Finite Group Databasebeta

← Group #11721528

Character table — Group #11721528

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73
size11222222233334444444466666666666666666612121212121212121212121212121212121212121212363636363636363636363636
order1223446121233666881224242424669991212121218181836363636363618181824242424363636727272727272727272727272244466121212121212
χ11111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111-1-11-1-1-1-1111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ411111111111111-1-11-1-1-1-1111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ5111111111−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321111−1−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
χ6111111111−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11+i321−i321+i321−i321+i321+i321−i321−i32
χ7111111111−1−i32−1+i32−1−i32−1+i321-1-11-1-1-1-1−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321+i321+i321−i321−i321−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3211-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32
χ8111111111−1−i32−1+i32−1−i32−1+i321-1-11-1-1-1-1−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321+i321+i321−i321−i321−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-1-1111+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32
χ9111111111−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321111−1+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
χ10111111111−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11−i321+i321−i321+i321−i321−i321+i321+i32
χ11111111111−1+i32−1−i32−1+i32−1−i321-1-11-1-1-1-1−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−i321−i321+i321+i321−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3211-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32
χ12111111111−1+i32−1−i32−1+i32−1−i321-1-11-1-1-1-1−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−i321−i321+i321+i321−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-1-1111−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i32
χ1311-11-111111111-11-1-111-1-1-1-1111-1-111111111111-1-1-11-11-1-1-1-111-1-111-1-111-1-11-11-111-1-11-11-1
χ1411-11-111111111-11-1-111-1-1-1-1111-1-111111111111-1-1-11-11-1-1-1-111-1-111-1-111-1-1-11-11-1-111-11-11
χ1511-11-111111111-1-11-1-1-111-1-1111-1-111111111111-1-1-1-11-11-1-1-1-1-111-1-111-1-1111-1-1111-1-1-11-11
χ1611-11-111111111-1-11-1-1-111-1-1111-1-111111111111-1-1-1-11-11-1-1-1-1-111-1-111-1-111-111-1-1-1111-11-1
χ1711-11-11111−1−i32−1+i32−1−i32−1+i32-11-1-111-1-11+i321−i321−1−i32−1+i321+i321−i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i32−1−i321+i32−1+i321−i32-11+i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-11-1−1−i32−1+i321+i321−i32−1−i321+i32−1+i321−i32
χ1811-11-11111−1−i32−1+i32−1−i32−1+i32-11-1-111-1-11+i321−i321−1−i32−1+i321+i321−i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i32−1−i321+i32−1+i321−i32-11+i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-11-111+i321−i32−1−i32−1+i321+i32−1−i321−i32−1+i32
χ1911-11-11111−1−i32−1+i32−1−i32−1+i32-1-11-1-1-1111+i321−i321−1−i32−1+i321+i321−i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i321+i32−1−i321−i32−1+i32-11+i321−i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321-1-11−1−i32−1+i321+i321−i321+i32−1−i321−i32−1+i32
χ2011-11-11111−1−i32−1+i32−1−i32−1+i32-1-11-1-1-1111+i321−i321−1−i32−1+i321+i321−i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i321+i32−1−i321−i32−1+i32-11+i321−i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-111-11+i321−i32−1−i32−1+i32−1−i321+i32−1+i321−i32
χ2111-11-11111−1+i32−1−i32−1+i32−1−i32-11-1-111-1-11−i321+i321−1+i32−1−i321−i321+i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i32−1+i321−i32−1−i321+i32-11−i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-11-1−1+i32−1−i321−i321+i32−1+i321−i32−1−i321+i32
χ2211-11-11111−1+i32−1−i32−1+i32−1−i32-11-1-111-1-11−i321+i321−1+i32−1−i321−i321+i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i32−1+i321−i32−1−i321+i32-11−i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-11-111−i321+i32−1+i32−1−i321−i32−1+i321+i32−1−i32
χ2311-11-11111−1+i32−1−i32−1+i32−1−i32-1-11-1-1-1111−i321+i321−1+i32−1−i321−i321+i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i321−i32−1+i321+i32−1−i32-11−i321+i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321-1-11−1+i32−1−i321−i321+i321−i32−1+i321+i32−1−i32
χ2411-11-11111−1+i32−1−i32−1+i32−1−i32-1-11-1-1-1111−i321+i321−1+i32−1−i321−i321+i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i321−i32−1+i321+i32−1−i32-11−i321+i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-111-11−i321+i32−1+i32−1−i32−1+i321−i32−1−i321+i32
χ2522222222222222222222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ2622222222222222-2-22-2-2-2-222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1111111111111000000000000
χ27222222222−1−i3−1+i3−1−i3−1+i322222222−1−i3−1+i3-11+i321−i32−1−i3−1+i3−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32-11+i321−i32−1−i3−1−i3−1+i3−1+i3-11+i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32000000000000
χ28222222222−1−i3−1+i3−1−i3−1+i32-2-22-2-2-2-2−1−i3−1+i3-11+i321−i32−1−i3−1+i3−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32-11+i321−i321+i31+i31−i31−i3-11+i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32000000000000
χ29222222222−1+i3−1−i3−1+i3−1−i322222222−1+i3−1−i3-11−i321+i32−1+i3−1−i3−1+i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i32-11−i321+i32−1+i3−1+i3−1−i3−1−i3-11−i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32000000000000
χ30222222222−1+i3−1−i3−1+i3−1−i32-2-22-2-2-2-2−1+i3−1−i3-11−i321+i32−1+i3−1−i3−1+i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i32-11−i321+i321−i31−i31+i31+i3-11−i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32000000000000
χ312222-2-22-2-22222200-2000022222-2-2-2-2222-2-2-2-2-2-22220000-2-2-2000000000000000000000000
χ322222-2-22-2-22222200-2000022-1-1-1-2-2-2-2-1-1-1111111-1-1-100001113−33−33−33−33−33−3000000000000
χ332222-2-22-2-22222200-2000022-1-1-1-2-2-2-2-1-1-1111111-1-1-10000111−33−33−33−33−33−33000000000000
χ342222-2-22-2-2−1−i3−1+i3−1−i3−1+i3200-20000−1−i3−1+i32−1−i3−1+i31+i31−i31+i31−i32−1−i3−1+i3-2-21+i31+i31−i31−i32−1−i3−1+i30000-21+i31−i3000000000000000000000000
χ352222-2-22-2-2−1−i3−1+i3−1−i3−1+i3200-20000−1−i3−1+i3-11+i321−i321+i31−i31+i31−i3-11+i321−i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i3200001−1−i32−1+i323−33−32ζ7+ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11000000000000
χ362222-2-22-2-2−1−i3−1+i3−1−i3−1+i3200-20000−1−i3−1+i3-11+i321−i321+i31−i31+i31−i3-11+i321−i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i3200001−1−i32−1+i32−33−33−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11000000000000
χ372222-2-22-2-2−1+i3−1−i3−1+i3−1−i3200-20000−1+i3−1−i32−1+i3−1−i31−i31+i31−i31+i32−1+i3−1−i3-2-21−i31−i31+i31+i32−1+i3−1−i30000-21−i31+i3000000000000000000000000
χ382222-2-22-2-2−1+i3−1−i3−1+i3−1−i3200-20000−1+i3−1−i3-11−i321+i321−i31+i31−i31+i3-11−i321+i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i3200001−1+i32−1−i323−33−3−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ11000000000000
χ392222-2-22-2-2−1+i3−1−i3−1+i3−1−i3200-20000−1+i3−1−i3-11−i321+i321−i31+i31−i31+i3-11−i321+i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i3200001−1+i32−1−i32−33−33ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ11000000000000
χ4022-222-22-2-22222-20020000-2-222222-2-2222-2-2-2-2-2-2-2-2-20000222000000000000000000000000
χ4122-222-22-2-22222-20020000-2-2-1-1-122-2-2-1-1-11111111110000-1-1-13−3−333−3−333−3−33000000000000
χ4222-222-22-2-22222-20020000-2-2-1-1-122-2-2-1-1-11111111110000-1-1-1−333−3−333−3−333−3000000000000
χ4322-222-22-2-2−1−i3−1+i3−1−i3−1+i3-200200001+i31−i32−1−i3−1+i3−1−i3−1+i31+i31−i32−1−i3−1+i3-2-21+i31+i31−i31−i3-21+i31−i300002−1−i3−1+i3000000000000000000000000
χ4422-222-22-2-2−1−i3−1+i3−1−i3−1+i3-200200001+i31−i3-11+i321−i32−1−i3−1+i31+i31−i3-11+i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i320000-11+i321−i323−3−332ζ7+ζ11−2ζ7−ζ11−2ζ7−ζ112ζ7+ζ11−ζ7−2ζ11ζ7+2ζ11ζ7+2ζ11−ζ7−2ζ11000000000000
χ4522-222-22-2-2−1−i3−1+i3−1−i3−1+i3-200200001+i31−i3-11+i321−i32−1−i3−1+i31+i31−i3-11+i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i320000-11+i321−i32−333−3−2ζ7−ζ112ζ7+ζ112ζ7+ζ11−2ζ7−ζ11ζ7+2ζ11−ζ7−2ζ11−ζ7−2ζ11ζ7+2ζ11000000000000
χ4622-222-22-2-2−1+i3−1−i3−1+i3−1−i3-200200001−i31+i32−1+i3−1−i3−1+i3−1−i31−i31+i32−1+i3−1−i3-2-21−i31−i31+i31+i3-21−i31+i300002−1+i3−1−i3000000000000000000000000
χ4722-222-22-2-2−1+i3−1−i3−1+i3−1−i3-200200001−i31+i3-11−i321+i32−1+i3−1−i31−i31+i3-11−i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i320000-11−i321+i323−3−33−ζ7−2ζ11ζ7+2ζ11ζ7+2ζ11−ζ7−2ζ112ζ7+ζ11−2ζ7−ζ11−2ζ7−ζ112ζ7+ζ11000000000000
χ4822-222-22-2-2−1+i3−1−i3−1+i3−1−i3-200200001−i31+i3-11−i321+i32−1+i3−1−i31−i31+i3-11−i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i320000-11−i321+i32−333−3ζ7+2ζ11−ζ7−2ζ11−ζ7−2ζ11ζ7+2ζ11−2ζ7−ζ112ζ7+ζ112ζ7+ζ11−2ζ7−ζ11000000000000
χ4922-22-222222222-22-2-222-2-2-2-2-1-1-1-2-222-1-1-1-1-1-1-1-1-11112-22-2111-1-111-1-111-1-111000000000000
χ5022-22-222222222-2-22-2-2-222-2-2-1-1-1-2-222-1-1-1-1-1-1-1-1-1111-22-2211111-1-111-1-111-1-1000000000000
χ5122-22-22222−1−i3−1+i3−1−i3−1+i3-22-2-222-2-21+i31−i3-11+i321−i321+i31−i3−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i321−1−i32−1+i32−1−i31+i3−1+i31−i31−1−i32−1+i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32000000000000
χ5222-22-22222−1−i3−1+i3−1−i3−1+i3-2-22-2-2-2221+i31−i3-11+i321−i321+i31−i3−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i321−1−i32−1+i321+i3−1−i31−i3−1+i31−1−i32−1+i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32000000000000
χ5322-22-22222−1+i3−1−i3−1+i3−1−i3-22-2-222-2-21−i31+i3-11−i321+i321−i31+i3−1+i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i321−1+i32−1−i32−1+i31−i3−1−i31+i31−1+i32−1−i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32000000000000
χ5422-22-22222−1+i3−1−i3−1+i3−1−i3-2-22-2-2-2221−i31+i3-11−i321+i321−i31+i3−1+i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i321−1+i32−1−i321−i3−1+i31+i3−1−i31−1+i32−1−i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32000000000000
χ554-40400-40044-4-400000000004440000-4-4-40000000000000000000000000000000000000000
χ564-40400-40044-4-40000000000-2-2-2000022223−2323−2323−230000000000000000000000000000000000
χ574-40400-40044-4-40000000000-2-2-20000222−2323−2323−23230000000000000000000000000000000000
χ584-40400-400−2−2i3−2+2i32+2i32−2i300000000004−2−2i3−2+2i30000-42+2i32−2i30000000000000000000000000000000000000000
χ594-40400-400−2−2i3−2+2i32+2i32−2i30000000000-21+i31−i300002−1−i3−1+i323−234ζ7+2ζ11−4ζ7−2ζ11−2ζ7−4ζ112ζ7+4ζ110000000000000000000000000000000000
χ604-40400-400−2−2i3−2+2i32+2i32−2i30000000000-21+i31−i300002−1−i3−1+i3−2323−4ζ7−2ζ114ζ7+2ζ112ζ7+4ζ11−2ζ7−4ζ110000000000000000000000000000000000
χ614-40400-400−2+2i3−2−2i32−2i32+2i300000000004−2+2i3−2−2i30000-42−2i32+2i30000000000000000000000000000000000000000
χ624-40400-400−2+2i3−2−2i32−2i32+2i30000000000-21−i31+i300002−1+i3−1−i323−23−2ζ7−4ζ112ζ7+4ζ114ζ7+2ζ11−4ζ7−2ζ110000000000000000000000000000000000
χ634-40400-400−2+2i3−2−2i32−2i32+2i30000000000-21−i31+i300002−1+i3−1−i3−23232ζ7+4ζ11−2ζ7−4ζ11−4ζ7−2ζ114ζ7+2ζ110000000000000000000000000000000000
χ64666-366-3-3-30000-366-3-3-3-3-30000000000000000000000000000000000000000000000000000
χ65666-366-3-3-30000-3-6-6-333330000000000000000000000000000000000000000000000000000
χ66666-3-6-6-3330000-300333−3333−330000000000000000000000000000000000000000000000000000
χ67666-3-6-6-3330000-3003−3333−33330000000000000000000000000000000000000000000000000000
χ6866-6-36-6-3330000300-333−33−33330000000000000000000000000000000000000000000000000000
χ6966-6-36-6-3330000300-3−333333−330000000000000000000000000000000000000000000000000000
χ7066-6-3-66-3-3-3000036-63-3-3330000000000000000000000000000000000000000000000000000
χ7166-6-3-66-3-3-300003-66333-3-30000000000000000000000000000000000000000000000000000
χ7212-120-600663−630000000000000000000000000000000000000000000000000000000000000000
χ7312-120-6006−63630000000000000000000000000000000000000000000000000000000000000000

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