Finite Group Databasebeta

← Group #13158437

Character table — Group #13158437

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171
size111122222222224444444466888888888881212121212121212121212121224242424243636363611112222222222444444446688888888888121212121212121212121212122424242424363636361111222222222244444444668888888888812121212121212121212121212242424242436363636
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χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-11111-1-1-1-1111-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-11111-1-1-1-1111-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-11111-1-1-1-1111-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-1-111111-1-11111-1-1-1-1-1-1-11111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-111111-1-11111-1-1-1-1-1-1-11111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-111111-1-11111-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1111-1-11111111111-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1111-1-11111111111-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1111-1-11111111111-1-1-1-1-1-1-111
χ51111111111111111111111-1-111111111111-11111-1-1-1-11111-1-1-111-1-1-1-11111111111111111111111-1-111111111111-11111-1-1-1-11111-1-1-111-1-1-1-11111111111111111111111-1-111111111111-11111-1-1-1-11111-1-1-111-1-1-1-1
χ61111111111111111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-111111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-111111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-111111-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-11111111-1-111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-11111111-1-111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-11111111-1-111-1-1
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χ1201111111111111111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+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+i321+i321+i321+i321+i321+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+i32−1+i321−i321−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−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32
χ1211111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-111111-1-111−1−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+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+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−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32
χ1221111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-11111111-1-111-1-1−1−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+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+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−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32
χ123222222-2-22222222222-2-2-2-222000000000-2-2-2000022-2-20000000000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3−1−i3−1−i30000000001+i31+i31+i30000−1−i3−1−i31+i31+i30000000000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3−1+i3−1+i30000000001−i31−i31−i30000−1+i3−1+i31−i31−i30000000000000
χ124222222-2-22222222222-2-2-2-2-2-2000000000-2-220000-2-2220000000000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i31+i31+i30000000001+i31+i3−1−i300001+i31+i3−1−i3−1−i30000000000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i31−i31−i30000000001−i31−i3−1+i300001−i31−i3−1+i3−1+i30000000000000
χ12522222-12222-1-1-12-1-1-1-12-1-1222222-1-1-1-1-1-1-1-120000-1-1-1-100002-1-1000000−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i3−1−i31+i321+i321+i32−1−i31+i321+i321+i321+i32−1−i31+i321+i32−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i32−1−i300001+i321+i321+i321+i320000−1−i31+i321+i32000000−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i3−1+i31−i321−i321−i32−1+i31−i321−i321−i321−i32−1+i31−i321−i32−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i32−1+i300001−i321−i321−i321−i320000−1+i31−i321−i32000000
χ12622222-12222-1-1-12-1-1-1-12-1-1222-2-2-2111111-1-120000-1-1-1-10000-211000000−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i3−1−i31+i321+i321+i32−1−i31+i321+i321+i321+i32−1−i31+i321+i32−1−i3−1−i3−1−i31+i31+i31+i3−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i300001+i321+i321+i321+i3200001+i3−1−i32−1−i32000000−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i3−1+i31−i321−i321−i32−1+i31−i321−i321−i321−i32−1+i31−i321−i32−1+i3−1+i3−1+i31−i31−i31−i3−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i300001−i321−i321−i321−i3200001−i3−1+i32−1+i32000000
χ12722222-12222-1-1-12-1-1-1-12-1-12-2-2222-1-1-1-1-1-1-1-1-2000011110000-211000000−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i3−1−i31+i321+i321+i32−1−i31+i321+i321+i321+i32−1−i31+i321+i32−1−i31+i31+i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i321+i30000−1−i32−1−i32−1−i32−1−i3200001+i3−1−i32−1−i32000000−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i3−1+i31−i321−i321−i32−1+i31−i321−i321−i321−i32−1+i31−i321−i32−1+i31−i31−i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i321−i30000−1+i32−1+i32−1+i32−1+i3200001−i3−1+i32−1+i32000000
χ12822222-12222-1-1-12-1-1-1-12-1-12-2-2-2-2-2111111-1-1-20000111100002-1-1000000−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i3−1−i31+i321+i321+i32−1−i31+i321+i321+i321+i32−1−i31+i321+i32−1−i31+i31+i31+i31+i31+i3−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i30000−1−i32−1−i32−1−i32−1−i320000−1−i31+i321+i32000000−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i3−1+i31−i321−i321−i32−1+i31−i321−i321−i321−i32−1+i31−i321−i32−1+i31−i31−i31−i31−i31−i3−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i30000−1+i32−1+i32−1+i32−1+i320000−1+i31−i321−i32000000
χ12922222-1-2-222-1-1-12-1-1-1-1-211-222000−i3i3−i3−i3i3i311-20000-1-11100000−i3i3000000−1−i3−1−i3−1−i3−1−i3−1−i31+i321+i31+i3−1−i3−1−i31+i321+i321+i32−1−i31+i321+i321+i321+i321+i3−1−i32−1−i321+i3−1−i3−1−i3000−3+i323−i32−3+i32−3+i323−i323−i32−1−i32−1−i321+i300001+i321+i32−1−i32−1−i3200000−3+i323−i32000000−1+i3−1+i3−1+i3−1+i3−1+i31−i321−i31−i3−1+i3−1+i31−i321−i321−i32−1+i31−i321−i321−i321−i321−i3−1+i32−1+i321−i3−1+i3−1+i30003+i32−3−i323+i323+i32−3−i32−3−i32−1+i32−1+i321−i300001−i321−i32−1+i32−1+i32000003+i32−3−i32000000
χ13022222-1-2-222-1-1-12-1-1-1-1-211-222000i3−i3i3i3−i3−i311-20000-1-11100000i3−i3000000−1−i3−1−i3−1−i3−1−i3−1−i31+i321+i31+i3−1−i3−1−i31+i321+i321+i32−1−i31+i321+i321+i321+i321+i3−1−i32−1−i321+i3−1−i3−1−i30003−i32−3+i323−i323−i32−3+i32−3+i32−1−i32−1−i321+i300001+i321+i32−1−i32−1−i32000003−i32−3+i32000000−1+i3−1+i3−1+i3−1+i3−1+i31−i321−i31−i3−1+i3−1+i31−i321−i321−i32−1+i31−i321−i321−i321−i321−i3−1+i32−1+i321−i3−1+i3−1+i3000−3−i323+i32−3−i32−3−i323+i323+i32−1+i32−1+i321−i300001−i321−i32−1+i32−1+i3200000−3−i323+i32000000
χ13122222-1-2-222-1-1-12-1-1-1-1-211-2-2-2000−i3i3−i3−i3i3i3112000011-1-100000i3−i3000000−1−i3−1−i3−1−i3−1−i3−1−i31+i321+i31+i3−1−i3−1−i31+i321+i321+i32−1−i31+i321+i321+i321+i321+i3−1−i32−1−i321+i31+i31+i3000−3+i323−i32−3+i32−3+i323−i323−i32−1−i32−1−i32−1−i30000−1−i32−1−i321+i321+i32000003−i32−3+i32000000−1+i3−1+i3−1+i3−1+i3−1+i31−i321−i31−i3−1+i3−1+i31−i321−i321−i32−1+i31−i321−i321−i321−i321−i3−1+i32−1+i321−i31−i31−i30003+i32−3−i323+i323+i32−3−i32−3−i32−1+i32−1+i32−1+i30000−1+i32−1+i321−i321−i3200000−3−i323+i32000000
χ13222222-1-2-222-1-1-12-1-1-1-1-211-2-2-2000i3−i3i3i3−i3−i3112000011-1-100000−i3i3000000−1−i3−1−i3−1−i3−1−i3−1−i31+i321+i31+i3−1−i3−1−i31+i321+i321+i32−1−i31+i321+i321+i321+i321+i3−1−i32−1−i321+i31+i31+i30003−i32−3+i323−i323−i32−3+i32−3+i32−1−i32−1−i32−1−i30000−1−i32−1−i321+i321+i3200000−3+i323−i32000000−1+i3−1+i3−1+i3−1+i3−1+i31−i321−i31−i3−1+i3−1+i31−i321−i321−i32−1+i31−i321−i321−i321−i321−i3−1+i32−1+i321−i31−i31−i3000−3−i323+i32−3−i32−3−i323+i323+i32−1+i32−1+i32−1+i30000−1+i32−1+i321−i321−i32000003+i32−3−i32000000
χ1332222-1222-1-1222-1-1-1-1-1-122-1002-1-122-1-1-1-1-1-1022220000-1-1-1-1000-1-10000−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i321+i32−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i32−1−i3−1−i31+i3200−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i320−1−i3−1−i3−1−i3−1−i300001+i321+i321+i321+i320001+i321+i320000−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i321−i32−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i32−1+i3−1+i31−i3200−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i320−1+i3−1+i3−1+i3−1+i300001−i321−i321−i321−i320001−i321−i320000
χ1342222-1222-1-1222-1-1-1-1-1-122-1002-1-122-1-1-1-1-1-10-2-2-2-200001111000110000−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i321+i32−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i32−1−i3−1−i31+i3200−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i3201+i31+i31+i31+i30000−1−i32−1−i32−1−i32−1−i32000−1−i32−1−i320000−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i321−i32−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i32−1+i3−1+i31−i3200−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i3201−i31−i31−i31−i30000−1+i32−1+i32−1+i32−1+i32000−1+i32−1+i320000
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χ1362222-1222-1-1222-1-1-1-1-1-122-100-211-2-21111-1-10-2-2220000-1-1-1-1000110000−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i321+i32−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i32−1−i3−1−i31+i32001+i3−1−i32−1−i321+i31+i3−1−i32−1−i32−1−i32−1−i321+i321+i3201+i31+i3−1−i3−1−i300001+i321+i321+i321+i32000−1−i32−1−i320000−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i321−i32−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i32−1+i3−1+i31−i32001−i3−1+i32−1+i321−i31−i3−1+i32−1+i32−1+i32−1+i321−i321−i3201−i31−i3−1+i3−1+i300001−i321−i321−i321−i32000−1+i32−1+i320000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.