-3-3-3-3-311-1-1-3-3-3-31111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000
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χ926-6−3+3i3−3−3i33−3i33+3i36-600−3+3i3−3−3i30000003−3i33+3i300000000-663−3i33+3i3−3+3i3−3−3i30000000000000000000000000000000000000000000000000000000000000000
χ936-6−3+3i3−3−3i33−3i33+3i3-22001−i31+i34−2+2i3−2−2i34−2+2i3−2−2i3−1+i3−1−i3-42−2i32+2i3-42−2i32+2i3000000002i−2i0000002ζ7−2ζ72ζ11−2ζ1100000000000000002i−2i2ζ7−2ζ72ζ11−2ζ112i−2i2ζ7−2ζ72ζ11−2ζ11000000000000000000000000
χ946-6−3+3i3−3−3i33−3i33+3i3-22001−i31+i34−2+2i3−2−2i34−2+2i3−2−2i3−1+i3−1−i3-42−2i32+2i3-42−2i32+2i300000000−2i2i000000−2ζ72ζ7−2ζ112ζ110000000000000000−2i2i−2ζ72ζ7−2ζ112ζ11−2i2i−2ζ72ζ7−2ζ112ζ11000000000000000000000000
χ956-6−3+3i3−3−3i33−3i33+3i3-22001−i31+i3−2−2i34−2+2i3−2+2i3−2−2i34−1+i3−1−i32+2i3-42−2i32−2i32+2i3-4000000002i−2i0000002ζ7−2ζ72ζ11−2ζ1100000000000000002ζ11−2ζ112i−2i2ζ7−2ζ72ζ7−2ζ72ζ11−2ζ112i−2i000000000000000000000000
χ966-6−3+3i3−3−3i33−3i33+3i3-22001−i31+i3−2−2i34−2+2i3−2+2i3−2−2i34−1+i3−1−i32+2i3-42−2i32−2i32+2i3-400000000−2i2i000000−2ζ72ζ7−2ζ112ζ110000000000000000−2ζ112ζ11−2i2i−2ζ72ζ7−2ζ72ζ7−2ζ112ζ11−2i2i000000000000000000000000
χ976-6−3+3i3−3−3i33−3i33+3i3-22001−i31+i3−2+2i3−2−2i34−2−2i34−2+2i3−1+i3−1−i32−2i32+2i3-42+2i3-42−2i3000000002i−2i0000002ζ7−2ζ72ζ11−2ζ1100000000000000002ζ7−2ζ72ζ11−2ζ112i−2i2ζ11−2ζ112i−2i2ζ7−2ζ7000000000000000000000000
χ986-6−3+3i3−3−3i33−3i33+3i3-22001−i31+i3−2+2i3−2−2i34−2−2i34−2+2i3−1+i3−1−i32−2i32+2i3-42+2i3-42−2i300000000−2i2i000000−2ζ72ζ7−2ζ112ζ110000000000000000−2ζ72ζ7−2ζ112ζ11−2i2i−2ζ112ζ11−2i2i−2ζ72ζ7000000000000000000000000

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