Finite Group Databasebeta

← Group #11723051

Character table — Group #11723051

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size123666666612161632323648481236666666121616323236484812366666661216163232364848
order132446121212122333346633612126121212126333312663361212612121212633331266
χ1111111111111111111111111111111111111111111111111111111
χ211111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32
χ311111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32
χ41111111111-11111-1-1-11111111111-11111-1-1-11111111111-11111-1-1-1
χ51111111111-1−1−i32−1+i32−1−i32−1+i32-11+i321−i321111111111-1−1−i32−1+i32−1−i32−1+i32-11+i321−i321111111111-1−1−i32−1+i32−1−i32−1+i32-11+i321−i32
χ61111111111-1−1+i32−1−i32−1+i32−1−i32-11−i321+i321111111111-1−1+i32−1−i32−1+i32−1−i32-11−i321+i321111111111-1−1+i32−1−i32−1+i32−1−i32-11−i321+i32
χ72-1222-1-1-1-1-1022-1-10002-1222-1-1-1-1-1022-1-10002-1222-1-1-1-1-1022-1-1000
χ82-1222-1-1-1-1-10−1−i3−1+i31+i321−i320002-1222-1-1-1-1-10−1−i3−1+i31+i321−i320002-1222-1-1-1-1-10−1−i3−1+i31+i321−i32000
χ92-1222-1-1-1-1-10−1+i3−1−i31−i321+i320002-1222-1-1-1-1-10−1+i3−1−i31−i321+i320002-1222-1-1-1-1-10−1+i3−1−i31−i321+i32000
χ10333-1-13-1-1-1-130000-100333-1-13-1-1-1-130000-100333-1-13-1-1-1-130000-100
χ11333-1-13-1-1-1-1-30000100333-1-13-1-1-1-1-30000100333-1-13-1-1-1-1-30000100
χ1266-22i−2i-22i2i−2i−2i0000000066-22i−2i-22i2i−2i−2i0000000066-22i−2i-22i2i−2i−2i00000000
χ1366-2−2i2i-2−2i−2i2i2i0000000066-2−2i2i-2−2i−2i2i2i0000000066-2−2i2i-2−2i−2i2i2i00000000
χ146-36-2-2-31111000000006-36-2-2-31111000000006-36-2-2-3111100000000
χ156-3-22i−2i1−ζ2+2ζ7+ζ10ζ2−ζ10+2ζ11−ζ2−2ζ7+ζ10ζ2−ζ10−2ζ11000000006-3-22i−2i1−ζ2+2ζ7+ζ10ζ2−ζ10+2ζ11−ζ2−2ζ7+ζ10ζ2−ζ10−2ζ11000000006-3-22i−2i1−ζ2+2ζ7+ζ10ζ2−ζ10+2ζ11−ζ2−2ζ7+ζ10ζ2−ζ10−2ζ1100000000
χ166-3-22i−2i1ζ2−ζ10+2ζ11−ζ2+2ζ7+ζ10ζ2−ζ10−2ζ11−ζ2−2ζ7+ζ10000000006-3-22i−2i1ζ2−ζ10+2ζ11−ζ2+2ζ7+ζ10ζ2−ζ10−2ζ11−ζ2−2ζ7+ζ10000000006-3-22i−2i1ζ2−ζ10+2ζ11−ζ2+2ζ7+ζ10ζ2−ζ10−2ζ11−ζ2−2ζ7+ζ1000000000
χ176-3-2−2i2i1−ζ2−2ζ7+ζ10ζ2−ζ10−2ζ11−ζ2+2ζ7+ζ10ζ2−ζ10+2ζ11000000006-3-2−2i2i1−ζ2−2ζ7+ζ10ζ2−ζ10−2ζ11−ζ2+2ζ7+ζ10ζ2−ζ10+2ζ11000000006-3-2−2i2i1−ζ2−2ζ7+ζ10ζ2−ζ10−2ζ11−ζ2+2ζ7+ζ10ζ2−ζ10+2ζ1100000000
χ186-3-2−2i2i1ζ2−ζ10−2ζ11−ζ2−2ζ7+ζ10ζ2−ζ10+2ζ11−ζ2+2ζ7+ζ10000000006-3-2−2i2i1ζ2−ζ10−2ζ11−ζ2−2ζ7+ζ10ζ2−ζ10+2ζ11−ζ2+2ζ7+ζ10000000006-3-2−2i2i1ζ2−ζ10−2ζ11−ζ2−2ζ7+ζ10ζ2−ζ10+2ζ11−ζ2+2ζ7+ζ1000000000
χ19111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ2011111111111−1−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+i32−1+i32−1+i32−1+i321−1−i321−1−i32−1+i321−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i321−1+i321−1−i32−1+i321
χ2111111111111−1+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+i32−1+i32−1+i32−1+i32−1−i321−1−i321−1+i32−1−i321−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321−1+i321−1+i32−1−i321−1+i32
χ221111111111-11111-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32
χ231111111111-1−1−i32−1+i32−1−i32−1+i32-11+i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−1−i321−1−i321−i32-11+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1+i321−1+i3211+i321−i32-1
χ241111111111-1−1+i32−1−i32−1+i32−1−i32-11−i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1−i321−1−i3211−i321+i32-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321−1+i321−1+i321+i32-11−i32
χ252-1222-1-1-1-1-1022-1-1000−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i321−i321−i320−1+i3−1+i31−i321−i32000−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i321+i321+i320−1−i3−1−i31+i321+i32000
χ262-1222-1-1-1-1-10−1−i3−1+i31+i321−i32000−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i321−i321−i3202−1−i3-11+i32000−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i321+i321+i320−1+i321−i32-1000
χ272-1222-1-1-1-1-10−1+i3−1−i31−i321+i32000−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i321−i321−i320−1−i321+i32-1000−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i321+i321+i3202−1+i3-11−i32000
χ28333-1-13-1-1-1-130000-100−3+3i32−3+3i32−3+3i321−i321−i32−3+3i321−i321−i321−i321−i32−3+3i3200001−i3200−3−3i32−3−3i32−3−3i321+i321+i32−3−3i321+i321+i321+i321+i32−3−3i3200001+i3200
χ29333-1-13-1-1-1-1-30000100−3+3i32−3+3i32−3+3i321−i321−i32−3+3i321−i321−i321−i321−i323−3i320000−1+i3200−3−3i32−3−3i32−3−3i321+i321+i32−3−3i321+i321+i321+i321+i323+3i320000−1−i3200
χ3066-22i−2i-22i2i−2i−2i00000000−3+3i3−3+3i31−i32ζ7−2ζ71−i32ζ72ζ7−2ζ7−2ζ700000000−3−3i3−3−3i31+i32ζ11−2ζ111+i32ζ112ζ11−2ζ11−2ζ1100000000
χ3166-2−2i2i-2−2i−2i2i2i00000000−3+3i3−3+3i31−i3−2ζ72ζ71−i3−2ζ7−2ζ72ζ72ζ700000000−3−3i3−3−3i31+i3−2ζ112ζ111+i3−2ζ11−2ζ112ζ112ζ1100000000
χ326-36-2-2-3111100000000−3+3i33−3i32−3+3i31−i31−i33−3i32−1+i32−1+i32−1+i32−1+i3200000000−3−3i33+3i32−3−3i31+i31+i33+3i32−1−i32−1−i32−1−i32−1−i3200000000
χ336-3-22i−2i1−ζ2+2ζ7+ζ10ζ2−ζ10+2ζ11−ζ2−2ζ7+ζ10ζ2−ζ10−2ζ1100000000−3+3i33−3i321−i32ζ7−2ζ7−1+i322ζ2+ζ10+2ζ11−2ζ2−2ζ7−ζ10−2ζ112ζ2+ζ10−2ζ11−2ζ2+2ζ7−ζ10+2ζ1100000000−3−3i33+3i321+i32ζ11−2ζ11−1−i32−ζ2−2ζ7−2ζ10−2ζ11ζ2+2ζ7+2ζ10−ζ2+2ζ7−2ζ10+2ζ11ζ2−2ζ7+2ζ1000000000
χ346-3-22i−2i1ζ2−ζ10+2ζ11−ζ2+2ζ7+ζ10ζ2−ζ10−2ζ11−ζ2−2ζ7+ζ1000000000−3+3i33−3i321−i32ζ7−2ζ7−1+i32−2ζ2−2ζ7−ζ10−2ζ112ζ2+ζ10+2ζ11−2ζ2+2ζ7−ζ10+2ζ112ζ2+ζ10−2ζ1100000000−3−3i33+3i321+i32ζ11−2ζ11−1−i32ζ2+2ζ7+2ζ10−ζ2−2ζ7−2ζ10−2ζ11ζ2−2ζ7+2ζ10−ζ2+2ζ7−2ζ10+2ζ1100000000
χ356-3-2−2i2i1−ζ2−2ζ7+ζ10ζ2−ζ10−2ζ11−ζ2+2ζ7+ζ10ζ2−ζ10+2ζ1100000000−3+3i33−3i321−i3−2ζ72ζ7−1+i322ζ2+ζ10−2ζ11−2ζ2+2ζ7−ζ10+2ζ112ζ2+ζ10+2ζ11−2ζ2−2ζ7−ζ10−2ζ1100000000−3−3i33+3i321+i3−2ζ112ζ11−1−i32−ζ2+2ζ7−2ζ10+2ζ11ζ2−2ζ7+2ζ10−ζ2−2ζ7−2ζ10−2ζ11ζ2+2ζ7+2ζ1000000000
χ366-3-2−2i2i1ζ2−ζ10−2ζ11−ζ2−2ζ7+ζ10ζ2−ζ10+2ζ11−ζ2+2ζ7+ζ1000000000−3+3i33−3i321−i3−2ζ72ζ7−1+i32−2ζ2+2ζ7−ζ10+2ζ112ζ2+ζ10−2ζ11−2ζ2−2ζ7−ζ10−2ζ112ζ2+ζ10+2ζ1100000000−3−3i33+3i321+i3−2ζ112ζ11−1−i32ζ2−2ζ7+2ζ10−ζ2+2ζ7−2ζ10+2ζ11ζ2+2ζ7+2ζ10−ζ2−2ζ7−2ζ10−2ζ1100000000
χ37111111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ3811111111111−1−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−i32−1−i32−1−i32−1−i32−1+i321−1+i321−1−i32−1+i321−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−1−i321−1−i32−1+i321−1−i32
χ3911111111111−1+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−i32−1−i32−1−i32−1−i321−1+i321−1+i32−1−i321−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i321−1−i321−1+i32−1−i321
χ401111111111-11111-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32
χ411111111111-1−1−i32−1+i32−1−i32−1+i32-11+i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1+i321−1+i3211+i321−i32-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−1−i321−1−i321−i32-11+i32
χ421111111111-1−1+i32−1−i32−1+i32−1−i32-11−i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321−1+i321−1+i321+i32-11−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1−i321−1−i3211−i321+i32-1
χ432-1222-1-1-1-1-1022-1-1000−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i321+i321+i320−1−i3−1−i31+i321+i32000−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i321−i321−i320−1+i3−1+i31−i321−i32000
χ442-1222-1-1-1-1-10−1−i3−1+i31+i321−i32000−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i321+i321+i320−1+i321−i32-1000−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i321−i321−i3202−1−i3-11+i32000
χ452-1222-1-1-1-1-10−1+i3−1−i31−i321+i32000−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i321+i321+i3202−1+i3-11−i32000−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i321−i321−i320−1−i321+i32-1000
χ46333-1-13-1-1-1-130000-100−3−3i32−3−3i32−3−3i321+i321+i32−3−3i321+i321+i321+i321+i32−3−3i3200001+i3200−3+3i32−3+3i32−3+3i321−i321−i32−3+3i321−i321−i321−i321−i32−3+3i3200001−i3200
χ47333-1-13-1-1-1-1-30000100−3−3i32−3−3i32−3−3i321+i321+i32−3−3i321+i321+i321+i321+i323+3i320000−1−i3200−3+3i32−3+3i32−3+3i321−i321−i32−3+3i321−i321−i321−i321−i323−3i320000−1+i3200
χ4866-22i−2i-22i2i−2i−2i00000000−3−3i3−3−3i31+i32ζ11−2ζ111+i32ζ112ζ11−2ζ11−2ζ1100000000−3+3i3−3+3i31−i32ζ7−2ζ71−i32ζ72ζ7−2ζ7−2ζ700000000
χ4966-2−2i2i-2−2i−2i2i2i00000000−3−3i3−3−3i31+i3−2ζ112ζ111+i3−2ζ11−2ζ112ζ112ζ1100000000−3+3i3−3+3i31−i3−2ζ72ζ71−i3−2ζ7−2ζ72ζ72ζ700000000
χ506-36-2-2-3111100000000−3−3i33+3i32−3−3i31+i31+i33+3i32−1−i32−1−i32−1−i32−1−i3200000000−3+3i33−3i32−3+3i31−i31−i33−3i32−1+i32−1+i32−1+i32−1+i3200000000
χ516-3-22i−2i1−ζ2+2ζ7+ζ10ζ2−ζ10+2ζ11−ζ2−2ζ7+ζ10ζ2−ζ10−2ζ1100000000−3−3i33+3i321+i32ζ11−2ζ11−1−i32−ζ2−2ζ7−2ζ10−2ζ11ζ2+2ζ7+2ζ10−ζ2+2ζ7−2ζ10+2ζ11ζ2−2ζ7+2ζ1000000000−3+3i33−3i321−i32ζ7−2ζ7−1+i322ζ2+ζ10+2ζ11−2ζ2−2ζ7−ζ10−2ζ112ζ2+ζ10−2ζ11−2ζ2+2ζ7−ζ10+2ζ1100000000
χ526-3-22i−2i1ζ2−ζ10+2ζ11−ζ2+2ζ7+ζ10ζ2−ζ10−2ζ11−ζ2−2ζ7+ζ1000000000−3−3i33+3i321+i32ζ11−2ζ11−1−i32ζ2+2ζ7+2ζ10−ζ2−2ζ7−2ζ10−2ζ11ζ2−2ζ7+2ζ10−ζ2+2ζ7−2ζ10+2ζ1100000000−3+3i33−3i321−i32ζ7−2ζ7−1+i32−2ζ2−2ζ7−ζ10−2ζ112ζ2+ζ10+2ζ11−2ζ2+2ζ7−ζ10+2ζ112ζ2+ζ10−2ζ1100000000
χ536-3-2−2i2i1−ζ2−2ζ7+ζ10ζ2−ζ10−2ζ11−ζ2+2ζ7+ζ10ζ2−ζ10+2ζ1100000000−3−3i33+3i321+i3−2ζ112ζ11−1−i32−ζ2+2ζ7−2ζ10+2ζ11ζ2−2ζ7+2ζ10−ζ2−2ζ7−2ζ10−2ζ11ζ2+2ζ7+2ζ1000000000−3+3i33−3i321−i3−2ζ72ζ7−1+i322ζ2+ζ10−2ζ11−2ζ2+2ζ7−ζ10+2ζ112ζ2+ζ10+2ζ11−2ζ2−2ζ7−ζ10−2ζ1100000000
χ546-3-2−2i2i1ζ2−ζ10−2ζ11−ζ2−2ζ7+ζ10ζ2−ζ10+2ζ11−ζ2+2ζ7+ζ1000000000−3−3i33+3i321+i3−2ζ112ζ11−1−i32ζ2−2ζ7+2ζ10−ζ2+2ζ7−2ζ10+2ζ11ζ2+2ζ7+2ζ10−ζ2−2ζ7−2ζ10−2ζ1100000000−3+3i33−3i321−i3−2ζ72ζ7−1+i32−2ζ2+2ζ7−ζ10+2ζ112ζ2+ζ10−2ζ11−2ζ2−2ζ7−ζ10−2ζ112ζ2+ζ10+2ζ1100000000

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