Finite Group Databasebeta

← Group #14516514

Character table — Group #14516514

Order 1944.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111222333666666121212121212181818181818181818181818181818242424242424272727727272727272818181108108108108108108
order133333266333666999999666999181818181818181818999999266999999266181818181818
χ1111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1111111-1-1-1-1-1-1-1-1-1
χ3111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ4111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-11−i321−i321−i321+i321+i321+i32
χ5111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ6111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-11+i321+i321+i321−i321−i321−i32
χ7222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1222222000-1-1-1-1-1-1000000000
χ8222222222222222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3222-1-1-1-1-1-1-1-1-1-1-1-1−1+i3−1+i3−1+i3−1−i3−1−i3−1−i30001−i321−i321−i321+i321+i321+i32000000000
χ9222222222222222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3222-1-1-1-1-1-1-1-1-1-1-1-1−1−i3−1−i3−1−i3−1+i3−1+i3−1+i30001+i321+i321+i321−i321−i321−i32000000000
χ10222-1-1-12222-1-1-1-1-12222222-1-1ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ4+ζ5-1-1-1-1-1-1000ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5000000000
χ11222-1-1-12222-1-1-1-1-12222222-1-1ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ+ζ8-1-1-1-1-1-1000ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8000000000
χ12222-1-1-12222-1-1-1-1-12222222-1-1ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ2+ζ7-1-1-1-1-1-1000ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7000000000
χ13222-1-1-12222-1-1-1-1-1−1+i3−1+i3−1+i3−1−i3−1−i3−1−i32-1-1ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ4+ζ51−i321−i321−i321+i321+i321+i32000ζ2+ζ4ζ+ζ5ζ7+ζ8ζ5+ζ7ζ4+ζ8ζ+ζ2000000000
χ14222-1-1-12222-1-1-1-1-1−1+i3−1+i3−1+i3−1−i3−1−i3−1−i32-1-1ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ+ζ81−i321−i321−i321+i321+i321+i32000ζ+ζ5ζ7+ζ8ζ2+ζ4ζ4+ζ8ζ+ζ2ζ5+ζ7000000000
χ15222-1-1-12222-1-1-1-1-1−1+i3−1+i3−1+i3−1−i3−1−i3−1−i32-1-1ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ2+ζ71−i321−i321−i321+i321+i321+i32000ζ7+ζ8ζ2+ζ4ζ+ζ5ζ+ζ2ζ5+ζ7ζ4+ζ8000000000
χ16222-1-1-12222-1-1-1-1-1−1−i3−1−i3−1−i3−1+i3−1+i3−1+i32-1-1ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ4+ζ51+i321+i321+i321−i321−i321−i32000ζ5+ζ7ζ4+ζ8ζ+ζ2ζ2+ζ4ζ+ζ5ζ7+ζ8000000000
χ17222-1-1-12222-1-1-1-1-1−1−i3−1−i3−1−i3−1+i3−1+i3−1+i32-1-1ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ+ζ81+i321+i321+i321−i321−i321−i32000ζ4+ζ8ζ+ζ2ζ5+ζ7ζ+ζ5ζ7+ζ8ζ2+ζ4000000000
χ18222-1-1-12222-1-1-1-1-1−1−i3−1−i3−1−i3−1+i3−1+i3−1+i32-1-1ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ2+ζ71+i321+i321+i321−i321−i321−i32000ζ+ζ2ζ5+ζ7ζ4+ζ8ζ7+ζ8ζ2+ζ4ζ+ζ5000000000
χ19333333-1-1-1333-1-1-1000000-1-1-1333-1-1-1-1-1-1-1-1-1000000333000000-1-1-1000000
χ20333333-1-1-1333-1-1-1000000-1-1-1333-1-1-1-1-1-1-1-1-1000000-3-3-3000000111000000
χ213−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i320003−3+3i32−3−3i322ζ+ζ4−ζ+ζ4−ζ−2ζ4ζ2+2ζ5ζ2−ζ5−2ζ2−ζ50000000000000002ζ+ζ4−ζ+ζ4−ζ−2ζ4ζ2+2ζ5ζ2−ζ5−2ζ2−ζ51−1+i32−1−i320000001−1+i32−1−i32ζζ4ζ7ζ2ζ5ζ8
χ223−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i320003−3+3i32−3−3i322ζ+ζ4−ζ+ζ4−ζ−2ζ4ζ2+2ζ5ζ2−ζ5−2ζ2−ζ50000000000000002ζ+ζ4−ζ+ζ4−ζ−2ζ4ζ2+2ζ5ζ2−ζ5−2ζ2−ζ5-11−i321+i32000000-11−i321+i32−ζ−ζ4−ζ7−ζ2−ζ5−ζ8
χ233−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i320003−3+3i32−3−3i32−ζ+ζ4−ζ−2ζ42ζ+ζ4ζ2−ζ5−2ζ2−ζ5ζ2+2ζ5000000000000000−ζ+ζ4−ζ−2ζ42ζ+ζ4ζ2−ζ5−2ζ2−ζ5ζ2+2ζ51−1+i32−1−i320000001−1+i32−1−i32ζ4ζ7ζζ8ζ2ζ5
χ243−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i320003−3+3i32−3−3i32−ζ+ζ4−ζ−2ζ42ζ+ζ4ζ2−ζ5−2ζ2−ζ5ζ2+2ζ5000000000000000−ζ+ζ4−ζ−2ζ42ζ+ζ4ζ2−ζ5−2ζ2−ζ5ζ2+2ζ5-11−i321+i32000000-11−i321+i32−ζ4−ζ7−ζ−ζ8−ζ2−ζ5
χ253−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i320003−3+3i32−3−3i32−ζ−2ζ42ζ+ζ4−ζ+ζ4−2ζ2−ζ5ζ2+2ζ5ζ2−ζ5000000000000000−ζ−2ζ42ζ+ζ4−ζ+ζ4−2ζ2−ζ5ζ2+2ζ5ζ2−ζ51−1+i32−1−i320000001−1+i32−1−i32ζ7ζζ4ζ5ζ8ζ2
χ263−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i320003−3+3i32−3−3i32−ζ−2ζ42ζ+ζ4−ζ+ζ4−2ζ2−ζ5ζ2+2ζ5ζ2−ζ5000000000000000−ζ−2ζ42ζ+ζ4−ζ+ζ4−2ζ2−ζ5ζ2+2ζ5ζ2−ζ5-11−i321+i32000000-11−i321+i32−ζ7−ζ−ζ4−ζ5−ζ8−ζ2
χ273−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i320003−3−3i32−3+3i32ζ2+2ζ5ζ2−ζ5−2ζ2−ζ5−ζ−2ζ42ζ+ζ4−ζ+ζ4000000000000000ζ2+2ζ5ζ2−ζ5−2ζ2−ζ5−ζ−2ζ42ζ+ζ4−ζ+ζ41−1−i32−1+i320000001−1−i32−1+i32ζ5ζ2ζ8ζζ7ζ4
χ283−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i320003−3−3i32−3+3i32ζ2+2ζ5ζ2−ζ5−2ζ2−ζ5−ζ−2ζ42ζ+ζ4−ζ+ζ4000000000000000ζ2+2ζ5ζ2−ζ5−2ζ2−ζ5−ζ−2ζ42ζ+ζ4−ζ+ζ4-11+i321−i32000000-11+i321−i32−ζ5−ζ2−ζ8−ζ−ζ7−ζ4
χ293−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i320003−3−3i32−3+3i32ζ2−ζ5−2ζ2−ζ5ζ2+2ζ52ζ+ζ4−ζ+ζ4−ζ−2ζ4000000000000000ζ2−ζ5−2ζ2−ζ5ζ2+2ζ52ζ+ζ4−ζ+ζ4−ζ−2ζ41−1−i32−1+i320000001−1−i32−1+i32ζ2ζ8ζ5ζ4ζζ7
χ303−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i320003−3−3i32−3+3i32ζ2−ζ5−2ζ2−ζ5ζ2+2ζ52ζ+ζ4−ζ+ζ4−ζ−2ζ4000000000000000ζ2−ζ5−2ζ2−ζ5ζ2+2ζ52ζ+ζ4−ζ+ζ4−ζ−2ζ4-11+i321−i32000000-11+i321−i32−ζ2−ζ8−ζ5−ζ4−ζ−ζ7
χ313−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i320003−3−3i32−3+3i32−2ζ2−ζ5ζ2+2ζ5ζ2−ζ5−ζ+ζ4−ζ−2ζ42ζ+ζ4000000000000000−2ζ2−ζ5ζ2+2ζ5ζ2−ζ5−ζ+ζ4−ζ−2ζ42ζ+ζ41−1−i32−1+i320000001−1−i32−1+i32ζ8ζ5ζ2ζ7ζ4ζ
χ323−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i320003−3−3i32−3+3i32−2ζ2−ζ5ζ2+2ζ5ζ2−ζ5−ζ+ζ4−ζ−2ζ42ζ+ζ4000000000000000−2ζ2−ζ5ζ2+2ζ5ζ2−ζ5−ζ+ζ4−ζ−2ζ42ζ+ζ4-11+i321−i32000000-11+i321−i32−ζ8−ζ5−ζ2−ζ7−ζ4−ζ
χ33666666666-3-3-3666000000-3-3-3000000000000000000000000000000000000
χ34666666-2-2-2666-2-2-2000000-2-2-2-3-3-3111111111000000000000000000000000
χ35666666-2-2-2-3-3-3-2-2-20000001110004-2-24-2-24-2-2000000000000000000000000
χ36666666-2-2-2-3-3-3-2-2-2000000111000-24-2-24-2-24-2000000000000000000000000
χ37666666-2-2-2-3-3-3-2-2-2000000111000-2-24-2-24-2-24000000000000000000000000
χ38666-3-3-3666-36-3-3-3-3000000-36-3000000000000000000000000000000000000
χ39666-3-3-3666-3-36-3-3-3000000-3-36000000000000000000000000000000000000
χ40666-3-3-3-2-2-26-3-3111000000-2113ζ+3ζ83ζ2+3ζ73ζ4+3ζ5−ζ−ζ8−ζ−ζ8−ζ−ζ8−ζ2−ζ7−ζ2−ζ7−ζ2−ζ7−ζ4−ζ5−ζ4−ζ5−ζ4−ζ5000000000000000000000000
χ41666-3-3-3-2-2-26-3-3111000000-2113ζ2+3ζ73ζ4+3ζ53ζ+3ζ8−ζ2−ζ7−ζ2−ζ7−ζ2−ζ7−ζ4−ζ5−ζ4−ζ5−ζ4−ζ5−ζ−ζ8−ζ−ζ8−ζ−ζ8000000000000000000000000
χ42666-3-3-3-2-2-26-3-3111000000-2113ζ4+3ζ53ζ+3ζ83ζ2+3ζ7−ζ4−ζ5−ζ4−ζ5−ζ4−ζ5−ζ−ζ8−ζ−ζ8−ζ−ζ8−ζ2−ζ7−ζ2−ζ7−ζ2−ζ7000000000000000000000000
χ43666-3-3-3-2-2-2-36-31110000001-210002ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ4+2ζ52ζ+2ζ82ζ2+2ζ7000000000000000000000000
χ44666-3-3-3-2-2-2-36-31110000001-210002ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ+2ζ82ζ2+2ζ72ζ4+2ζ5000000000000000000000000
χ45666-3-3-3-2-2-2-36-31110000001-210002ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ2+2ζ72ζ4+2ζ52ζ+2ζ8000000000000000000000000
χ46666-3-3-3-2-2-2-3-3611100000011-20002ζ+2ζ82ζ4+2ζ52ζ2+2ζ72ζ2+2ζ72ζ+2ζ82ζ4+2ζ52ζ4+2ζ52ζ2+2ζ72ζ+2ζ8000000000000000000000000
χ47666-3-3-3-2-2-2-3-3611100000011-20002ζ2+2ζ72ζ+2ζ82ζ4+2ζ52ζ4+2ζ52ζ2+2ζ72ζ+2ζ82ζ+2ζ82ζ4+2ζ52ζ2+2ζ7000000000000000000000000
χ48666-3-3-3-2-2-2-3-3611100000011-20002ζ4+2ζ52ζ2+2ζ72ζ+2ζ82ζ+2ζ82ζ4+2ζ52ζ2+2ζ72ζ2+2ζ72ζ+2ζ82ζ4+2ζ5000000000000000000000000
χ496−3+3i3−3−3i3-33−3i323+3i326−3+3i3−3−3i3000-33−3i323+3i324ζ+2ζ4−2ζ+2ζ4−2ζ−4ζ42ζ2+4ζ52ζ2−2ζ5−4ζ2−2ζ5000000000000000−2ζ−ζ4ζ−ζ4ζ+2ζ4−ζ2−2ζ5−ζ2+ζ52ζ2+ζ5000000000000000000
χ506−3+3i3−3−3i3-33−3i323+3i326−3+3i3−3−3i3000-33−3i323+3i32−2ζ+2ζ4−2ζ−4ζ44ζ+2ζ42ζ2−2ζ5−4ζ2−2ζ52ζ2+4ζ5000000000000000ζ−ζ4ζ+2ζ4−2ζ−ζ4−ζ2+ζ52ζ2+ζ5−ζ2−2ζ5000000000000000000
χ516−3+3i3−3−3i3-33−3i323+3i326−3+3i3−3−3i3000-33−3i323+3i32−2ζ−4ζ44ζ+2ζ4−2ζ+2ζ4−4ζ2−2ζ52ζ2+4ζ52ζ2−2ζ5000000000000000ζ+2ζ4−2ζ−ζ4ζ−ζ42ζ2+ζ5−ζ2−2ζ5−ζ2+ζ5000000000000000000
χ526−3−3i3−3+3i3-33+3i323−3i326−3−3i3−3+3i3000-33+3i323−3i322ζ2+4ζ52ζ2−2ζ5−4ζ2−2ζ5−2ζ−4ζ44ζ+2ζ4−2ζ+2ζ4000000000000000−ζ2−2ζ5−ζ2+ζ52ζ2+ζ5ζ+2ζ4−2ζ−ζ4ζ−ζ4000000000000000000
χ536−3−3i3−3+3i3-33+3i323−3i326−3−3i3−3+3i3000-33+3i323−3i322ζ2−2ζ5−4ζ2−2ζ52ζ2+4ζ54ζ+2ζ4−2ζ+2ζ4−2ζ−4ζ4000000000000000−ζ2+ζ52ζ2+ζ5−ζ2−2ζ5−2ζ−ζ4ζ−ζ4ζ+2ζ4000000000000000000
χ546−3−3i3−3+3i3-33+3i323−3i326−3−3i3−3+3i3000-33+3i323−3i32−4ζ2−2ζ52ζ2+4ζ52ζ2−2ζ5−2ζ+2ζ4−2ζ−4ζ44ζ+2ζ40000000000000002ζ2+ζ5−ζ2−2ζ5−ζ2+ζ5ζ−ζ4ζ+2ζ4−2ζ−ζ4000000000000000000
χ559−9+9i32−9−9i329−9+9i32−9−9i32-33−3i323+3i32000-33−3i323+3i320000000000000000000000000003−3+3i32−3−3i32000000-11−i321+i32000000
χ569−9+9i32−9−9i329−9+9i32−9−9i32-33−3i323+3i32000-33−3i323+3i32000000000000000000000000000-33−3i323+3i320000001−1+i32−1−i32000000
χ579−9−9i32−9+9i329−9−9i32−9+9i32-33+3i323−3i32000-33+3i323−3i320000000000000000000000000003−3−3i32−3+3i32000000-11+i321−i32000000
χ589−9−9i32−9+9i329−9−9i32−9+9i32-33+3i323−3i32000-33+3i323−3i32000000000000000000000000000-33+3i323−3i320000001−1−i32−1+i32000000
χ5918−9+9i3−9−9i3-99−9i329+9i32-63−3i33+3i30003−3+3i32−3−3i32000000000000000000000000000000000000000000000
χ6018−9−9i3−9+9i3-99+9i329−9i32-63+3i33−3i30003−3−3i32−3+3i32000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 9 (ζ9 = 1); i = ζ2.