Finite Group Databasebeta

← Group #13048445

Character table — Group #13048445

Order 1296.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size111111222222333333333366666666666669999121212121212121212121212121212121212121212181818181818181818242424242424242424242424363636363636363636363636
order1233663336663344661212121233466121212121212121212121212999999121212121212121212181818181818266666666999999181818181818363636363636363636363636
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111−1−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
χ3111111111111111111111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111−1+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
χ411111111111111-1-111-1-1-1-11111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ511111111111111-1-111-1-1-1-11111111111111-1-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-1-1-1-1-1-1−1−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−i321−i321−i321−i321−i32
χ611111111111111-1-111-1-1-1-11111111111111-1-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-1-1-1-1-1-1−1+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+i321+i321+i321+i321+i32
χ7111111111111−1−i32−1+i3211−1−i32−1+i321111−1−i32−1+i321−1−i32−1+i3211−1−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+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i32111−1−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
χ8111111111111−1−i32−1+i3211−1−i32−1+i321111−1−i32−1+i321−1−i32−1+i3211−1−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−i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i321−1+i321−1−i32111−1−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
χ9111111111111−1−i32−1+i3211−1−i32−1+i321111−1−i32−1+i321−1−i32−1+i3211−1−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+i321111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−1−i32−1−i32−1+i321111−1−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
χ10111111111111−1−i32−1+i32-1-1−1−i32−1+i32-1-1-1-1−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-1-11+i321+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
χ11111111111111−1−i32−1+i32-1-1−1−i32−1+i32-1-1-1-1−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1+i321−1+i321−1−i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i321−1+i321−1−i32-1-1-11+i321+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
χ12111111111111−1−i32−1+i32-1-1−1−i32−1+i32-1-1-1-1−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321−i321−i32−1+i321−1−i32−1−i32−1+i321111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−1−i32−1−i32−1+i321-1-1-11+i321+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
χ13111111111111−1+i32−1−i3211−1+i32−1−i321111−1+i32−1−i321−1+i32−1−i3211−1+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−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i32111−1+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
χ14111111111111−1+i32−1−i3211−1+i32−1−i321111−1+i32−1−i321−1+i32−1−i3211−1+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−i321111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−1+i32−1+i32−1−i321111−1+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
χ15111111111111−1+i32−1−i3211−1+i32−1−i321111−1+i32−1−i321−1+i32−1−i3211−1+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+i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i321−1−i321−1+i32111−1+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
χ16111111111111−1+i32−1−i32-1-1−1+i32−1−i32-1-1-1-1−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-1-11−i321−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
χ17111111111111−1+i32−1−i32-1-1−1+i32−1−i32-1-1-1-1−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321+i321+i32−1−i321−1+i32−1+i32−1−i321111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−1+i32−1+i32−1−i321-1-1-11−i321−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
χ18111111111111−1+i32−1−i32-1-1−1+i32−1−i32-1-1-1-1−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−1−i321−1+i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i321−1−i321−1+i32-1-1-11−i321−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
χ19222222-1-1-1-1-1-12200220000-1-12-1-1222222220000222222-1-1-1-1-1-1-1-1-1222222000000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ20222222-1-1-1-1-1-12200220000-1-12-1-1222222220000−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-1-1-1-1-1-1-1-1-1−1−i3−1−i3−1−i3−1+i3−1+i3−1+i30000000001+i321+i321+i321−i321−i321−i321+i321+i321+i321−i321−i321−i32000000000000
χ21222222-1-1-1-1-1-12200220000-1-12-1-1222222220000−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-1-1-1-1-1-1-1-1-1−1+i3−1+i3−1+i3−1−i3−1−i3−1−i30000000001−i321−i321−i321+i321+i321+i321−i321−i321−i321+i321+i321+i32000000000000
χ22222222-1-1-1-1-1-1−1−i3−1+i300−1−i3−1+i300001+i321−i3221+i321−i3222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i300002−1−i3−1+i32−1−i3−1+i3-1-1-11+i321+i321+i321−i321−i321−i322−1−i3−1+i32−1−i3−1+i3000000000-11+i321−i32-11+i321−i32-11+i321−i32-11+i321−i32000000000000
χ23222222-1-1-1-1-1-1−1−i3−1+i300−1−i3−1+i300001+i321−i3221+i321−i3222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i30000−1−i3−1+i32−1+i32−1−i3-1-1-11+i321+i321+i321−i321−i321−i32−1−i3−1+i32−1+i32−1−i30000000001+i321−i32-11−i32-11+i321+i321−i32-11−i32-11+i32000000000000
χ24222222-1-1-1-1-1-1−1−i3−1+i300−1−i3−1+i300001+i321−i3221+i321−i3222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i30000−1+i32−1−i3−1−i3−1+i32-1-1-11+i321+i321+i321−i321−i321−i32−1+i32−1−i3−1−i3−1+i320000000001−i32-11+i321+i321−i32-11−i32-11+i321+i321−i32-1000000000000
χ25222222-1-1-1-1-1-1−1+i3−1−i300−1+i3−1−i300001−i321+i3221−i321+i3222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i300002−1+i3−1−i32−1+i3−1−i3-1-1-11−i321−i321−i321+i321+i321+i322−1+i3−1−i32−1+i3−1−i3000000000-11−i321+i32-11−i321+i32-11−i321+i32-11−i321+i32000000000000
χ26222222-1-1-1-1-1-1−1+i3−1−i300−1+i3−1−i300001−i321+i3221−i321+i3222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i30000−1−i32−1+i3−1+i3−1−i32-1-1-11−i321−i321−i321+i321+i321+i32−1−i32−1+i3−1+i3−1−i320000000001+i32-11−i321−i321+i32-11+i32-11−i321−i321+i32-1000000000000
χ27222222-1-1-1-1-1-1−1+i3−1−i300−1+i3−1−i300001−i321+i3221−i321+i3222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i30000−1+i3−1−i32−1−i32−1+i3-1-1-11−i321−i321−i321+i321+i321+i32−1+i3−1−i32−1−i32−1+i30000000001−i321+i32-11+i32-11−i321−i321+i32-11+i32-11−i32000000000000
χ282-222-2-2222-2-2-2222i−2i-2-22i2i−2i−2i220-2-2000000002i−2i2i−2i-1-1-1-1-1-1000000000111111000000000-1-1-1-1-1-1111111i−ii−ii−ii−ii−ii−i
χ292-222-2-2222-2-2-2222i−2i-2-22i2i−2i−2i220-2-2000000002i−2i2i−2i1+i321+i321+i321−i321−i321−i32000000000−1−i32−1−i32−1−i32−1+i32−1+i32−1+i320000000001+i321+i321+i321−i321−i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ7ζ7−ζ7
χ302-222-2-2222-2-2-2222i−2i-2-22i2i−2i−2i220-2-2000000002i−2i2i−2i1−i321−i321−i321+i321+i321+i32000000000−1+i32−1+i32−1+i32−1−i32−1−i32−1−i320000000001−i321−i321−i321+i321+i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ11ζ11−ζ11
χ312-222-2-2222-2-2-222−2i2i-2-2−2i−2i2i2i220-2-200000000−2i2i−2i2i-1-1-1-1-1-1000000000111111000000000-1-1-1-1-1-1111111−ii−ii−ii−ii−ii−ii
χ322-222-2-2222-2-2-222−2i2i-2-2−2i−2i2i2i220-2-200000000−2i2i−2i2i1+i321+i321+i321−i321−i321−i32000000000−1−i32−1−i32−1−i32−1+i32−1+i32−1+i320000000001+i321+i321+i321−i321−i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ7−ζ7ζ7
χ332-222-2-2222-2-2-222−2i2i-2-2−2i−2i2i2i220-2-200000000−2i2i−2i2i1−i321−i321−i321+i321+i321+i32000000000−1+i32−1+i32−1+i32−1−i32−1−i32−1−i320000000001−i321−i321−i321+i321+i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ11−ζ11ζ11
χ342-222-2-2222-2-2-2−1−i3−1+i32i−2i1+i31−i32i2i−2i−2i−1−i3−1+i301+i31−i3000000002ζ11−2ζ112ζ7−2ζ7-11+i321−i32-11+i321−i320000000001−1−i32−1+i321−1−i32−1+i32000000000-11+i321−i32-11+i321−i321−1−i32−1+i321−1−i32−1+i32i−iζ11−ζ11ζ7−ζ7i−iζ11−ζ11ζ7−ζ7
χ352-222-2-2222-2-2-2−1−i3−1+i32i−2i1+i31−i32i2i−2i−2i−1−i3−1+i301+i31−i3000000002ζ11−2ζ112ζ7−2ζ71+i321−i32-11−i32-11+i32000000000−1−i32−1+i321−1+i321−1−i320000000001+i321−i32-11−i32-11+i32−1−i32−1+i321−1+i321−1−i32ζ11−ζ11ζ7−ζ7i−iζ7−ζ7i−iζ11−ζ11
χ362-222-2-2222-2-2-2−1−i3−1+i32i−2i1+i31−i32i2i−2i−2i−1−i3−1+i301+i31−i3000000002ζ11−2ζ112ζ7−2ζ71−i32-11+i321+i321−i32-1000000000−1+i321−1−i32−1−i32−1+i3210000000001−i32-11+i321+i321−i32-1−1+i321−1−i32−1−i32−1+i321ζ7−ζ7i−iζ11−ζ11ζ11−ζ11ζ7−ζ7i−i
χ372-222-2-2222-2-2-2−1−i3−1+i3−2i2i1+i31−i3−2i−2i2i2i−1−i3−1+i301+i31−i300000000−2ζ112ζ11−2ζ72ζ7-11+i321−i32-11+i321−i320000000001−1−i32−1+i321−1−i32−1+i32000000000-11+i321−i32-11+i321−i321−1−i32−1+i321−1−i32−1+i32−ii−ζ11ζ11−ζ7ζ7−ii−ζ11ζ11−ζ7ζ7
χ382-222-2-2222-2-2-2−1−i3−1+i3−2i2i1+i31−i3−2i−2i2i2i−1−i3−1+i301+i31−i300000000−2ζ112ζ11−2ζ72ζ71+i321−i32-11−i32-11+i32000000000−1−i32−1+i321−1+i321−1−i320000000001+i321−i32-11−i32-11+i32−1−i32−1+i321−1+i321−1−i32−ζ11ζ11−ζ7ζ7−ii−ζ7ζ7−ii−ζ11ζ11
χ392-222-2-2222-2-2-2−1−i3−1+i3−2i2i1+i31−i3−2i−2i2i2i−1−i3−1+i301+i31−i300000000−2ζ112ζ11−2ζ72ζ71−i32-11+i321+i321−i32-1000000000−1+i321−1−i32−1−i32−1+i3210000000001−i32-11+i321+i321−i32-1−1+i321−1−i32−1−i32−1+i321−ζ7ζ7−ii−ζ11ζ11−ζ11ζ11−ζ7ζ7−ii
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χ46333333333333333333333333-133-1-1-1-1-1-1-1-13333000000-1-1-1-1-1-1-1-1-1000000-1-1-1-1-1-1-1-1-1000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.