Finite Group Databasebeta

← Group #13158509

Character table — Group #13158509

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171
size111122222222224444444444888888888812121212121212121212121218182424242424243636361111222222222244444444448888888888121212121212121212121212181824242424242436363611112222222222444444444488888888881212121212121212121212121818242424242424363636
order12223344666666223666121212126666666612128888242424242424242444441212121244436663312126666666636661212121266666666121224242424242424242424242412121212121212121212123666331212666666663666121212126666666612122424242424242424242424241212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-11111-1-1-1-1-1-11-111-1-1-1-1-1111111111111111111111111111111111111-1-11111-1-1-1-1-1-11-111-1-1-1-1-1111111111111111111111111111111111111-1-11111-1-1-1-1-1-11-111-1-1-1-1-1
χ31111111111111111111111111111111111-1-111-1-1-1-11111-1-1-11-1-111-1-1-11111111111111111111111111111111111-1-111-1-1-1-11111-1-1-11-1-111-1-1-11111111111111111111111111111111111-1-111-1-1-1-11111-1-1-11-1-111-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111
χ511111111111111-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11-1-111111111111111-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11-1-111111111111111-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11-1-1
χ611111111111111-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-11-1-111-11111111111111111-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-11-1-111-11111111111111111-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-11-1-111-111
χ711111111111111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-11-111-1-1-11111111111111111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-11-111-1-1-11111111111111111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-11-111-1-1-111
χ811111111111111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111111111111111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111111111111111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1
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χ6822222-12222-1-12-122-1-1-1-12-12-122-1-1-1-1-1-1-1-100220000-1-1-1-1000200-1-1000−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i3−1+i31−i321−i32−1+i31−i32−1+i3−1+i31−i321−i321−i321−i32−1+i31−i32−1+i31−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i3200−1+i3−1+i300001−i321−i321−i321−i32000−1+i3001−i321−i32000−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i3−1−i31+i321+i32−1−i31+i32−1−i3−1−i31+i321+i321+i321+i32−1−i31+i32−1−i31+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i3200−1−i3−1−i300001+i321+i321+i321+i32000−1−i3001+i321+i32000
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χ11911111111111111-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11-1-1−1−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−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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−i321+i321+i321+i321+i321+i321+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+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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+i321−i321−i321−i321−i321−i321−i32−1+i321−i321−i32
χ12011111111111111-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-11-1-111-111−1−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−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−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+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i32
χ12111111111111111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-11-111-1-1-111−1−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−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32−1−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+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32
χ12211111111111111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1−1−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−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−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−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+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+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+i321−i321−i32
χ123222222-2-2222222002222-2-2-2-200000000-2-200000000000022000000-200−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i300−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3000000001+i31+i3000000000000−1−i3−1−i30000001+i300−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i300−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3000000001−i31−i3000000000000−1+i3−1+i30000001−i300
χ124222222-2-2222222002222-2-2-2-200000000-2-2000000000000-2-2000000200−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i300−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3000000001+i31+i30000000000001+i31+i3000000−1−i300−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i300−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3000000001−i31−i30000000000001−i31−i3000000−1+i300
χ12522222-12222-1-12-122-1-1-1-12-12-122-1-1-1-1-1-1-1-100220000-1-1-1-1000200-1-1000−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i3−1−i31+i321+i32−1−i31+i32−1−i3−1−i31+i321+i321+i321+i32−1−i31+i32−1−i31+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i3200−1−i3−1−i300001+i321+i321+i321+i32000−1−i3001+i321+i32000−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i3−1+i31−i321−i32−1+i31−i32−1+i3−1+i31−i321−i321−i321−i32−1+i31−i32−1+i31−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i3200−1+i3−1+i300001−i321−i321−i321−i32000−1+i3001−i321−i32000
χ12622222-12222-1-12-122-1-1-1-12-12-122-1-1-1-1-1-1-1-100-2-200001111000-20011000−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i3−1−i31+i321+i32−1−i31+i32−1−i3−1−i31+i321+i321+i321+i32−1−i31+i32−1−i31+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i32001+i31+i30000−1−i32−1−i32−1−i32−1−i320001+i300−1−i32−1−i32000−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i3−1+i31−i321−i32−1+i31−i32−1+i3−1+i31−i321−i321−i321−i32−1+i31−i32−1+i31−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i32001−i31−i30000−1+i32−1+i32−1+i32−1+i320001−i300−1+i32−1+i32000
χ12722222-12222-1-12-1-2-2-1-1-1-12-12-1-2-2111111-1-100220000-1-1-1-1000-20011000−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i3−1−i31+i321+i32−1−i31+i321+i31+i31+i321+i321+i321+i32−1−i31+i32−1−i31+i321+i31+i3−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i3200−1−i3−1−i300001+i321+i321+i321+i320001+i300−1−i32−1−i32000−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i3−1+i31−i321−i32−1+i31−i321−i31−i31−i321−i321−i321−i32−1+i31−i32−1+i31−i321−i31−i3−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i3200−1+i3−1+i300001−i321−i321−i321−i320001−i300−1+i32−1+i32000
χ12822222-12222-1-12-1-2-2-1-1-1-12-12-1-2-2111111-1-100-2-200001111000200-1-1000−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i3−1−i31+i321+i32−1−i31+i321+i31+i31+i321+i321+i321+i32−1−i31+i32−1−i31+i321+i31+i3−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32001+i31+i30000−1−i32−1−i32−1−i32−1−i32000−1−i3001+i321+i32000−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i3−1+i31−i321−i32−1+i31−i321−i31−i31−i321−i321−i321−i32−1+i31−i32−1+i31−i321−i31−i3−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32001−i31−i30000−1+i32−1+i32−1+i32−1+i32000−1+i3001−i321−i32000
χ1292222-1222-1-122-1222-1-1-1-1-12-12-1-122-1-1-1-1-1-12200-1-1-1-100000020-1-100000−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i321+i32−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i321+i321+i32−1−i31+i32−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i32−1−i3−1−i3001+i321+i321+i321+i32000000−1−i301+i321+i3200000−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i321−i32−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i321−i321−i32−1+i31−i32−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i32−1+i3−1+i3001−i321−i321−i321−i32000000−1+i301−i321−i3200000
χ1302222-1222-1-122-1222-1-1-1-1-12-12-1-122-1-1-1-1-1-1-2-2001111000000-201100000−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i321+i32−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i321+i321+i32−1−i31+i32−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i31+i300−1−i32−1−i32−1−i32−1−i320000001+i30−1−i32−1−i3200000−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i321−i32−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i321−i321−i32−1+i31−i32−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i31−i300−1+i32−1+i32−1+i32−1+i320000001−i30−1+i32−1+i3200000
χ1312222-1222-1-122-12-2-2-1-1-1-1-12-1211-2-21111-1-12200-1-1-1-1000000-201100000−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i321+i32−1−i3−1−i31+i32−1−i31+i31+i31+i321+i321+i321+i321+i32−1−i31+i32−1−i3−1−i32−1−i321+i31+i3−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i3−1−i3001+i321+i321+i321+i320000001+i30−1−i32−1−i3200000−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i321−i32−1+i3−1+i31−i32−1+i31−i31−i31−i321−i321−i321−i321−i32−1+i31−i32−1+i3−1+i32−1+i321−i31−i3−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i3−1+i3001−i321−i321−i321−i320000001−i30−1+i32−1+i3200000
χ1322222-1222-1-122-12-2-2-1-1-1-1-12-1211-2-21111-1-1-2-200111100000020-1-100000−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i321+i32−1−i3−1−i31+i32−1−i31+i31+i31+i321+i321+i321+i321+i32−1−i31+i32−1−i3−1−i32−1−i321+i31+i3−1−i32−1−i32−1−i32−1−i321+i321+i321+i31+i300−1−i32−1−i32−1−i32−1−i32000000−1−i301+i321+i3200000−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i321−i32−1+i3−1+i31−i32−1+i31−i31−i31−i321−i321−i321−i321−i32−1+i31−i32−1+i3−1+i32−1+i321−i31−i3−1+i32−1+i32−1+i32−1+i321−i321−i321−i31−i300−1+i32−1+i32−1+i32−1+i32000000−1+i301−i321−i3200000
χ1332-22-2222-2-2-2-2-222002-2-2222-2-2000000002-20000000000000000000002i−2i−1−i31+i3−1−i31+i3−1−i3−1−i3−1−i31+i31+i31+i31+i31+i3−1−i3−1−i300−1−i31+i31+i3−1−i3−1−i3−1−i31+i31+i300000000−1−i31+i30000000000000000000002ζ22−2ζ22−1+i31−i3−1+i31−i3−1+i3−1+i3−1+i31−i31−i31−i31−i31−i3−1+i3−1+i300−1+i31−i31−i3−1+i3−1+i3−1+i31−i31−i300000000−1+i31−i30000000000000000000002ζ14−2ζ14
χ1342-22-2222-2-2-2-2-222002-2-2222-2-2000000002-2000000000000000000000−2i2i−1−i31+i3−1−i31+i3−1−i3−1−i3−1−i31+i31+i31+i31+i31+i3−1−i3−1−i300−1−i31+i31+i3−1−i3−1−i3−1−i31+i31+i300000000−1−i31+i3000000000000000000000−2ζ222ζ22−1+i31−i3−1+i31−i3−1+i3−1+i3−1+i31−i31−i31−i31−i31−i3−1+i3−1+i300−1+i31−i31−i3−1+i3−1+i3−1+i31−i31−i300000000−1+i31−i3000000000000000000000−2ζ142ζ14
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.