Finite Group Databasebeta

← Group #13181815

Character table — Group #13181815

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size126668888889161618242424242424323232323236108144144126668888889161618242424242424323232323236108144144
order132663333332336666666333332466262666666662666666666666662466
χ1111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-111111111111111111111111111-1-1-1-1
χ311111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i321−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1−i3211−1+i32−1−i3211111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i321−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1−i3211−1+i32−1−i32
χ411111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i321−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1−i32-1-11−i321+i3211111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i321−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1−i32-1-11−i321+i32
χ511111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i321−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1+i3211−1−i32−1+i3211111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i321−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1+i3211−1−i32−1+i32
χ611111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i321−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1+i32-1-11+i321−i3211111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i321−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1+i32-1-11+i321−i32
χ722222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-122000022222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1220000
χ8222221−i321−i321−i321+i321+i321+i322−1+i3−1−i321−i321−i321−i321+i321+i321+i32-1-1-1−1+i3−1−i30000222221−i321−i321−i321+i321+i321+i322−1+i3−1−i321−i321−i321−i321+i321+i321+i32-1-1-1−1+i3−1−i30000
χ9222221+i321+i321+i321−i321−i321−i322−1−i3−1+i321+i321+i321+i321−i321−i321−i32-1-1-1−1−i3−1+i30000222221+i321+i321+i321−i321−i321−i322−1−i3−1+i321+i321+i321+i321−i321−i321−i32-1-1-1−1−i3−1+i30000
χ102-12-1-12-1-12-1-1222-12-1-12-1-12-1-1-1-100002-12-1-12-1-12-1-1222-12-1-12-1-12-1-1-1-10000
χ112-12-1-1-12-1-12-1222-1-12-1-12-1-12-1-1-100002-12-1-1-12-1-12-1222-1-12-1-12-1-12-1-1-10000
χ122-12-1-1-1-12-1-12222-1-1-12-1-12-1-12-1-100002-12-1-1-1-12-1-12222-1-1-12-1-12-1-12-1-10000
χ132-12-1-1−1+i31−i321−i32−1−i31+i321+i322−1+i3−1−i3-1−1+i31−i321−i32−1−i31+i321+i322-1-11−i321+i3200002-12-1-1−1+i31−i321−i32−1−i31+i321+i322−1+i3−1−i3-1−1+i31−i321−i32−1−i31+i321+i322-1-11−i321+i320000
χ142-12-1-11−i32−1+i31−i321+i32−1−i31+i322−1+i3−1−i3-11−i32−1+i31−i321+i32−1−i31+i32-12-11−i321+i3200002-12-1-11−i32−1+i31−i321+i32−1−i31+i322−1+i3−1−i3-11−i32−1+i31−i321+i32−1−i31+i32-12-11−i321+i320000
χ152-12-1-11−i321−i32−1+i31+i321+i32−1−i32−1+i3−1−i3-11−i321−i32−1+i31+i321+i32−1−i3-1-121−i321+i3200002-12-1-11−i321−i32−1+i31+i321+i32−1−i32−1+i3−1−i3-11−i321−i32−1+i31+i321+i32−1−i3-1-121−i321+i320000
χ162-12-1-1−1−i31+i321+i32−1+i31−i321−i322−1−i3−1+i3-1−1−i31+i321+i32−1+i31−i321−i322-1-11+i321−i3200002-12-1-1−1−i31+i321+i32−1+i31−i321−i322−1−i3−1+i3-1−1−i31+i321+i32−1+i31−i321−i322-1-11+i321−i320000
χ172-12-1-11+i32−1−i31+i321−i32−1+i31−i322−1−i3−1+i3-11+i32−1−i31+i321−i32−1+i31−i32-12-11+i321−i3200002-12-1-11+i32−1−i31+i321−i32−1+i31−i322−1−i3−1+i3-11+i32−1−i31+i321−i32−1+i31−i32-12-11+i321−i320000
χ182-12-1-11+i321+i32−1−i31−i321−i32−1+i32−1−i3−1+i3-11+i321+i32−1−i31−i321−i32−1+i3-1-121+i321−i3200002-12-1-11+i321+i32−1−i31−i321−i32−1+i32−1−i3−1+i3-11+i321+i32−1−i31−i321−i32−1+i3-1-121+i321−i320000
χ1966222333333-200-2-1-1-1-1-1-100000000066222333333-200-2-1-1-1-1-1-1000000000
χ2066222−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32-200-21−i321−i321−i321+i321+i321+i3200000000066222−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32-200-21−i321−i321−i321+i321+i321+i32000000000
χ2166222−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32-200-21+i321+i321+i321−i321−i321−i3200000000066222−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32-200-21+i321+i321+i321−i321−i321−i32000000000
χ226-32−1+2i3−1−2i33−3+3i32−3−3i323−3−3i32−3+3i32-2001-11−i321+i32-11+i321−i320000000006-32−1+2i3−1−2i33−3+3i32−3−3i323−3−3i32−3+3i32-2001-11−i321+i32-11+i321−i32000000000
χ236-32−1+2i3−1−2i3−3+3i32−3−3i323−3−3i32−3+3i323-20011−i321+i32-11+i321−i32-10000000006-32−1+2i3−1−2i3−3+3i32−3−3i323−3−3i32−3+3i323-20011−i321+i32-11+i321−i32-1000000000
χ246-32−1+2i3−1−2i3−3−3i323−3+3i32−3+3i323−3−3i32-20011+i32-11−i321−i32-11+i320000000006-32−1+2i3−1−2i3−3−3i323−3+3i32−3+3i323−3−3i32-20011+i32-11−i321−i32-11+i32000000000
χ256-32−1−2i3−1+2i33−3−3i32−3+3i323−3+3i32−3−3i32-2001-11+i321−i32-11−i321+i320000000006-32−1−2i3−1+2i33−3−3i32−3+3i323−3+3i32−3−3i32-2001-11+i321−i32-11−i321+i32000000000
χ266-32−1−2i3−1+2i3−3+3i323−3−3i32−3−3i323−3+3i32-20011−i32-11+i321+i32-11−i320000000006-32−1−2i3−1+2i3−3+3i323−3−3i32−3−3i323−3+3i32-20011−i32-11+i321+i32-11−i32000000000
χ276-32−1−2i3−1+2i3−3−3i32−3+3i323−3+3i32−3−3i323-20011+i321−i32-11−i321+i32-10000000006-32−1−2i3−1+2i3−3−3i32−3+3i323−3+3i32−3−3i323-20011+i321−i32-11−i321+i32-1000000000
χ2899-3-3-30000001001000000000003-10099-3-3-30000001001000000000003-100
χ2999-3-3-3000000100100000000000-310099-3-3-3000000100100000000000-3100
χ3018-9-633000000200-100000000000000018-9-633000000200-1000000000000000
χ31111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3211111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ3311111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i321−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1−i3211−1+i32−1−i32-1-1-1-1-11−i321−i321−i321+i321+i321+i32-11−i321+i32-11−i321−i321−i321+i321+i321+i32-1-1-11−i321+i32-1-11−i321+i32
χ3411111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i321−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1−i32-1-11−i321+i32-1-1-1-1-11−i321−i321−i321+i321+i321+i32-11−i321+i32-11−i321−i321−i321+i321+i321+i32-1-1-11−i321+i3211−1+i32−1−i32
χ3511111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i321−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1+i3211−1−i32−1+i32-1-1-1-1-11+i321+i321+i321−i321−i321−i32-11+i321−i32-11+i321+i321+i321−i321−i321−i32-1-1-11+i321−i32-1-11+i321−i32
χ3611111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i321−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1+i32-1-11+i321−i32-1-1-1-1-11+i321+i321+i321−i321−i321−i32-11+i321−i32-11+i321+i321+i321−i321−i321−i32-1-1-11+i321−i3211−1−i32−1+i32
χ3722222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1220000-2-2-2-2-2111111-2-2-2-2111111111-2-20000
χ38222221−i321−i321−i321+i321+i321+i322−1+i3−1−i321−i321−i321−i321+i321+i321+i32-1-1-1−1+i3−1−i30000-2-2-2-2-2−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-21−i31+i3-2−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111−i31+i30000
χ39222221+i321+i321+i321−i321−i321−i322−1−i3−1+i321+i321+i321+i321−i321−i321−i32-1-1-1−1−i3−1+i30000-2-2-2-2-2−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-21+i31−i3-2−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111+i31−i30000
χ402-12-1-12-1-12-1-1222-12-1-12-1-12-1-1-1-10000-21-211-211-211-2-2-21-211-211-211110000
χ412-12-1-1-12-1-12-1222-1-12-1-12-1-12-1-1-10000-21-2111-211-21-2-2-211-211-211-21110000
χ422-12-1-1-1-12-1-12222-1-1-12-1-12-1-12-1-10000-21-21111-211-2-2-2-2111-211-211-2110000
χ432-12-1-1−1+i31−i321−i32−1−i31+i321+i322−1+i3−1−i3-1−1+i31−i321−i32−1−i31+i321+i322-1-11−i321+i320000-21-2111−i3−1+i32−1+i321+i3−1−i32−1−i32-21−i31+i311−i3−1+i32−1+i321+i3−1−i32−1−i32-211−1+i32−1−i320000
χ442-12-1-11−i32−1+i31−i321+i32−1−i31+i322−1+i3−1−i3-11−i32−1+i31−i321+i32−1−i31+i32-12-11−i321+i320000-21-211−1+i321−i3−1+i32−1−i321+i3−1−i32-21−i31+i31−1+i321−i3−1+i32−1−i321+i3−1−i321-21−1+i32−1−i320000
χ452-12-1-11−i321−i32−1+i31+i321+i32−1−i32−1+i3−1−i3-11−i321−i32−1+i31+i321+i32−1−i3-1-121−i321+i320000-21-211−1+i32−1+i321−i3−1−i32−1−i321+i3-21−i31+i31−1+i32−1+i321−i3−1−i32−1−i321+i311-2−1+i32−1−i320000
χ462-12-1-1−1−i31+i321+i32−1+i31−i321−i322−1−i3−1+i3-1−1−i31+i321+i32−1+i31−i321−i322-1-11+i321−i320000-21-2111+i3−1−i32−1−i321−i3−1+i32−1+i32-21+i31−i311+i3−1−i32−1−i321−i3−1+i32−1+i32-211−1−i32−1+i320000
χ472-12-1-11+i32−1−i31+i321−i32−1+i31−i322−1−i3−1+i3-11+i32−1−i31+i321−i32−1+i31−i32-12-11+i321−i320000-21-211−1−i321+i3−1−i32−1+i321−i3−1+i32-21+i31−i31−1−i321+i3−1−i32−1+i321−i3−1+i321-21−1−i32−1+i320000
χ482-12-1-11+i321+i32−1−i31−i321−i32−1+i32−1−i3−1+i3-11+i321+i32−1−i31−i321−i32−1+i3-1-121+i321−i320000-21-211−1−i32−1−i321+i3−1+i32−1+i321−i3-21+i31−i31−1−i32−1−i321+i3−1+i32−1+i321−i311-2−1−i32−1+i320000
χ4966222333333-200-2-1-1-1-1-1-1000000000-6-6-2-2-2-3-3-3-3-3-32002111111000000000
χ5066222−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32-200-21−i321−i321−i321+i321+i321+i32000000000-6-6-2-2-23−3i323−3i323−3i323+3i323+3i323+3i322002−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32000000000
χ5166222−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32-200-21+i321+i321+i321−i321−i321−i32000000000-6-6-2-2-23+3i323+3i323+3i323−3i323−3i323−3i322002−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32000000000
χ526-32−1+2i3−1−2i33−3+3i32−3−3i323−3−3i32−3+3i32-2001-11−i321+i32-11+i321−i32000000000-63-21−2i31+2i3-33−3i323+3i32-33+3i323−3i32200-11−1+i32−1−i321−1−i32−1+i32000000000
χ536-32−1+2i3−1−2i3−3+3i32−3−3i323−3−3i32−3+3i323-20011−i321+i32-11+i321−i32-1000000000-63-21−2i31+2i33−3i323+3i32-33+3i323−3i32-3200-1−1+i32−1−i321−1−i32−1+i321000000000
χ546-32−1+2i3−1−2i3−3−3i323−3+3i32−3+3i323−3−3i32-20011+i32-11−i321−i32-11+i32000000000-63-21−2i31+2i33+3i32-33−3i323−3i32-33+3i32200-1−1−i321−1+i32−1+i321−1−i32000000000
χ556-32−1−2i3−1+2i33−3−3i32−3+3i323−3+3i32−3−3i32-2001-11+i321−i32-11−i321+i32000000000-63-21+2i31−2i3-33+3i323−3i32-33−3i323+3i32200-11−1−i32−1+i321−1+i32−1−i32000000000
χ566-32−1−2i3−1+2i3−3+3i323−3−3i32−3−3i323−3+3i32-20011−i32-11+i321+i32-11−i32000000000-63-21+2i31−2i33−3i32-33+3i323+3i32-33−3i32200-1−1+i321−1−i32−1−i321−1+i32000000000
χ576-32−1−2i3−1+2i3−3−3i32−3+3i323−3+3i32−3−3i323-20011+i321−i32-11−i321+i32-1000000000-63-21+2i31−2i33+3i323−3i32-33−3i323+3i32-3200-1−1−i32−1+i321−1+i32−1−i321000000000
χ5899-3-3-30000001001000000000003-100-9-9333000000-100-100000000000-3100
χ5999-3-3-3000000100100000000000-3100-9-9333000000-100-1000000000003-100
χ6018-9-633000000200-1000000000000000-1896-3-3000000-2001000000000000000

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