Finite Group Databasebeta

← Group #11721335

Character table — Group #11721335

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size111333333333334446666666666666666661212121212121212121212484848484848484848484848
order13326699181818181818266441212121236363636363636363636363626618181818181818183366999918181818
χ11111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ31111111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ411111111111111-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ511111111111111-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1−1+i32−1−i321−i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ611111111111111-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1−1−i32−1+i321+i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ7111111−1+i32−1−i32−1+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−i32111−1+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
χ8111111−1+i32−1−i32−1+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−i32111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i3211−1+i32−1−i3211−1+i32
χ9111111−1+i32−1−i32−1+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−i32111−1+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−i3211−1+i32−1−i321
χ10111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3211-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32
χ11111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1−i321−i321+i32−1−i3211−1+i321+i32-1-11−i32
χ12111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32−1−i32−1+i321+i321−i321−1+i32−1−i321-11−i321+i32-1
χ13111111−1−i32−1+i32−1−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+i32111−1−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
χ14111111−1−i32−1+i32−1−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+i32111−1−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+i3211−1−i32−1+i321
χ15111111−1−i32−1+i32−1−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+i32111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i3211−1−i32−1+i3211−1−i32
χ16111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3211-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32
χ17111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32−1+i32−1−i321−i321+i321−1−i32−1+i321-11+i321−i32-1
χ18111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1+i321+i321−i32−1+i3211−1−i321−i32-1-11+i32
χ1933333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13-1-1-13-1-1-1000000000000
χ2033333333333333-3-3-3-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-3111-3111000000000000
χ21333333−3+3i32−3−3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32333-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i32-1-1-1−3+3i321−i321−i321−i32−3−3i321+i321+i321+i32000000000000
χ22333333−3+3i32−3−3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32-3-3-3-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321113−3i32−1+i32−1+i32−1+i323+3i32−1−i32−1−i32−1−i32000000000000
χ23333333−3−3i32−3+3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32333-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i32-1-1-1−3−3i321+i321+i321+i32−3+3i321−i321−i321−i32000000000000
χ24333333−3−3i32−3+3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32-3-3-3-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321113+3i32−1−i32−1−i32−1−i323−3i32−1+i32−1+i32−1+i32000000000000
χ253−3+3i32−3−3i323−3+3i32−3−3i32000000003−3+3i32−3−3i3233−3+3i32−3+3i32−3−3i32−3−3i320000000000003−3+3i32−3−3i3200000000000000000000
χ263−3+3i32−3−3i323−3+3i32−3−3i32000000003−3+3i32−3−3i32-1-11−i321−i321+i321+i322ζ2ζ2ζ42ζ42ζ72ζ72ζ22ζ22ζ52ζ52ζ82ζ8-11−i321+i3202ζ2ζ42ζ702ζ22ζ52ζ8000000000000
χ273−3+3i32−3−3i323−3+3i32−3−3i32000000003−3+3i32−3−3i32-1-11−i321−i321+i321+i322ζ42ζ42ζ72ζ72ζ2ζ2ζ82ζ82ζ22ζ22ζ52ζ5-11−i321+i3202ζ42ζ72ζ02ζ82ζ22ζ5000000000000
χ283−3+3i32−3−3i323−3+3i32−3−3i32000000003−3+3i32−3−3i32-1-11−i321−i321+i321+i322ζ72ζ72ζ2ζ2ζ42ζ42ζ52ζ52ζ82ζ82ζ22ζ2-11−i321+i3202ζ72ζ2ζ402ζ52ζ82ζ2000000000000
χ293−3+3i32−3−3i323−3+3i32−3−3i3200000000-33−3i323+3i3233−3+3i32−3+3i32−3−3i32−3−3i32000000000000-33−3i323+3i3200000000000000000000
χ303−3+3i32−3−3i323−3+3i32−3−3i3200000000-33−3i323+3i32-1-11−i321−i321+i321+i322ζ2ζ2ζ42ζ42ζ72ζ72ζ22ζ22ζ52ζ52ζ82ζ81−1+i32−1−i320−2ζ−2ζ4−2ζ70−2ζ2−2ζ5−2ζ8000000000000
χ313−3+3i32−3−3i323−3+3i32−3−3i3200000000-33−3i323+3i32-1-11−i321−i321+i321+i322ζ42ζ42ζ72ζ72ζ2ζ2ζ82ζ82ζ22ζ22ζ52ζ51−1+i32−1−i320−2ζ4−2ζ7−2ζ0−2ζ8−2ζ2−2ζ5000000000000
χ323−3+3i32−3−3i323−3+3i32−3−3i3200000000-33−3i323+3i32-1-11−i321−i321+i321+i322ζ72ζ72ζ2ζ2ζ42ζ42ζ52ζ52ζ82ζ82ζ22ζ21−1+i32−1−i320−2ζ7−2ζ−2ζ40−2ζ5−2ζ8−2ζ2000000000000
χ333−3−3i32−3+3i323−3−3i32−3+3i32000000003−3−3i32−3+3i3233−3−3i32−3−3i32−3+3i32−3+3i320000000000003−3−3i32−3+3i3200000000000000000000
χ343−3−3i32−3+3i323−3−3i32−3+3i32000000003−3−3i32−3+3i32-1-11+i321+i321−i321−i322ζ22ζ22ζ82ζ82ζ52ζ52ζ42ζ42ζ2ζ2ζ72ζ7-11+i321−i3202ζ22ζ82ζ502ζ42ζ2ζ7000000000000
χ353−3−3i32−3+3i323−3−3i32−3+3i32000000003−3−3i32−3+3i32-1-11+i321+i321−i321−i322ζ52ζ52ζ22ζ22ζ82ζ82ζ2ζ2ζ72ζ72ζ42ζ4-11+i321−i3202ζ52ζ22ζ802ζ2ζ72ζ4000000000000
χ363−3−3i32−3+3i323−3−3i32−3+3i32000000003−3−3i32−3+3i32-1-11+i321+i321−i321−i322ζ82ζ82ζ52ζ52ζ22ζ22ζ72ζ72ζ42ζ42ζ2ζ-11+i321−i3202ζ82ζ52ζ202ζ72ζ42ζ000000000000
χ373−3−3i32−3+3i323−3−3i32−3+3i3200000000-33+3i323−3i3233−3−3i32−3−3i32−3+3i32−3+3i32000000000000-33+3i323−3i3200000000000000000000
χ383−3−3i32−3+3i323−3−3i32−3+3i3200000000-33+3i323−3i32-1-11+i321+i321−i321−i322ζ22ζ22ζ82ζ82ζ52ζ52ζ42ζ42ζ2ζ2ζ72ζ71−1−i32−1+i320−2ζ2−2ζ8−2ζ50−2ζ4−2ζ−2ζ7000000000000
χ393−3−3i32−3+3i323−3−3i32−3+3i3200000000-33+3i323−3i32-1-11+i321+i321−i321−i322ζ52ζ52ζ22ζ22ζ82ζ82ζ2ζ2ζ72ζ72ζ42ζ41−1−i32−1+i320−2ζ5−2ζ2−2ζ80−2ζ−2ζ7−2ζ4000000000000
χ403−3−3i32−3+3i323−3−3i32−3+3i3200000000-33+3i323−3i32-1-11+i321+i321−i321−i322ζ82ζ82ζ52ζ52ζ22ζ22ζ72ζ72ζ42ζ42ζ2ζ1−1−i32−1+i320−2ζ8−2ζ5−2ζ20−2ζ7−2ζ4−2ζ000000000000
χ41666-2-2-266-2-2-2-2-2-20002-22-22-22-22-22-22-22-22-200000000000000000000000
χ42666-2-2-266-2-2-2-2-2-2000-22-22-22-22-22-22-22-22-2200000000000000000000000
χ43666-2-2-2−3+3i3−3−3i31−i31−i31−i31+i31+i31+i30002-22-22-2−1+i31−i3−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i3−1−i31+i300000000000000000000000
χ44666-2-2-2−3+3i3−3−3i31−i31−i31−i31+i31+i31+i3000-22-22-221−i3−1+i31−i3−1+i31−i3−1+i31+i3−1−i31+i3−1−i31+i3−1−i300000000000000000000000
χ45666-2-2-2−3−3i3−3+3i31+i31+i31+i31−i31−i31−i30002-22-22-2−1−i31+i3−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i3−1+i31−i300000000000000000000000
χ46666-2-2-2−3−3i3−3+3i31+i31+i31+i31−i31−i31−i3000-22-22-221+i3−1−i31+i3−1−i31+i3−1−i31−i3−1+i31−i3−1+i31−i3−1+i300000000000000000000000
χ476−3+3i3−3−3i3-21−i31+i3004ζ4ζ44ζ74ζ24ζ54ζ80002-2−1+i31−i3−1−i31+i32ζ−2ζ2ζ4−2ζ42ζ7−2ζ72ζ2−2ζ22ζ5−2ζ52ζ8−2ζ800000000000000000000000
χ486−3+3i3−3−3i3-21−i31+i3004ζ4ζ44ζ74ζ24ζ54ζ8000-221−i3−1+i31+i3−1−i3−2ζ2ζ−2ζ42ζ4−2ζ72ζ7−2ζ22ζ2−2ζ52ζ5−2ζ82ζ800000000000000000000000
χ496−3+3i3−3−3i3-21−i31+i3004ζ44ζ74ζ4ζ84ζ24ζ50002-2−1+i31−i3−1−i31+i32ζ4−2ζ42ζ7−2ζ72ζ−2ζ2ζ8−2ζ82ζ2−2ζ22ζ5−2ζ500000000000000000000000
χ506−3+3i3−3−3i3-21−i31+i3004ζ44ζ74ζ4ζ84ζ24ζ5000-221−i3−1+i31+i3−1−i3−2ζ42ζ4−2ζ72ζ7−2ζ2ζ−2ζ82ζ8−2ζ22ζ2−2ζ52ζ500000000000000000000000
χ516−3+3i3−3−3i3-21−i31+i3004ζ74ζ4ζ44ζ54ζ84ζ20002-2−1+i31−i3−1−i31+i32ζ7−2ζ72ζ−2ζ2ζ4−2ζ42ζ5−2ζ52ζ8−2ζ82ζ2−2ζ200000000000000000000000
χ526−3+3i3−3−3i3-21−i31+i3004ζ74ζ4ζ44ζ54ζ84ζ2000-221−i3−1+i31+i3−1−i3−2ζ72ζ7−2ζ2ζ−2ζ42ζ4−2ζ52ζ5−2ζ82ζ8−2ζ22ζ200000000000000000000000
χ536−3−3i3−3+3i3-21+i31−i3004ζ24ζ84ζ54ζ44ζ4ζ70002-2−1−i31+i3−1+i31−i32ζ2−2ζ22ζ8−2ζ82ζ5−2ζ52ζ4−2ζ42ζ−2ζ2ζ7−2ζ700000000000000000000000
χ546−3−3i3−3+3i3-21+i31−i3004ζ24ζ84ζ54ζ44ζ4ζ7000-221+i3−1−i31−i3−1+i3−2ζ22ζ2−2ζ82ζ8−2ζ52ζ5−2ζ42ζ4−2ζ2ζ−2ζ72ζ700000000000000000000000
χ556−3−3i3−3+3i3-21+i31−i3004ζ54ζ24ζ84ζ4ζ74ζ40002-2−1−i31+i3−1+i31−i32ζ5−2ζ52ζ2−2ζ22ζ8−2ζ82ζ−2ζ2ζ7−2ζ72ζ4−2ζ400000000000000000000000
χ566−3−3i3−3+3i3-21+i31−i3004ζ54ζ24ζ84ζ4ζ74ζ4000-221+i3−1−i31−i3−1+i3−2ζ52ζ5−2ζ22ζ2−2ζ82ζ8−2ζ2ζ−2ζ72ζ7−2ζ42ζ400000000000000000000000
χ576−3−3i3−3+3i3-21+i31−i3004ζ84ζ54ζ24ζ74ζ44ζ0002-2−1−i31+i3−1+i31−i32ζ8−2ζ82ζ5−2ζ52ζ2−2ζ22ζ7−2ζ72ζ4−2ζ42ζ−2ζ00000000000000000000000
χ586−3−3i3−3+3i3-21+i31−i3004ζ84ζ54ζ24ζ74ζ44ζ000-221+i3−1−i31−i3−1+i3−2ζ82ζ8−2ζ52ζ5−2ζ22ζ2−2ζ72ζ7−2ζ42ζ4−2ζ2ζ00000000000000000000000

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