Finite Group Databasebeta

← Group #13158581

Character table — Group #13158581

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171
size111122222222224444444466888888888881212121212121212121212121224242424243636363611112222222222444444446688888888888121212121212121212121212122424242424363636361111222222222244444444668888888888812121212121212121212121212242424242436363636
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χ3111111111111111111111111-1-1-1-1-111-1-1-1-1111-1-11111-1-1-1-1-1-1-11111-1-1111111111111111111111111-1-1-1-1-111-1-1-1-1111-1-11111-1-1-1-1-1-1-11111-1-1111111111111111111111111-1-1-1-1-111-1-1-1-1111-1-11111-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111-1-1-1-1-111-1-1-1-1-1-111111111111-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-111-1-1-1-1-1-111111111111-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-111-1-1-1-1-1-111111111111-1-1-1-1-1-1-111
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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
χ1211111111111111111111111-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111-1-111−1−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+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+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−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−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
χ1221111111111111111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1-1-11111111-1-111-1-1−1−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+i32−1−i32−1−i321+i321+i321+i321+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−i32−1+i32−1+i321−i321−i321−i321−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
χ123222222-2-22222222222-2-2-2-22200000-2-2000000-20022-2-20000000000000−1−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−i3000001+i31+i30000001+i300−1−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+i3000001−i31−i30000001−i300−1+i3−1+i31−i31−i30000000000000
χ124222222-2-22222222222-2-2-2-2-2-200000-2-2000000200-2-2220000000000000−1−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+i3000001+i31+i3000000−1−i3001+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−i3000001−i31−i3000000−1+i3001−i31−i3−1+i3−1+i30000000000000
χ12522222-12222-1-1-12-1-1-1-1-1-122222-1-122-1-1-1-1-1-100200-1-1-1-100002-1-1000000−1−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+i321+i321+i32−1−i3−1−i3−1−i3−1−i3−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i3200−1−i3001+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−i321−i321−i32−1+i3−1+i3−1+i3−1+i3−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i3200−1+i3001−i321−i321−i321−i320000−1+i31−i321−i32000000
χ12622222-12222-1-1-12-1-1-1-1-1-12222-211-2-2-1-1111100200-1-1-1-10000-211000000−1−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+i321+i321+i32−1−i3−1−i3−1−i3−1−i31+i3−1−i32−1−i321+i31+i31+i321+i32−1−i32−1−i32−1−i32−1−i3200−1−i3001+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−i321−i321−i32−1+i3−1+i3−1+i3−1+i31−i3−1+i32−1+i321−i31−i31−i321−i32−1+i32−1+i32−1+i32−1+i3200−1+i3001−i321−i321−i321−i3200001−i3−1+i32−1+i32000000
χ12722222-12222-1-1-12-1-1-1-1-1-122-2-22-1-122-1-1-1-1-1-100-20011110000-211000000−1−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+i321+i321+i32−1−i3−1−i31+i31+i3−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i32001+i300−1−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−i321−i321−i32−1+i3−1+i31−i31−i3−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i32001−i300−1+i32−1+i32−1+i32−1+i3200001−i3−1+i32−1+i32000000
χ12822222-12222-1-1-12-1-1-1-1-1-122-2-2-211-2-2-1-1111100-200111100002-1-1000000−1−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+i321+i321+i32−1−i3−1−i31+i31+i31+i3−1−i32−1−i321+i31+i31+i321+i32−1−i32−1−i32−1−i32−1−i32001+i300−1−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−i321−i321−i32−1+i3−1+i31−i31−i31−i3−1+i32−1+i321−i31−i31−i321−i32−1+i32−1+i32−1+i32−1+i32001−i300−1+i32−1+i32−1+i32−1+i320000−1+i31−i321−i32000000
χ12922222-1-2-222-1-1-12-1-1-1-111-2-2220−i3i30011−i3−i3i3i300-200-1-11100000−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+i32−1−i32−1−i321+i31+i3−1−i3−1−i30−3+i323−i3200−1−i32−1−i32−3+i32−3+i323−i323−i32001+i3001+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−i32−1+i32−1+i321−i31−i3−1+i3−1+i303+i32−3−i3200−1+i32−1+i323+i323+i32−3−i32−3−i32001−i3001−i321−i32−1+i32−1+i32000003+i32−3−i32000000
χ13022222-1-2-222-1-1-12-1-1-1-111-2-2220i3−i30011i3i3−i3−i300-200-1-11100000i3−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+i32−1−i32−1−i321+i31+i3−1−i3−1−i303−i32−3+i3200−1−i32−1−i323−i323−i32−3+i32−3+i32001+i3001+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−i32−1+i32−1+i321−i31−i3−1+i3−1+i30−3−i323+i3200−1+i32−1+i32−3−i32−3−i323+i323+i32001−i3001−i321−i32−1+i32−1+i3200000−3−i323+i32000000
χ13122222-1-2-222-1-1-12-1-1-1-111-2-2-2-20−i3i30011−i3−i3i3i30020011-1-100000i3−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+i32−1−i32−1−i321+i31+i31+i31+i30−3+i323−i3200−1−i32−1−i32−3+i32−3+i323−i323−i3200−1−i300−1−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−i32−1+i32−1+i321−i31−i31−i31−i303+i32−3−i3200−1+i32−1+i323+i323+i32−3−i32−3−i3200−1+i300−1+i32−1+i321−i321−i3200000−3−i323+i32000000
χ13222222-1-2-222-1-1-12-1-1-1-111-2-2-2-20i3−i30011i3i3−i3−i30020011-1-100000−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+i32−1−i32−1−i321+i31+i31+i31+i303−i32−3+i3200−1−i32−1−i323−i323−i32−3+i32−3+i3200−1−i300−1−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−i32−1+i32−1+i321−i31−i31−i31−i30−3−i323+i3200−1+i32−1+i32−3−i32−3−i323+i323+i3200−1+i300−1+i32−1+i321−i321−i32000003+i32−3−i32000000
χ1332222-1222-1-1222-1-1-1-1-122-1-100222-1-1-1-1-1-1-1-1220220000-1-1-1-1000-1-10000−1−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+i32−1−i3−1−i31+i321+i3200−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i32−1−i3−1−i30−1−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−i32−1+i3−1+i31−i321−i3200−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i32−1+i3−1+i30−1+i3−1+i300001−i321−i321−i321−i320001−i321−i320000
χ1342222-1222-1-1222-1-1-1-1-122-1-100222-1-1-1-1-1-1-1-1-2-20-2-200001111000110000−1−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+i32−1−i3−1−i31+i321+i3200−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i321+i31+i301+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−i32−1+i3−1+i31−i321−i3200−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i321−i31−i301−i31−i30000−1+i32−1+i32−1+i32−1+i32000−1+i32−1+i320000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.