Finite Group Databasebeta

← Group #72276589

Character table — Group #72276589

Order 2688.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130
size11112222224444888888888888333366666612121212242424242424242424242424333366666612121212242424242424242424242424777714141414141428282828565656565656565656565656777714141414141428282828565656565656565656565656
order12222222222222224444444444714141414141414141414141414141428282828282828282828714141414141414141414141414141428282828282828282828366666666666666612121212121212121212366666666666666612121212121212121212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111-1-1-11-111-1-1-1-1111111111111111-1-1-11-111-1-1-1-1111111111111111-1-1-11-111-1-1-1-1111111111111111-1-1-11-111-1-1-1-1111111111111111-1-1-11-111-1-1-1-1
χ311111111111111-11-1-1-11-1-111-1-111111111111111-11-1-1-11-1-111-1-111111111111111-11-1-1-11-1-111-1-111111111111111-11-1-1-11-1-111-1-111111111111111-11-1-1-11-1-111-1-1
χ411111111111111-1-111-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-111
χ51111111111-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1
χ61111111111-1-1-1-11-1-1-11-1-1-111111111111111-1-1-1-11-1-1-11-1-1-111111111111111-1-1-1-11-1-1-11-1-1-111111111111111-1-1-1-11-1-1-11-1-1-111111111111111-1-1-1-11-1-1-11-1-1-11111
χ71111111111-1-1-1-1-11-1-1-1111-1-1111111111111-1-1-1-1-11-1-1-1111-1-1111111111111-1-1-1-1-11-1-1-1111-1-1111111111111-1-1-1-1-11-1-1-1111-1-1111111111111-1-1-1-1-11-1-1-1111-1-111
χ81111111111-1-1-1-1-1-111-1-11111-1-11111111111-1-1-1-1-1-111-1-11111-1-11111111111-1-1-1-1-1-111-1-11111-1-11111111111-1-1-1-1-1-111-1-11111-1-11111111111-1-1-1-1-1-111-1-11111-1-1
χ922222-2-22-2-20000002-20000000022222-2-22-2-20000002-20000000022222-2-22-2-20000002-20000000022222-2-22-2-20000002-20000000022222-2-22-2-20000002-200000000
χ1022222-2-22-2-2000000-220000000022222-2-22-2-2000000-220000000022222-2-22-2-2000000-220000000022222-2-22-2-2000000-220000000022222-2-22-2-2000000-2200000000
χ112222-22-2-22-2000002000-20000002222-22-2-22-2000002000-20000002222-22-2-22-2000002000-20000002222-22-2-22-2000002000-20000002222-22-2-22-2000002000-2000000
χ122222-22-2-22-200000-200020000002222-22-2-22-200000-200020000002222-22-2-22-200000-200020000002222-22-2-22-200000-200020000002222-22-2-22-200000-20002000000
χ132222-2-22-2-2200002000-200000002222-2-22-2-2200002000-200000002222-2-22-2-2200002000-200000002222-2-22-2-2200002000-200000002222-2-22-2-2200002000-20000000
χ142222-2-22-2-220000-2000200000002222-2-22-2-220000-2000200000002222-2-22-2-220000-2000200000002222-2-22-2-220000-2000200000002222-2-22-2-220000-200020000000
χ152-2-22222-2-2-2000000000000002i−2i2-2-22222-2-2-2000000000000002i−2i2-2-22222-2-2-2000000000000002i−2i2-2-22222-2-2-2000000000000002i−2i2-2-22222-2-2-2000000000000002i−2i
χ162-2-22222-2-2-200000000000000−2i2i2-2-22222-2-2-200000000000000−2i2i2-2-22222-2-2-200000000000000−2i2i2-2-22222-2-2-200000000000000−2i2i2-2-22222-2-2-200000000000000−2i2i
χ172-2-222-2-2-22222-2-20000000000002-2-222-2-2-22222-2-20000000000002-2-222-2-2-22222-2-20000000000002-2-222-2-2-22222-2-20000000000002-2-222-2-2-22222-2-2000000000000
χ182-2-222-2-2-222-2-2220000000000002-2-222-2-2-222-2-2220000000000002-2-222-2-2-222-2-2220000000000002-2-222-2-2-222-2-2220000000000002-2-222-2-2-222-2-222000000000000
χ192-2-22-22-22-2200000000002-200002-2-22-22-22-2200000000002-200002-2-22-22-22-2200000000002-200002-2-22-22-22-2200000000002-200002-2-22-22-22-2200000000002-20000
χ202-2-22-22-22-220000000000-2200002-2-22-22-22-220000000000-2200002-2-22-22-22-220000000000-2200002-2-22-22-22-220000000000-2200002-2-22-22-22-220000000000-220000
χ212-2-22-2-2222-20000000000002-2002-2-22-2-2222-20000000000002-2002-2-22-2-2222-20000000000002-2002-2-22-2-2222-20000000000002-2002-2-22-2-2222-20000000000002-200
χ222-2-22-2-2222-2000000000000-22002-2-22-2-2222-2000000000000-22002-2-22-2-2222-2000000000000-22002-2-22-2-2222-2000000000000-22002-2-22-2-2222-2000000000000-2200
χ2344-4-40000002-22-200000000000044-4-40000002-22-200000000000044-4-40000002-22-200000000000044-4-40000002-22-200000000000044-4-40000002-22-2000000000000
χ2444-4-4000000-22-2200000000000044-4-4000000-22-2200000000000044-4-4000000-22-2200000000000044-4-4000000-22-2200000000000044-4-4000000-22-22000000000000
χ254-44-40000002-2-220000000000004-44-40000002-2-220000000000004-44-40000002-2-220000000000004-44-40000002-2-220000000000004-44-40000002-2-22000000000000
χ264-44-4000000-222-20000000000004-44-4000000-222-20000000000004-44-4000000-222-20000000000004-44-4000000-222-20000000000004-44-4000000-222-2000000000000
χ27111111111111111111111111111111111111111111111111111111111111111111111111111111−1+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−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
χ28111111111111111-1-1-11-111-1-1-1-1111111111111111-1-1-11-111-1-1-1-1111111111111111-1-1-11-111-1-1-1-1−1+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+i321−i321−i321−i32−1+i321−i32−1+i32−1+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−i321+i321+i321+i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i32
χ2911111111111111-11-1-1-11-1-111-1-111111111111111-11-1-1-11-1-111-1-111111111111111-11-1-1-11-1-111-1-1−1+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+i321−i32−1+i321−i321−i321−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−i321+i32−1−i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32
χ3011111111111111-1-111-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-111−1+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+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+i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32
χ311111111111-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32
χ321111111111-1-1-1-11-1-1-11-1-1-111111111111111-1-1-1-11-1-1-11-1-1-111111111111111-1-1-1-11-1-1-11-1-1-11111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i321−i321−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−i321+i321+i321+i321+i32−1−i321+i321+i321+i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32
χ331111111111-1-1-1-1-11-1-1-1111-1-1111111111111-1-1-1-1-11-1-1-1111-1-1111111111111-1-1-1-1-11-1-1-1111-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i321−i321−i321−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−i321+i321+i321+i321+i321+i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32
χ341111111111-1-1-1-1-1-111-1-11111-1-11111111111-1-1-1-1-1-111-1-11111-1-11111111111-1-1-1-1-1-111-1-11111-1-1−1+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+i32−1+i321−i321−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−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ3522222-2-22-2-20000002-20000000022222-2-22-2-20000002-20000000022222-2-22-2-20000002-200000000−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i31−i3000000−1+i31−i300000000−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i31+i3000000−1−i31+i300000000
χ3622222-2-22-2-2000000-220000000022222-2-22-2-2000000-220000000022222-2-22-2-2000000-2200000000−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i31−i30000001−i3−1+i300000000−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i31+i30000001+i3−1−i300000000
χ372222-22-2-22-2000002000-20000002222-22-2-22-2000002000-20000002222-22-2-22-2000002000-2000000−1+i3−1+i3−1+i3−1+i31−i3−1+i31−i31−i3−1+i31−i300000−1+i30001−i3000000−1−i3−1−i3−1−i3−1−i31+i3−1−i31+i31+i3−1−i31+i300000−1−i30001+i3000000
χ382222-22-2-22-200000-200020000002222-22-2-22-200000-200020000002222-22-2-22-200000-20002000000−1+i3−1+i3−1+i3−1+i31−i3−1+i31−i31−i3−1+i31−i3000001−i3000−1+i3000000−1−i3−1−i3−1−i3−1−i31+i3−1−i31+i31+i3−1−i31+i3000001+i3000−1−i3000000
χ392222-2-22-2-2200002000-200000002222-2-22-2-2200002000-200000002222-2-22-2-2200002000-20000000−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i31−i3−1+i30000−1+i30001−i30000000−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i31+i3−1−i30000−1−i30001+i30000000
χ402222-2-22-2-220000-2000200000002222-2-22-2-220000-2000200000002222-2-22-2-220000-200020000000−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i31−i3−1+i300001−i3000−1+i30000000−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i31+i3−1−i300001+i3000−1−i30000000
χ412-2-22222-2-2-2000000000000002i−2i2-2-22222-2-2-2000000000000002i−2i2-2-22222-2-2-2000000000000002i−2i−1+i31−i31−i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i3000000000000002ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ79−1−i31+i31+i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i3000000000000002ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ83
χ422-2-22222-2-2-200000000000000−2i2i2-2-22222-2-2-200000000000000−2i2i2-2-22222-2-2-200000000000000−2i2i−1+i31−i31−i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i300000000000000−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−1−i31+i31+i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i300000000000000−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83
χ432-2-222-2-2-22222-2-20000000000002-2-222-2-2-22222-2-20000000000002-2-222-2-2-22222-2-2000000000000−1+i31−i31−i3−1+i3−1+i31−i31−i31−i3−1+i3−1+i3−1+i3−1+i31−i31−i3000000000000−1−i31+i31+i3−1−i3−1−i31+i31+i31+i3−1−i3−1−i3−1−i3−1−i31+i31+i3000000000000
χ442-2-222-2-2-222-2-2220000000000002-2-222-2-2-222-2-2220000000000002-2-222-2-2-222-2-222000000000000−1+i31−i31−i3−1+i3−1+i31−i31−i31−i3−1+i3−1+i31−i31−i3−1+i3−1+i3000000000000−1−i31+i31+i3−1−i3−1−i31+i31+i31+i3−1−i3−1−i31+i31+i3−1−i3−1−i3000000000000
χ452-2-22-22-22-2200000000002-200002-2-22-22-22-2200000000002-200002-2-22-22-22-2200000000002-20000−1+i31−i31−i3−1+i31−i3−1+i31−i3−1+i31−i3−1+i30000000000−1+i31−i30000−1−i31+i31+i3−1−i31+i3−1−i31+i3−1−i31+i3−1−i30000000000−1−i31+i30000
χ462-2-22-22-22-220000000000-2200002-2-22-22-22-220000000000-2200002-2-22-22-22-220000000000-220000−1+i31−i31−i3−1+i31−i3−1+i31−i3−1+i31−i3−1+i300000000001−i3−1+i30000−1−i31+i31+i3−1−i31+i3−1−i31+i3−1−i31+i3−1−i300000000001+i3−1−i30000
χ472-2-22-2-2222-20000000000002-2002-2-22-2-2222-20000000000002-2002-2-22-2-2222-20000000000002-200−1+i31−i31−i3−1+i31−i31−i3−1+i3−1+i3−1+i31−i3000000000000−1+i31−i300−1−i31+i31+i3−1−i31+i31+i3−1−i3−1−i3−1−i31+i3000000000000−1−i31+i300
χ482-2-22-2-2222-2000000000000-22002-2-22-2-2222-2000000000000-22002-2-22-2-2222-2000000000000-2200−1+i31−i31−i3−1+i31−i31−i3−1+i3−1+i3−1+i31−i30000000000001−i3−1+i300−1−i31+i31+i3−1−i31+i31+i3−1−i3−1−i3−1−i31+i30000000000001+i3−1−i300
χ4944-4-40000002-22-200000000000044-4-40000002-22-200000000000044-4-40000002-22-2000000000000−2+2i3−2+2i32−2i32−2i3000000−1+i31−i3−1+i31−i3000000000000−2−2i3−2−2i32+2i32+2i3000000−1−i31+i3−1−i31+i3000000000000
χ5044-4-4000000-22-2200000000000044-4-4000000-22-2200000000000044-4-4000000-22-22000000000000−2+2i3−2+2i32−2i32−2i30000001−i3−1+i31−i3−1+i3000000000000−2−2i3−2−2i32+2i32+2i30000001+i3−1−i31+i3−1−i3000000000000
χ514-44-40000002-2-220000000000004-44-40000002-2-220000000000004-44-40000002-2-22000000000000−2+2i32−2i3−2+2i32−2i3000000−1+i31−i31−i3−1+i3000000000000−2−2i32+2i3−2−2i32+2i3000000−1−i31+i31+i3−1−i3000000000000
χ524-44-4000000-222-20000000000004-44-4000000-222-20000000000004-44-4000000-222-2000000000000−2+2i32−2i3−2+2i32−2i30000001−i3−1+i3−1+i31−i3000000000000−2−2i32+2i3−2−2i32+2i30000001+i3−1−i3−1−i31+i3000000000000
χ53111111111111111111111111111111111111111111111111111111111111111111111111111111−1−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+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
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Here ζ is a primitive root of unity of order 84 (ζ84 = 1); i = ζ21.