Finite Group Databasebeta

← Group #11721635

Character table — Group #11721635

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73
size11222222233334444444466666666666666666612121212121212121212121212121212121212121212363636363636363636363636
order1223446663366226666121233366666666666121212126666666666666666121212121212246688121224242424
χ11111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1
χ41111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111
χ5111111111−1+i32−1−i32−1+i32−1−i32111111111−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+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−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ6111111111−1+i32−1−i32−1+i32−1−i32111111111−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+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−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321+i32-1-11−i321+i321−i321−i321+i321+i32
χ7111111111−1+i32−1−i32−1+i32−1−i32-1-1-1-1-1-1111−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32-1-1−1+i32−1−i321−i321−i321+i321+i32
χ8111111111−1+i32−1−i32−1+i32−1−i32-1-1-1-1-1-1111−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321+i32111−i321+i32−1+i32−1+i32−1−i32−1−i32
χ9111111111−1−i32−1+i32−1−i32−1+i32111111111−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−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+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ10111111111−1−i32−1+i32−1−i32−1+i32111111111−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−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+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321−i32-1-11+i321−i321+i321+i321−i321−i32
χ11111111111−1−i32−1+i32−1−i32−1+i32-1-1-1-1-1-1111−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32-1-1−1−i32−1+i321+i321+i321−i321−i32
χ12111111111−1−i32−1+i32−1−i32−1+i32-1-1-1-1-1-1111−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321−i32111+i321−i32−1−i32−1−i32−1+i32−1+i32
χ1311-11-11-1-1111111-111-1-11-1111-1-1-1-1-1-1-1-1111-1-1111-11-111-1-111-1-111-1-11-11-11-11-1111-1-1-11-11-1
χ1411-11-11-1-1111111-111-1-11-1111-1-1-1-1-1-1-1-1111-1-1111-11-111-1-111-1-111-1-11-11-11-1-11-1-1-1111-11-11
χ1511-11-11-1-111111-11-1-1111-1111-1-1-1-1-1-1-1-1111-1-111-11-11-1-111-1-111-1-1111-11-11-11-111-11-1-1-11-11
χ1611-11-11-1-111111-11-1-1111-1111-1-1-1-1-1-1-1-1111-1-111-11-11-1-111-1-111-1-1111-11-11-1-11-1-11-1111-11-1
χ1711-11-11-1-11−1+i32−1−i32−1+i32−1−i321-111-1-11-11−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i321−1+i32−1−i321−i321+i32−1+i32−1−i32−1+i321−i32−1−i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-1−1+i321−i32−1−i321+i321-1−1+i32−1−i321-11−i321+i32−1+i321−i32−1−i321+i32
χ1811-11-11-1-11−1+i32−1−i32−1+i32−1−i321-111-1-11-11−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i321−1+i32−1−i321−i321+i32−1+i32−1−i32−1+i321−i32−1−i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-1−1+i321−i32−1−i321+i32-111−i321+i32-11−1+i32−1−i321−i32−1+i321+i32−1−i32
χ1911-11-11-1-11−1+i32−1−i32−1+i32−1−i32-11-1-1111-11−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i321−1+i32−1−i321−i321+i32−1+i32−1−i321−i32−1+i321+i32−1−i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321-1−1+i321−i32−1−i321+i321-1−1+i32−1−i32-111−i321+i321−i32−1+i321+i32−1−i32
χ2011-11-11-1-11−1+i32−1−i32−1+i32−1−i32-11-1-1111-11−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i321−1+i32−1−i321−i321+i32−1+i32−1−i321−i32−1+i321+i32−1−i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321-1−1+i321−i32−1−i321+i32-111−i321+i321-1−1+i32−1−i32−1+i321−i32−1−i321+i32
χ2111-11-11-1-11−1−i32−1+i32−1−i32−1+i321-111-1-11-11−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i321−1−i32−1+i321+i321−i32−1−i32−1+i32−1−i321+i32−1+i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-1−1−i321+i32−1+i321−i321-1−1−i32−1+i321-11+i321−i32−1−i321+i32−1+i321−i32
χ2211-11-11-1-11−1−i32−1+i32−1−i32−1+i321-111-1-11-11−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i321−1−i32−1+i321+i321−i32−1−i32−1+i32−1−i321+i32−1+i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-1−1−i321+i32−1+i321−i32-111+i321−i32-11−1−i32−1+i321+i32−1−i321−i32−1+i32
χ2311-11-11-1-11−1−i32−1+i32−1−i32−1+i32-11-1-1111-11−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i321−1−i32−1+i321+i321−i32−1−i32−1+i321+i32−1−i321−i32−1+i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321-1−1−i321+i32−1+i321−i321-1−1−i32−1+i32-111+i321−i321+i32−1−i321−i32−1+i32
χ2411-11-11-1-11−1−i32−1+i32−1−i32−1+i32-11-1-1111-11−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i321−1−i32−1+i321+i321−i32−1−i32−1+i321+i32−1−i321−i32−1+i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321-1−1−i321+i32−1+i321−i32-111+i321−i321-1−1−i32−1+i32−1−i321+i32−1+i321−i32
χ25222222222222222222222-1-1-122-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ262222222222222-2-2-2-2-2-222-1-1-122-1-1-1-1-1-1-1-1-12222-2-2-2-2111111111111-1-1-1-1-1-1000000000000
χ27222222222−1+i3−1−i3−1+i3−1−i322222222-11−i321+i32−1+i3−1−i3-1-11−i321−i321+i321+i32-11−i321+i32−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-1-11−i321−i321+i321+i32000000000000
χ28222222222−1+i3−1−i3−1+i3−1−i3-2-2-2-2-2-222-11−i321+i32−1+i3−1−i3-1-11−i321−i321+i321+i32-11−i321+i32−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i31111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-11−i321−i321+i321+i32000000000000
χ29222222222−1−i3−1+i3−1−i3−1+i322222222-11+i321−i32−1−i3−1+i3-1-11+i321+i321−i321−i32-11+i321−i32−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-1-11+i321+i321−i321−i32000000000000
χ30222222222−1−i3−1+i3−1−i3−1+i3-2-2-2-2-2-222-11+i321−i32−1−i3−1+i3-1-11+i321+i321−i321−i32-11+i321−i32−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i31111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-11+i321+i321−i321−i32000000000000
χ312222-2-22222222000000-2-222222222222222-2-2-2-20000000000000000-2-2-2-2-2-2000000000000
χ322222-2-22222222000000-2-2-1-1-122-1-1-1-1-1-1-1-1-1-2-2-2-20000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3111111000000000000
χ332222-2-22222222000000-2-2-1-1-122-1-1-1-1-1-1-1-1-1-2-2-2-20000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3111111000000000000
χ342222-2-2222−1+i3−1−i3−1+i3−1−i3000000-2-22−1+i3−1−i3−1+i3−1−i322−1+i3−1+i3−1−i3−1−i32−1+i3−1−i31−i31+i31−i31+i30000000000000000-2-21−i31−i31+i31+i3000000000000
χ352222-2-2222−1+i3−1−i3−1+i3−1−i3000000-2-2-11−i321+i32−1+i3−1−i3-1-11−i321−i321+i321+i32-11−i321+i321−i31+i31−i31+i30000i3−i3i3−i3−3−i323+i32−3−i323+i323−i32−3+i323−i32−3+i3211−1+i32−1+i32−1−i32−1−i32000000000000
χ362222-2-2222−1+i3−1−i3−1+i3−1−i3000000-2-2-11−i321+i32−1+i3−1−i3-1-11−i321−i321+i321+i32-11−i321+i321−i31+i31−i31+i30000−i3i3−i3i33+i32−3−i323+i32−3−i32−3+i323−i32−3+i323−i3211−1+i32−1+i32−1−i32−1−i32000000000000
χ372222-2-2222−1−i3−1+i3−1−i3−1+i3000000-2-22−1−i3−1+i3−1−i3−1+i322−1−i3−1−i3−1+i3−1+i32−1−i3−1+i31+i31−i31+i31−i30000000000000000-2-21+i31+i31−i31−i3000000000000
χ382222-2-2222−1−i3−1+i3−1−i3−1+i3000000-2-2-11+i321−i32−1−i3−1+i3-1-11+i321+i321−i321−i32-11+i321−i321+i31−i31+i31−i30000i3−i3i3−i33−i32−3+i323−i32−3+i32−3−i323+i32−3−i323+i3211−1−i32−1−i32−1+i32−1+i32000000000000
χ392222-2-2222−1−i3−1+i3−1−i3−1+i3000000-2-2-11+i321−i32−1−i3−1+i3-1-11+i321+i321−i321−i32-11+i321−i321+i31−i31+i31−i30000−i3i3−i3i3−3+i323−i32−3+i323−i323+i32−3−i323+i32−3−i3211−1−i32−1−i32−1+i32−1+i32000000000000
χ4022-222-2-2-222222000000-22222-2-2-2-2-2-2-2-222222-2-20000000000000000-22-22-22000000000000
χ4122-222-2-2-222222000000-22-1-1-1-2-2111111-1-1-122-2-20000i3−i3−i3i3i3−i3−i3i3i3−i3−i3i31-11-11-1000000000000
χ4222-222-2-2-222222000000-22-1-1-1-2-2111111-1-1-122-2-20000−i3i3i3−i3−i3i3i3−i3−i3i3i3−i31-11-11-1000000000000
χ4322-222-2-2-22−1+i3−1−i3−1+i3−1−i3000000-222−1+i3−1−i31−i31+i3-2-21−i31−i31+i31+i32−1+i3−1−i3−1+i3−1−i31−i31+i30000000000000000-221−i3−1+i31+i3−1−i3000000000000
χ4422-222-2-2-22−1+i3−1−i3−1+i3−1−i3000000-22-11−i321+i321−i31+i311−1+i32−1+i32−1−i32−1−i32-11−i321+i32−1+i3−1−i31−i31+i30000i3−i3−i3i3−3−i323+i323+i32−3−i323−i32−3+i32−3+i323−i321-1−1+i321−i32−1−i321+i32000000000000
χ4522-222-2-2-22−1+i3−1−i3−1+i3−1−i3000000-22-11−i321+i321−i31+i311−1+i32−1+i32−1−i32−1−i32-11−i321+i32−1+i3−1−i31−i31+i30000−i3i3i3−i33+i32−3−i32−3−i323+i32−3+i323−i323−i32−3+i321-1−1+i321−i32−1−i321+i32000000000000
χ4622-222-2-2-22−1−i3−1+i3−1−i3−1+i3000000-222−1−i3−1+i31+i31−i3-2-21+i31+i31−i31−i32−1−i3−1+i3−1−i3−1+i31+i31−i30000000000000000-221+i3−1−i31−i3−1+i3000000000000
χ4722-222-2-2-22−1−i3−1+i3−1−i3−1+i3000000-22-11+i321−i321+i31−i311−1−i32−1−i32−1+i32−1+i32-11+i321−i32−1−i3−1+i31+i31−i30000i3−i3−i3i33−i32−3+i32−3+i323−i32−3−i323+i323+i32−3−i321-1−1−i321+i32−1+i321−i32000000000000
χ4822-222-2-2-22−1−i3−1+i3−1−i3−1+i3000000-22-11+i321−i321+i31−i311−1−i32−1−i32−1+i32−1+i32-11+i321−i32−1−i3−1+i31+i31−i30000−i3i3i3−i3−3+i323−i323−i32−3+i323+i32−3−i32−3−i323+i321-1−1−i321+i32−1+i321−i32000000000000
χ4922-22-22-2-2222222-222-2-22-2-1-1-1-2-2111111-1-1-1-2-2222-22-2-1-111-1-111-1-111-11-11-11000000000000
χ5022-22-22-2-222222-22-2-2222-2-1-1-1-2-2111111-1-1-1-2-222-22-2211-1-111-1-111-1-1-11-11-11000000000000
χ5122-22-22-2-22−1+i3−1−i3−1+i3−1−i32-222-2-22-2-11−i321+i321−i31+i311−1+i32−1+i32−1−i32−1−i32-11−i321+i321−i31+i3−1+i3−1−i3−1+i31−i3−1−i31+i3-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-111−i32−1+i321+i32−1−i32000000000000
χ5222-22-22-2-22−1+i3−1−i3−1+i3−1−i3-22-2-2222-2-11−i321+i321−i31+i311−1+i32−1+i32−1−i32−1−i32-11−i321+i321−i31+i3−1+i3−1−i31−i3−1+i31+i3−1−i311-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-111−i32−1+i321+i32−1−i32000000000000
χ5322-22-22-2-22−1−i3−1+i3−1−i3−1+i32-222-2-22-2-11+i321−i321+i31−i311−1−i32−1−i32−1+i32−1+i32-11+i321−i321+i31−i3−1−i3−1+i3−1−i31+i3−1+i31−i3-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-111+i32−1−i321−i32−1+i32000000000000
χ5422-22-22-2-22−1−i3−1+i3−1−i3−1+i3-22-2-2222-2-11+i321−i321+i31−i311−1−i32−1−i32−1+i32−1+i32-11+i321−i321+i31−i3−1−i3−1+i31+i3−1−i31−i3−1+i311-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-111+i32−1−i321−i32−1+i32000000000000
χ554-4040000-444-4-40000000044400000000-4-4-400000000000000000000000000000000000000
χ564-4040000-444-4-400000000-2-2-2002i3−2i32i3−2i32i3−2i322200000000000000000000000000000000000000
χ574-4040000-444-4-400000000-2-2-200−2i32i3−2i32i3−2i32i322200000000000000000000000000000000000000
χ584-4040000-4−2+2i3−2−2i32−2i32+2i3000000004−2+2i3−2−2i300000000-42−2i32+2i300000000000000000000000000000000000000
χ594-4040000-4−2+2i3−2−2i32−2i32+2i300000000-21−i31+i3002i3−2i3−3−i33+i33−i3−3+i32−1+i3−1−i300000000000000000000000000000000000000
χ604-4040000-4−2+2i3−2−2i32−2i32+2i300000000-21−i31+i300−2i32i33+i3−3−i3−3+i33−i32−1+i3−1−i300000000000000000000000000000000000000
χ614-4040000-4−2−2i3−2+2i32+2i32−2i3000000004−2−2i3−2+2i300000000-42+2i32−2i300000000000000000000000000000000000000
χ624-4040000-4−2−2i3−2+2i32+2i32−2i300000000-21+i31−i3002i3−2i33−i3−3+i3−3−i33+i32−1−i3−1+i300000000000000000000000000000000000000
χ634-4040000-4−2−2i3−2+2i32+2i32−2i300000000-21+i31−i300−2i32i3−3+i33−i33+i3−3−i32−1−i3−1+i300000000000000000000000000000000000000
χ64666-366-3-3-3000066-3-3-3-3-3-30000000000000000000000000000000000000000000000000000
χ65666-366-3-3-30000-6-63333-3-30000000000000000000000000000000000000000000000000000
χ66666-3-6-6-3-3-30000003i3−3i33i3−3i3330000000000000000000000000000000000000000000000000000
χ67666-3-6-6-3-3-3000000−3i33i3−3i33i3330000000000000000000000000000000000000000000000000000
χ6866-6-36-633-30000003i3−3i3−3i33i33-30000000000000000000000000000000000000000000000000000
χ6966-6-36-633-3000000−3i33i33i3−3i33-30000000000000000000000000000000000000000000000000000
χ7066-6-3-6633-300006-6-3-333-330000000000000000000000000000000000000000000000000000
χ7166-6-3-6633-30000-6633-3-3-330000000000000000000000000000000000000000000000000000
χ7212-120-6006i3−6i360000000000000000000000000000000000000000000000000000000000000000
χ7312-120-600−6i36i360000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).