Finite Group Databasebeta

← Group #13141237

Character table — Group #13141237

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size111111333333333333333333333344444412121212121212121212121212121212121212121212121212121212121212121212121212121212484848484848484848484848484848484848484848484848
order12336622336666666666666666664412121212224466666666666666661212121212121212121212121212121212121212333333666666121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111−1−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
χ311111111111111111111111111111111111111111111111111111111111111111111111111−1+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
χ41111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1−1−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−i321−i321−i321−i321−i32
χ61111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1−1+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+i321+i321+i321+i321+i32
χ711111111−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321111−1−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+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32
χ811111111−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321111−1−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+i321−1+i321−1−i32−1−i32−1+i321−1+i321−1−i32−1−i32−1−i32−1+i32−1+i3211−1+i32−1+i3211−1−i32−1−i32
χ911111111−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321111−1−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+i321−1−i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i321−1+i32−1+i3211−1−i32−1−i32−1−i32−1−i32−1+i32−1+i3211
χ1011111111−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-1-1-1-1-111-1-1-1-11+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321111−1−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−i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32
χ1111111111−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-1-1-1-1-111-1-1-1-11+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321111−1−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−i32−1+i321−1+i321−1−i32−1−i32−1+i321−1+i321−1−i321+i321+i321−i321−i32-1-11−i321−i32-1-11+i321+i32
χ1211111111−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-1-1-1-1-111-1-1-1-11+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321111−1−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+i321−1−i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i3211−i321−i32-1-11+i321+i321+i321+i321−i321−i32-1-1
χ1311111111−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321111−1+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−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32
χ1411111111−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321111−1+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−i321−1+i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i321−1−i32−1−i3211−1+i32−1+i32−1+i32−1+i32−1−i32−1−i3211
χ1511111111−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321111−1+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−i321−1−i321−1+i32−1+i32−1−i321−1−i321−1+i32−1+i32−1+i32−1−i32−1−i3211−1−i32−1−i3211−1+i32−1+i32
χ1611111111−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-1-1-1-1-111-1-1-1-11−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321111−1+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+i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32
χ1711111111−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-1-1-1-1-111-1-1-1-11−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321111−1+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−i321−1+i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i3211+i321+i32-1-11−i321−i321−i321−i321+i321+i32-1-1
χ1811111111−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-1-1-1-1-111-1-1-1-11−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321111−1+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+i32−1−i321−1−i321−1+i32−1+i32−1−i321−1−i321−1+i321−i321−i321+i321+i32-1-11+i321+i32-1-11−i321−i32
χ192-222-2-22-22222222222-2-2-2-2-2-2-2-2-2-22i−2i2i2i−2i−2i0000000000000000000000000000000000002i−2i2i−2i-1-1-1-1-1-1111111i−ii−ii−ii−ii−ii−i
χ202-222-2-22-22222222222-2-2-2-2-2-2-2-2-2-22i−2i2i2i−2i−2i0000000000000000000000000000000000002i−2i2i−2i1+i321+i321+i321−i321−i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ7ζ7−ζ7
χ212-222-2-22-22222222222-2-2-2-2-2-2-2-2-2-22i−2i2i2i−2i−2i0000000000000000000000000000000000002i−2i2i−2i1−i321−i321−i321+i321+i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ11ζ11−ζ11
χ222-222-2-22-22222222222-2-2-2-2-2-2-2-2-2-2−2i2i−2i−2i2i2i000000000000000000000000000000000000−2i2i−2i2i-1-1-1-1-1-1111111−ii−ii−ii−ii−ii−ii
χ232-222-2-22-22222222222-2-2-2-2-2-2-2-2-2-2−2i2i−2i−2i2i2i000000000000000000000000000000000000−2i2i−2i2i1+i321+i321+i321−i321−i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ7−ζ7ζ7
χ242-222-2-22-22222222222-2-2-2-2-2-2-2-2-2-2−2i2i−2i−2i2i2i000000000000000000000000000000000000−2i2i−2i2i1−i321−i321−i321+i321+i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ11−ζ11ζ11
χ252-222-2-22-2−1−i3−1+i322−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-2-21+i31+i31+i31+i31−i31−i31−i31−i32i−2i2i2i−2i−2i0000000000000000000000000000000000002ζ11−2ζ112ζ7−2ζ7-11+i321−i32-11+i321−i321−1−i32−1+i321−1−i32−1+i32i−iζ11−ζ11ζ7−ζ7i−iζ11−ζ11ζ7−ζ7
χ262-222-2-22-2−1−i3−1+i322−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-2-21+i31+i31+i31+i31−i31−i31−i31−i32i−2i2i2i−2i−2i0000000000000000000000000000000000002ζ11−2ζ112ζ7−2ζ71+i321−i32-11−i32-11+i32−1−i32−1+i321−1+i321−1−i32ζ11−ζ11ζ7−ζ7i−iζ7−ζ7i−iζ11−ζ11
χ272-222-2-22-2−1−i3−1+i322−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-2-21+i31+i31+i31+i31−i31−i31−i31−i32i−2i2i2i−2i−2i0000000000000000000000000000000000002ζ11−2ζ112ζ7−2ζ71−i32-11+i321+i321−i32-1−1+i321−1−i32−1−i32−1+i321ζ7−ζ7i−iζ11−ζ11ζ11−ζ11ζ7−ζ7i−i
χ282-222-2-22-2−1−i3−1+i322−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-2-21+i31+i31+i31+i31−i31−i31−i31−i3−2i2i−2i−2i2i2i000000000000000000000000000000000000−2ζ112ζ11−2ζ72ζ7-11+i321−i32-11+i321−i321−1−i32−1+i321−1−i32−1+i32−ii−ζ11ζ11−ζ7ζ7−ii−ζ11ζ11−ζ7ζ7
χ292-222-2-22-2−1−i3−1+i322−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-2-21+i31+i31+i31+i31−i31−i31−i31−i3−2i2i−2i−2i2i2i000000000000000000000000000000000000−2ζ112ζ11−2ζ72ζ71+i321−i32-11−i32-11+i32−1−i32−1+i321−1+i321−1−i32−ζ11ζ11−ζ7ζ7−ii−ζ7ζ7−ii−ζ11ζ11
χ302-222-2-22-2−1−i3−1+i322−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-2-21+i31+i31+i31+i31−i31−i31−i31−i3−2i2i−2i−2i2i2i000000000000000000000000000000000000−2ζ112ζ11−2ζ72ζ71−i32-11+i321+i321−i32-1−1+i321−1−i32−1−i32−1+i321−ζ7ζ7−ii−ζ11ζ11−ζ11ζ11−ζ7ζ7−ii
χ312-222-2-22-2−1+i3−1−i322−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-2-21−i31−i31−i31−i31+i31+i31+i31+i32i−2i2i2i−2i−2i0000000000000000000000000000000000002ζ7−2ζ72ζ11−2ζ11-11−i321+i32-11−i321+i321−1+i32−1−i321−1+i32−1−i32i−iζ7−ζ7ζ11−ζ11i−iζ7−ζ7ζ11−ζ11
χ322-222-2-22-2−1+i3−1−i322−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-2-21−i31−i31−i31−i31+i31+i31+i31+i32i−2i2i2i−2i−2i0000000000000000000000000000000000002ζ7−2ζ72ζ11−2ζ111+i32-11−i321−i321+i32-1−1−i321−1+i32−1+i32−1−i321ζ11−ζ11i−iζ7−ζ7ζ7−ζ7ζ11−ζ11i−i
χ332-222-2-22-2−1+i3−1−i322−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-2-21−i31−i31−i31−i31+i31+i31+i31+i32i−2i2i2i−2i−2i0000000000000000000000000000000000002ζ7−2ζ72ζ11−2ζ111−i321+i32-11+i32-11−i32−1+i32−1−i321−1−i321−1+i32ζ7−ζ7ζ11−ζ11i−iζ11−ζ11i−iζ7−ζ7
χ342-222-2-22-2−1+i3−1−i322−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-2-21−i31−i31−i31−i31+i31+i31+i31+i3−2i2i−2i−2i2i2i000000000000000000000000000000000000−2ζ72ζ7−2ζ112ζ11-11−i321+i32-11−i321+i321−1+i32−1−i321−1+i32−1−i32−ii−ζ7ζ7−ζ11ζ11−ii−ζ7ζ7−ζ11ζ11
χ352-222-2-22-2−1+i3−1−i322−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-2-21−i31−i31−i31−i31+i31+i31+i31+i3−2i2i−2i−2i2i2i000000000000000000000000000000000000−2ζ72ζ7−2ζ112ζ111+i32-11−i321−i321+i32-1−1−i321−1+i32−1+i32−1−i321−ζ11ζ11−ii−ζ7ζ7−ζ7ζ7−ζ11ζ11−ii
χ362-222-2-22-2−1+i3−1−i322−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-2-21−i31−i31−i31−i31+i31+i31+i31+i3−2i2i−2i−2i2i2i000000000000000000000000000000000000−2ζ72ζ7−2ζ112ζ111−i321+i32-11+i32-11−i32−1+i32−1−i321−1−i321−1+i32−ζ7ζ7−ζ11ζ11−ii−ζ11ζ11−ii−ζ7ζ7
χ373333333333333333333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13333000000000000000000000000
χ383333333333333333333333333333-3-3-3-3-3-311-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-3-3-3-3000000000000000000000000
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χ916-6−3+3i3−3−3i33−3i33+3i36-600−3+3i3−3−3i30000003−3i33+3i3000000006i−6i6ζ76ζ11−6ζ7−6ζ110000000000000000000000000000000000000000000000000000000000000000
χ926-6−3+3i3−3−3i33−3i33+3i36-600−3+3i3−3−3i30000003−3i33+3i300000000−6i6i−6ζ7−6ζ116ζ76ζ110000000000000000000000000000000000000000000000000000000000000000
χ936-6−3+3i3−3−3i33−3i33+3i3-22001−i31+i34−2+2i3−2−2i34−2+2i3−2−2i3−1+i3−1−i30-42−2i32+2i30-42−2i32+2i30000002-200−1+i31−i3−1−i31+i32-2−1+i31−i3−1−i31+i32-2−1+i31−i3−1−i31+i300000000000000000000000000000000000000000000
χ946-6−3+3i3−3−3i33−3i33+3i3-22001−i31+i34−2+2i3−2−2i34−2+2i3−2−2i3−1+i3−1−i30-42−2i32+2i30-42−2i32+2i3000000-22001−i3−1+i31+i3−1−i3-221−i3−1+i31+i3−1−i3-221−i3−1+i31+i3−1−i300000000000000000000000000000000000000000000
χ956-6−3+3i3−3−3i33−3i33+3i3-22001−i31+i3−2−2i34−2+2i3−2+2i3−2−2i34−1+i3−1−i302+2i3-42−2i302−2i32+2i3-40000002-200−1+i31−i3−1−i31+i3−1−i31+i32-2−1+i31−i3−1+i31−i3−1−i31+i32-200000000000000000000000000000000000000000000
χ966-6−3+3i3−3−3i33−3i33+3i3-22001−i31+i3−2−2i34−2+2i3−2+2i3−2−2i34−1+i3−1−i302+2i3-42−2i302−2i32+2i3-4000000-22001−i3−1+i31+i3−1−i31+i3−1−i3-221−i3−1+i31−i3−1+i31+i3−1−i3-2200000000000000000000000000000000000000000000
χ976-6−3+3i3−3−3i33−3i33+3i3-22001−i31+i3−2+2i3−2−2i34−2−2i34−2+2i3−1+i3−1−i302−2i32+2i3-402+2i3-42−2i30000002-200−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i32-2−1−i31+i32-2−1+i31−i300000000000000000000000000000000000000000000
χ986-6−3+3i3−3−3i33−3i33+3i3-22001−i31+i3−2+2i3−2−2i34−2−2i34−2+2i3−1+i3−1−i302−2i32+2i3-402+2i3-42−2i3000000-22001−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i3-221+i3−1−i3-221−i3−1+i300000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.