Finite Group Databasebeta

← Group #11721691

Character table — Group #11721691

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73
size11222222233334444444466666666666666666612121212121212121212121212121212121212121212363636363636363636363636
order1223446121233662466612121233366666121212121212121212126666666666612121212121212121212122266668824242424
χ11111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111-1-11-1-11-1-1111111111111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111-1-11-1-11-1-1111111111111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111−1−i32−1+i32−1−i32−1+i32111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32
χ6111111111−1−i32−1+i32−1−i32−1+i32111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32
χ7111111111−1−i32−1+i32−1−i32−1+i32-1-11-1-11-1-11−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32
χ8111111111−1−i32−1+i32−1−i32−1+i32-1-11-1-11-1-11−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32
χ9111111111−1+i32−1−i32−1+i32−1−i32111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32
χ10111111111−1+i32−1−i32−1+i32−1−i32111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32
χ11111111111−1+i32−1−i32−1+i32−1−i32-1-11-1-11-1-11−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32
χ12111111111−1+i32−1−i32−1+i32−1−i32-1-11-1-11-1-11−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32
χ1311-11-111-1-111111-1-1111-1-1111-1-1111-1-1-1-1-1-1-1-11111-1-1-1111111-1-1111-1-1-1-1-1-11-11-11-11-11-11-1
χ1411-11-111-1-111111-1-1111-1-1111-1-1111-1-1-1-1-1-1-1-11111-1-1-1111111-1-1111-1-1-1-1-1-1-11-11-11-11-11-11
χ1511-11-111-1-11111-11-1-1-1111111-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1111111111111-11-11-1-11-11-11
χ1611-11-111-1-11111-11-1-1-1111111-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111111111-11-11-111-11-11-1
χ1711-11-111-1-1−1−i32−1+i32−1−i32−1+i321-1-1111-1-11−1−i32−1+i321+i321−i321−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321-1−1−i321+i32−1+i321−i321-1−1−i321+i32−1+i321−i32
χ1811-11-111-1-1−1−i32−1+i32−1−i32−1+i321-1-1111-1-11−1−i32−1+i321+i321−i321−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i32-111+i32−1−i321−i32−1+i32-111+i32−1−i321−i32−1+i32
χ1911-11-111-1-1−1−i32−1+i32−1−i32−1+i32-11-1-1-11111−1−i32−1+i321+i321−i321−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i32−1−i32−1+i321+i321−i32-11+i321−i32-1-11+i321+i321−i321−i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321-1−1−i321+i32−1+i321−i32-111+i32−1−i321−i32−1+i32
χ2011-11-111-1-1−1−i32−1+i32−1−i32−1+i32-11-1-1-11111−1−i32−1+i321+i321−i321−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i32−1−i32−1+i321+i321−i32-11+i321−i32-1-11+i321+i321−i321−i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-111+i32−1−i321−i32−1+i321-1−1−i321+i32−1+i321−i32
χ2111-11-111-1-1−1+i32−1−i32−1+i32−1−i321-1-1111-1-11−1+i32−1−i321−i321+i321−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321-1−1+i321−i32−1−i321+i321-1−1+i321−i32−1−i321+i32
χ2211-11-111-1-1−1+i32−1−i32−1+i32−1−i321-1-1111-1-11−1+i32−1−i321−i321+i321−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i32-111−i32−1+i321+i32−1−i32-111−i32−1+i321+i32−1−i32
χ2311-11-111-1-1−1+i32−1−i32−1+i32−1−i32-11-1-1-11111−1+i32−1−i321−i321+i321−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i32−1+i32−1−i321−i321+i32-11−i321+i32-1-11−i321−i321+i321+i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321-1−1+i321−i32−1−i321+i32-111−i32−1+i321+i32−1−i32
χ2411-11-111-1-1−1+i32−1−i32−1+i32−1−i32-11-1-1-11111−1+i32−1−i321−i321+i321−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i32−1+i32−1−i321−i321+i32-11−i321+i32-1-11−i321−i321+i321+i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-111−i32−1+i321+i32−1−i321-1−1+i321−i32−1−i321+i32
χ25222222222222222222222-1-1-122-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1000000000000
χ262222222222222-2-22-2-22-2-2-1-1-122-1-1-122-1-1-1-1-1-122-2-2-1-1-1111111-2-2-1-1-1111111000000000000
χ27222222222−1−i3−1+i3−1−i3−1+i322222222-11+i321−i32−1−i3−1+i3-11+i321−i32−1−i3−1+i3-1-11+i321+i321−i321−i32−1−i3−1+i3−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32000000000000
χ28222222222−1−i3−1+i3−1−i3−1+i3-2-22-2-22-2-2-11+i321−i32−1−i3−1+i3-11+i321−i32−1−i3−1+i3-1-11+i321+i321−i321−i32−1−i3−1+i31+i31−i3-11+i321−i3211−1−i32−1−i32−1+i32−1+i321+i31−i3-11+i321−i3211−1−i32−1−i32−1+i32−1+i32000000000000
χ29222222222−1+i3−1−i3−1+i3−1−i322222222-11−i321+i32−1+i3−1−i3-11−i321+i32−1+i3−1−i3-1-11−i321−i321+i321+i32−1+i3−1−i3−1+i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i32−1+i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i32000000000000
χ30222222222−1+i3−1−i3−1+i3−1−i3-2-22-2-22-2-2-11−i321+i32−1+i3−1−i3-11−i321+i32−1+i3−1−i3-1-11−i321−i321+i321+i32−1+i3−1−i31−i31+i3-11−i321+i3211−1+i32−1+i32−1−i32−1−i321−i31+i3-11−i321+i3211−1+i32−1+i32−1−i32−1−i32000000000000
χ312222-2-22-2-2222200200-20022222222-2-2-2-2-2-2-2-2-2-20022200000000-2-2-2000000000000000000
χ322222-2-22-2-2222200200-200-1-1-122-1-1-1-2-2111111-2-200-1-1-1−i3i3−i3i3−i3i300111−i3i3−i3i3−i3i3000000000000
χ332222-2-22-2-2222200200-200-1-1-122-1-1-1-2-2111111-2-200-1-1-1i3−i3i3−i3i3−i300111i3−i3i3−i3i3−i3000000000000
χ342222-2-22-2-2−1−i3−1+i3−1−i3−1+i300200-2002−1−i3−1+i3−1−i3−1+i32−1−i3−1+i31+i31−i3-2-21+i31+i31−i31−i31+i31−i3002−1−i3−1+i300000000-21+i31−i3000000000000000000
χ352222-2-22-2-2−1−i3−1+i3−1−i3−1+i300200-200-11+i321−i32−1−i3−1+i3-11+i321−i321+i31−i311−1−i32−1−i32−1+i32−1+i321+i31−i300-11+i321−i32−i3i3−3+i323−i323+i32−3−i32001−1−i32−1+i32−i3i3−3+i323−i323+i32−3−i32000000000000
χ362222-2-22-2-2−1−i3−1+i3−1−i3−1+i300200-200-11+i321−i32−1−i3−1+i3-11+i321−i321+i31−i311−1−i32−1−i32−1+i32−1+i321+i31−i300-11+i321−i32i3−i33−i32−3+i32−3−i323+i32001−1−i32−1+i32i3−i33−i32−3+i32−3−i323+i32000000000000
χ372222-2-22-2-2−1+i3−1−i3−1+i3−1−i300200-2002−1+i3−1−i3−1+i3−1−i32−1+i3−1−i31−i31+i3-2-21−i31−i31+i31+i31−i31+i3002−1+i3−1−i300000000-21−i31+i3000000000000000000
χ382222-2-22-2-2−1+i3−1−i3−1+i3−1−i300200-200-11−i321+i32−1+i3−1−i3-11−i321+i321−i31+i311−1+i32−1+i32−1−i32−1−i321−i31+i300-11−i321+i32−i3i33+i32−3−i32−3+i323−i32001−1+i32−1−i32−i3i33+i32−3−i32−3+i323−i32000000000000
χ392222-2-22-2-2−1+i3−1−i3−1+i3−1−i300200-200-11−i321+i32−1+i3−1−i3-11−i321+i321−i31+i311−1+i32−1+i32−1−i32−1−i321−i31+i300-11−i321+i32i3−i3−3−i323+i323−i32−3+i32001−1+i32−1−i32i3−i3−3−i323+i323−i32−3+i32000000000000
χ4022-222-2222222200-200-200222-2-222222222222-2-200-2-2-200000000-2-2-2000000000000000000
χ4122-222-2222222200-200-200-1-1-1-2-2-1-1-122-1-1-1-1-1-1-2-200111−i3i3−i3i3−i3i300111i3−i3i3−i3i3−i3000000000000
χ4222-222-2222222200-200-200-1-1-1-2-2-1-1-122-1-1-1-1-1-1-2-200111i3−i3i3−i3i3−i300111−i3i3−i3i3−i3i3000000000000
χ4322-222-2222−1−i3−1+i3−1−i3−1+i300-200-2002−1−i3−1+i31+i31−i32−1−i3−1+i3−1−i3−1+i322−1−i3−1−i3−1+i3−1+i31+i31−i300-21+i31−i300000000-21+i31−i3000000000000000000
χ4422-222-2222−1−i3−1+i3−1−i3−1+i300-200-200-11+i321−i321+i31−i3-11+i321−i32−1−i3−1+i3-1-11+i321+i321−i321−i321+i31−i3001−1−i32−1+i32−i3i3−3+i323−i323+i32−3−i32001−1−i32−1+i32i3−i33−i32−3+i32−3−i323+i32000000000000
χ4522-222-2222−1−i3−1+i3−1−i3−1+i300-200-200-11+i321−i321+i31−i3-11+i321−i32−1−i3−1+i3-1-11+i321+i321−i321−i321+i31−i3001−1−i32−1+i32i3−i33−i32−3+i32−3−i323+i32001−1−i32−1+i32−i3i3−3+i323−i323+i32−3−i32000000000000
χ4622-222-2222−1+i3−1−i3−1+i3−1−i300-200-2002−1+i3−1−i31−i31+i32−1+i3−1−i3−1+i3−1−i322−1+i3−1+i3−1−i3−1−i31−i31+i300-21−i31+i300000000-21−i31+i3000000000000000000
χ4722-222-2222−1+i3−1−i3−1+i3−1−i300-200-200-11−i321+i321−i31+i3-11−i321+i32−1+i3−1−i3-1-11−i321−i321+i321+i321−i31+i3001−1+i32−1−i32−i3i33+i32−3−i32−3+i323−i32001−1+i32−1−i32i3−i3−3−i323+i323−i32−3+i32000000000000
χ4822-222-2222−1+i3−1−i3−1+i3−1−i300-200-200-11−i321+i321−i31+i3-11−i321+i32−1+i3−1−i3-1-11−i321−i321+i321+i321−i31+i3001−1+i32−1−i32i3−i3−3−i323+i323−i32−3+i32001−1+i32−1−i32−i3i33+i32−3−i32−3+i323−i32000000000000
χ4922-22-222-2-222222-2-2222-2-2-1-1-1-2-2-1-1-1-2-21111112222111-1-1-1-1-1-1-2-2-1-1-1111111000000000000
χ5022-22-222-2-22222-22-2-2-2222-1-1-1-2-2-1-1-1-2-211111122-2-211111111122-1-1-1-1-1-1-1-1-1000000000000
χ5122-22-222-2-2−1−i3−1+i3−1−i3−1+i32-2-2222-2-2-11+i321−i321+i31−i3-11+i321−i321+i31−i311−1−i32−1−i32−1+i32−1+i32−1−i3−1+i3−1−i3−1+i31−1−i32−1+i32-1-11+i321+i321−i321−i321+i31−i3-11+i321−i3211−1−i32−1−i32−1+i32−1+i32000000000000
χ5222-22-222-2-2−1−i3−1+i3−1−i3−1+i3-22-2-2-2222-11+i321−i321+i31−i3-11+i321−i321+i31−i311−1−i32−1−i32−1+i32−1+i32−1−i3−1+i31+i31−i31−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32000000000000
χ5322-22-222-2-2−1+i3−1−i3−1+i3−1−i32-2-2222-2-2-11−i321+i321−i31+i3-11−i321+i321−i31+i311−1+i32−1+i32−1−i32−1−i32−1+i3−1−i3−1+i3−1−i31−1+i32−1−i32-1-11−i321−i321+i321+i321−i31+i3-11−i321+i3211−1+i32−1+i32−1−i32−1−i32000000000000
χ5422-22-222-2-2−1+i3−1−i3−1+i3−1−i3-22-2-2-2222-11−i321+i321−i31+i3-11−i321+i321−i31+i311−1+i32−1+i32−1−i32−1−i32−1+i3−1−i31−i31+i31−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i32000000000000
χ554-40400-40044-4-40000000044400-4-4-400000000000000000000000000000000000000000000
χ564-40400-40044-4-400000000-2-2-2002220023−2323−2323−23000000000000000000000000000000000000
χ574-40400-40044-4-400000000-2-2-20022200−2323−2323−2323000000000000000000000000000000000000
χ584-40400-400−2−2i3−2+2i32+2i32−2i3000000004−2−2i3−2+2i300-42+2i32−2i300000000000000000000000000000000000000000000
χ594-40400-400−2−2i3−2+2i32+2i32−2i300000000-21+i31−i3002−1−i3−1+i30023−234ζ7+2ζ11−4ζ7−2ζ11−2ζ7−4ζ112ζ7+4ζ11000000000000000000000000000000000000
χ604-40400-400−2−2i3−2+2i32+2i32−2i300000000-21+i31−i3002−1−i3−1+i300−2323−4ζ7−2ζ114ζ7+2ζ112ζ7+4ζ11−2ζ7−4ζ11000000000000000000000000000000000000
χ614-40400-400−2+2i3−2−2i32−2i32+2i3000000004−2+2i3−2−2i300-42−2i32+2i300000000000000000000000000000000000000000000
χ624-40400-400−2+2i3−2−2i32−2i32+2i300000000-21−i31+i3002−1+i3−1−i30023−23−2ζ7−4ζ112ζ7+4ζ114ζ7+2ζ11−4ζ7−2ζ11000000000000000000000000000000000000
χ634-40400-400−2+2i3−2−2i32−2i32+2i300000000-21−i31+i3002−1+i3−1−i300−23232ζ7+4ζ11−2ζ7−4ζ11−4ζ7−2ζ114ζ7+2ζ11000000000000000000000000000000000000
χ64666-366-3-3-3000066-3-3-3-3-3-30000000000000000000000000000000000000000000000000000
χ65666-366-3-3-30000-6-6-333-3330000000000000000000000000000000000000000000000000000
χ66666-3-6-6-333000000-3−3i33i33−3i33i30000000000000000000000000000000000000000000000000000
χ67666-3-6-6-333000000-33i3−3i333i3−3i30000000000000000000000000000000000000000000000000000
χ6866-6-36-6-3-3-30000003−3i33i333i3−3i30000000000000000000000000000000000000000000000000000
χ6966-6-36-6-3-3-300000033i3−3i33−3i33i30000000000000000000000000000000000000000000000000000
χ7066-6-3-66-33300006-63-3-3-3330000000000000000000000000000000000000000000000000000
χ7166-6-3-66-3330000-66333-3-3-30000000000000000000000000000000000000000000000000000
χ7212-120-600663−630000000000000000000000000000000000000000000000000000000000000000
χ7312-120-6006−63630000000000000000000000000000000000000000000000000000000000000000

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