Finite Group Databasebeta

← Group #13062317

Character table — Group #13062317

Order 1344.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106
size111122222233333333666666666666666666666666666666666666666666666666666666666666666666662828282828282828565656565656565656565656
order12442224447714142828282822224444141414141414141414141414141414141414141414141414141414141414282828282828282828282828282828282828282828282828282828282828336612121212666666121212121212
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
χ411111-1-11-1-11111111111-1-111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-11-1-11-1-1
χ511111-1-11-1-11111111111-1-111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i32
χ611111-1-11-1-11111111111-1-111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i32
χ71111-11-1-11-1111111111-11-11-11-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-11-1-11-1-11-1-11-1
χ81111-11-1-11-1111111111-11-11-11-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i32−1−i321+i321−i32−1+i321−i321+i32−1−i321+i321−i32−1+i321−i32
χ91111-11-1-11-1111111111-11-11-11-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i32−1+i321−i321+i32−1−i321+i321−i32−1+i321−i321+i32−1−i321+i32
χ101111-1-11-1-11111111111-1-111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11-1-11-1-11-1-11
χ111111-1-11-1-11111111111-1-111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i32−1−i321−i321−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32
χ121111-1-11-1-11111111111-1-111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i32−1+i321+i321+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32
χ1311-1-111-1-1-111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1111111111111-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-111-111-1-1-11-1-11
χ1411-1-111-1-1-111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1111111111111-1-1111111-1-111-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i321+i321+i32−1−i321−i321−i32−1+i32
χ1511-1-111-1-1-111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1111111111111-1-1111111-1-111-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i321−i321−i32−1+i321+i321+i32−1−i32
χ1611-1-11-11-11-11111-1-1-1-1-1-11-111-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-11-111-11-11-1-11-1
χ1711-1-11-11-11-11111-1-1-1-1-1-11-111-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1111111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i321+i32−1−i32−1+i321−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32
χ1811-1-11-11-11-11111-1-1-1-1-1-11-111-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1111111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i321−i32−1+i32−1−i321+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32
χ1911-1-1-1111-1-11111-1-1-1-1-11-1-11-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-111-1111-1-11-1-1
χ2011-1-1-1111-1-11111-1-1-1-1-11-1-11-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1111111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i32−1−i32−1−i321−i32−1+i32−1+i32−1−i321+i321+i32−1+i321−i321−i32
χ2111-1-1-1111-1-11111-1-1-1-1-11-1-11-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1111111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i32−1+i32−1+i321+i32−1−i32−1−i32−1+i321−i321−i32−1−i321+i321+i32
χ2211-1-1-1-1-11111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111111111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ2311-1-1-1-1-11111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111111111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321+i321−i321−i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ2411-1-1-1-1-11111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111111111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321−i321+i321+i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ25333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-1-1-13333-1-1-1-1-1-100000000000000000000
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
χ273333333333−1−i72−1+i72−1−i72−1+i72−1−i72−1−i72−1+i72−1+i72-1-1-1-1-1-1-1-1ζ2−ζ22−ζ46−ζ50+ζ58−ζ74−ζ2−ζ22+ζ46−ζ50−ζ58+ζ74−ζ2+ζ22−ζ46+ζ50−ζ58−ζ74−ζ10−ζ26+ζ34−ζ38+ζ62−ζ82−ζ10+ζ26−ζ34−ζ38−ζ62+ζ82ζ10−ζ26−ζ34+ζ38−ζ62−ζ82−1−i72−1+i72ζ2−ζ22−ζ46−ζ50+ζ58−ζ74−ζ2−ζ22+ζ46−ζ50−ζ58+ζ74−ζ2+ζ22−ζ46+ζ50−ζ58−ζ74−ζ10−ζ26+ζ34−ζ38+ζ62−ζ82−ζ10+ζ26−ζ34−ζ38−ζ62+ζ82ζ10−ζ26−ζ34+ζ38−ζ62−ζ82−1−i72−1+i72ζ2−ζ22−ζ46−ζ50+ζ58−ζ74−ζ2−ζ22+ζ46−ζ50−ζ58+ζ74−ζ2+ζ22−ζ46+ζ50−ζ58−ζ74−ζ10−ζ26+ζ34−ζ38+ζ62−ζ82−ζ10+ζ26−ζ34−ζ38−ζ62+ζ82ζ10−ζ26−ζ34+ζ38−ζ62−ζ82ζ2−ζ22−ζ46−ζ50+ζ58−ζ74−ζ2−ζ22+ζ46−ζ50−ζ58+ζ74−ζ2+ζ22−ζ46+ζ50−ζ58−ζ74−ζ10−ζ26+ζ34−ζ38+ζ62−ζ82−ζ10+ζ26−ζ34−ζ38−ζ62+ζ82ζ10−ζ26−ζ34+ζ38−ζ62−ζ82−1−i72−1+i72ζ2−ζ22−ζ46−ζ50+ζ58−ζ74−ζ2−ζ22+ζ46−ζ50−ζ58+ζ74−ζ2+ζ22−ζ46+ζ50−ζ58−ζ74−ζ10−ζ26+ζ34−ζ38+ζ62−ζ82−ζ10+ζ26−ζ34−ζ38−ζ62+ζ82ζ10−ζ26−ζ34+ζ38−ζ62−ζ82ζ2−ζ22−ζ46−ζ50+ζ58−ζ74−ζ2−ζ22+ζ46−ζ50−ζ58+ζ74−ζ2+ζ22−ζ46+ζ50−ζ58−ζ74−ζ10−ζ26+ζ34−ζ38+ζ62−ζ82−ζ10+ζ26−ζ34−ζ38−ζ62+ζ82ζ10−ζ26−ζ34+ζ38−ζ62−ζ82−1−i72−1+i72ζ2−ζ22−ζ46−ζ50+ζ58−ζ74−ζ2−ζ22+ζ46−ζ50−ζ58+ζ74−ζ2+ζ22−ζ46+ζ50−ζ58−ζ74−ζ10−ζ26+ζ34−ζ38+ζ62−ζ82−ζ10+ζ26−ζ34−ζ38−ζ62+ζ82ζ10−ζ26−ζ34+ζ38−ζ62−ζ82−1−i72−1+i72−1−i72−1+i72ζ2−ζ22−ζ46−ζ50+ζ58−ζ74−ζ2−ζ22+ζ46−ζ50−ζ58+ζ74−ζ2+ζ22−ζ46+ζ50−ζ58−ζ74−ζ10−ζ26+ζ34−ζ38+ζ62−ζ82−ζ10+ζ26−ζ34−ζ38−ζ62+ζ82ζ10−ζ26−ζ34+ζ38−ζ62−ζ8200000000000000000000
χ283333333333−1−i72−1+i72−1−i72−1+i72−1−i72−1−i72−1+i72−1+i72-1-1-1-1-1-1-1-1−ζ2−ζ22+ζ46−ζ50−ζ58+ζ74−ζ2+ζ22−ζ46+ζ50−ζ58−ζ74ζ2−ζ22−ζ46−ζ50+ζ58−ζ74−ζ10+ζ26−ζ34−ζ38−ζ62+ζ82ζ10−ζ26−ζ34+ζ38−ζ62−ζ82−ζ10−ζ26+ζ34−ζ38+ζ62−ζ82−1−i72−1+i72−ζ2−ζ22+ζ46−ζ50−ζ58+ζ74−ζ2+ζ22−ζ46+ζ50−ζ58−ζ74ζ2−ζ22−ζ46−ζ50+ζ58−ζ74−ζ10+ζ26−ζ34−ζ38−ζ62+ζ82ζ10−ζ26−ζ34+ζ38−ζ62−ζ82−ζ10−ζ26+ζ34−ζ38+ζ62−ζ82−1−i72−1+i72−ζ2−ζ22+ζ46−ζ50−ζ58+ζ74−ζ2+ζ22−ζ46+ζ50−ζ58−ζ74ζ2−ζ22−ζ46−ζ50+ζ58−ζ74−ζ10+ζ26−ζ34−ζ38−ζ62+ζ82ζ10−ζ26−ζ34+ζ38−ζ62−ζ82−ζ10−ζ26+ζ34−ζ38+ζ62−ζ82−ζ2−ζ22+ζ46−ζ50−ζ58+ζ74−ζ2+ζ22−ζ46+ζ50−ζ58−ζ74ζ2−ζ22−ζ46−ζ50+ζ58−ζ74−ζ10+ζ26−ζ34−ζ38−ζ62+ζ82ζ10−ζ26−ζ34+ζ38−ζ62−ζ82−ζ10−ζ26+ζ34−ζ38+ζ62−ζ82−1−i72−1+i72−ζ2−ζ22+ζ46−ζ50−ζ58+ζ74−ζ2+ζ22−ζ46+ζ50−ζ58−ζ74ζ2−ζ22−ζ46−ζ50+ζ58−ζ74−ζ10+ζ26−ζ34−ζ38−ζ62+ζ82ζ10−ζ26−ζ34+ζ38−ζ62−ζ82−ζ10−ζ26+ζ34−ζ38+ζ62−ζ82−ζ2−ζ22+ζ46−ζ50−ζ58+ζ74−ζ2+ζ22−ζ46+ζ50−ζ58−ζ74ζ2−ζ22−ζ46−ζ50+ζ58−ζ74−ζ10+ζ26−ζ34−ζ38−ζ62+ζ82ζ10−ζ26−ζ34+ζ38−ζ62−ζ82−ζ10−ζ26+ζ34−ζ38+ζ62−ζ82−1−i72−1+i72−ζ2−ζ22+ζ46−ζ50−ζ58+ζ74−ζ2+ζ22−ζ46+ζ50−ζ58−ζ74ζ2−ζ22−ζ46−ζ50+ζ58−ζ74−ζ10+ζ26−ζ34−ζ38−ζ62+ζ82ζ10−ζ26−ζ34+ζ38−ζ62−ζ82−ζ10−ζ26+ζ34−ζ38+ζ62−ζ82−1−i72−1+i72−1−i72−1+i72−ζ2−ζ22+ζ46−ζ50−ζ58+ζ74−ζ2+ζ22−ζ46+ζ50−ζ58−ζ74ζ2−ζ22−ζ46−ζ50+ζ58−ζ74−ζ10+ζ26−ζ34−ζ38−ζ62+ζ82ζ10−ζ26−ζ34+ζ38−ζ62−ζ82−ζ10−ζ26+ζ34−ζ38+ζ62−ζ8200000000000000000000
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Here ζ is a primitive root of unity of order 84 (ζ84 = 1); i = ζ21.