Finite Group Databasebeta

← Group #13060790

Character table — Group #13060790

Order 1344.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106
size111122222233333333666666666666666666666666666666666666666666666666666666666666666666662828282828282828565656565656565656565656
order124424888877141428282828224488881414141414141414141414141414282828282828282828282828282856565656565656565656565656565656565656565656565656565656565656563366121212126612122424242424242424
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32
χ311111111111111111111111111111111111111111111111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32
χ4111111-1-1-1-1111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ5111111-1-1-1-1111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1−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−i32
χ6111111-1-1-1-1111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1+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+i32
χ71111-1-111-1-1111111111-11-111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1
χ81111-1-111-1-1111111111-11-111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32
χ91111-1-111-1-1111111111-11-111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32
χ101111-1-1-1-111111111111-11-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-111-1-111
χ111111-1-1-1-111111111111-11-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−1−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
χ121111-1-1-1-111111111111-11-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−1+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
χ1311-1-11-1i−ii−i1111-1-1-1-1-1-111i−ii−i-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-111-1-1i−ii−ii−ii−i
χ1411-1-11-1i−ii−i1111-1-1-1-1-1-111i−ii−i-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321+i321−i32ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79
χ1511-1-11-1i−ii−i1111-1-1-1-1-1-111i−ii−i-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−i321+i32ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83
χ1611-1-11-1−ii−ii1111-1-1-1-1-1-111−ii−ii-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-111-1-1−ii−ii−ii−ii
χ1711-1-11-1−ii−ii1111-1-1-1-1-1-111−ii−ii-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321+i321−i32−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79
χ1811-1-11-1−ii−ii1111-1-1-1-1-1-111−ii−ii-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−i321+i32−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83
χ1911-1-1-11i−i−ii1111-1-1-1-1-111-1i−i−ii-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1-1-111i−i−iii−i−ii
χ2011-1-1-11i−i−ii1111-1-1-1-1-111-1i−i−ii-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321−i32−1−i32−1+i32ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79
χ2111-1-1-11i−i−ii1111-1-1-1-1-111-1i−i−ii-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321+i32−1+i32−1−i32ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83
χ2211-1-1-11−iii−i1111-1-1-1-1-111-1−iii−i-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1-1-111−iii−i−iii−i
χ2311-1-1-11−iii−i1111-1-1-1-1-111-1−iii−i-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321−i32−1−i32−1+i32−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79
χ2411-1-1-11−iii−i1111-1-1-1-1-111-1−iii−i-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321+i32−1+i32−1−i32−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83
χ25333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13333-1-1-1-1-1-133-1-1-1-1-1-133-1-1-1-1-1-133-1-1-1-1-1-100000000000000000000
χ263333333333−1−i72−1+i72−1−i72−1+i72−1−i72−1−i72−1+i72−1+i7233333333−1−i72−1−i72−1−i72−1+i72−1+i72−1+i72−1−i72−1+i72−1−i72−1−i72−1−i72−1+i72−1+i72−1+i72−1−i72−1−i72−1−i72−1+i72−1+i72−1+i72−1−i72−1−i72−1−i72−1+i72−1+i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1−i72−1−i72−1+i72−1+i72−1+i72−1−i72−1+i72−1−i72−1−i72−1−i72−1+i72−1+i72−1+i72−1−i72−1+i72−1−i72−1−i72−1−i72−1+i72−1+i72−1+i72−1−i72−1+i72−1−i72−1−i72−1−i72−1+i72−1+i72−1+i7200000000000000000000
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Here ζ is a primitive root of unity of order 84 (ζ84 = 1); i = ζ21.