Finite Group Databasebeta

← Group #11762166

Character table — Group #11762166

Order 1080.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42
size124444444445888888888888910182020202020203636364590135135135135
order13333333515152151515151515151515151515266666666103030264444
χ1111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1
χ3111111111111111111111111-11-1111111-1-1-1-1-1ii−i−i
χ4111111111111111111111111-11-1111111-1-1-1-1-1−i−iii
χ511111111111-11111111111111-11-1-1-1-1-1-1111-1-1i−ii−i
χ611111111111-11111111111111-11-1-1-1-1-1-1111-1-1−ii−ii
χ711111111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11
χ811111111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1
χ92-122-1-1-1-12-1-122222-1-1-1-1-1-1-1-12-1-122-1-1-1-12-1-12-10000
χ102-122-1-1-1-12-1-122222-1-1-1-1-1-1-1-1-2-1122-1-1-1-1-211-210000
χ112-122-1-1-1-12-1-1-22222-1-1-1-1-1-1-1-121-1-2-211112-1-1-210000
χ122-122-1-1-1-12-1-1-22222-1-1-1-1-1-1-1-1-211-2-21111-2112-10000
χ13441-211-2-2444411-2-21111-2-2-2-20401-211-2-2000000000
χ14441-211-2-2444-411-2-21111-2-2-2-20-40-12-1-122000000000
χ1544444444-1-1-10-1-1-1-1-1-1-1-1-1-1-1-1404000000-1-1-1000000
χ1644444444-1-1-10-1-1-1-1-1-1-1-1-1-1-1-1-40-4000000111000000
χ1744-21-2-2114444-2-211-2-2-2-21111040-21-2-211000000000
χ1844-21-2-211444-4-2-211-2-2-2-211110-402-122-1-1000000000
χ194-21-2−1−3i32−1+3i32114-2-2411-2-2−1−3i32−1−3i32−1+3i32−1+3i3211110-201-2−1−3i32−1+3i3211000000000
χ204-21-2−1−3i32−1+3i32114-2-2-411-2-2−1−3i32−1−3i32−1+3i32−1+3i321111020-121+3i321−3i32-1-1000000000
χ214-21-2−1+3i32−1−3i32114-2-2411-2-2−1+3i32−1+3i32−1−3i32−1−3i3211110-201-2−1+3i32−1−3i3211000000000
χ224-21-2−1+3i32−1−3i32114-2-2-411-2-2−1+3i32−1+3i32−1−3i32−1−3i321111020-121−3i321+3i32-1-1000000000
χ234-244-2-2-2-2-11−i1521+i1520-1-1-1-11−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i15240-2000000-11−i1521+i152000000
χ244-244-2-2-2-2-11−i1521+i1520-1-1-1-11−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i152-4020000001−1+i152−1−i152000000
χ254-244-2-2-2-2-11+i1521−i1520-1-1-1-11+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i15240-2000000-11+i1521−i152000000
χ264-244-2-2-2-2-11+i1521−i1520-1-1-1-11+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i152-4020000001−1−i152−1+i152000000
χ274-2-2111−1−3i32−1+3i324-2-24-2-2111111−1−3i32−1+3i32−1−3i32−1+3i320-20-2111−1−3i32−1+3i32000000000
χ284-2-2111−1−3i32−1+3i324-2-2-4-2-2111111−1−3i32−1+3i32−1−3i32−1+3i320202-1-1-11+3i321−3i32000000000
χ294-2-2111−1+3i32−1−3i324-2-24-2-2111111−1+3i32−1−3i32−1+3i32−1−3i320-20-2111−1+3i32−1−3i32000000000
χ304-2-2111−1+3i32−1−3i324-2-2-4-2-2111111−1+3i32−1−3i32−1+3i32−1−3i320202-1-1-11−3i321+3i32000000000
χ31882-422-4-4-2-2-20−1−352−1+35211−1−352−1+352−1+352−1−3521111000000000000000000
χ32882-422-4-4-2-2-20−1+352−1−35211−1+352−1−352−1−352−1+3521111000000000000000000
χ3388-42-4-422-2-2-2011−1−352−1+3521111−1−352−1+352−1+352−1−352000000000000000000
χ3488-42-4-422-2-2-2011−1+352−1−3521111−1+352−1−352−1−352−1+352000000000000000000
χ358-42-4−1−3i3−1+3i322-21−i151+i150−1+352−1−35211ζ14−2ζ22+ζ26−2ζ58ζ2−2ζ34+ζ38−2ζ46−2ζ14+ζ22−2ζ26+ζ58−2ζ2+ζ34−2ζ38+ζ46−1+i152−1+i152−1−i152−1−i152000000000000000000
χ368-42-4−1−3i3−1+3i322-21+i151−i150−1−352−1+35211ζ2−2ζ34+ζ38−2ζ46ζ14−2ζ22+ζ26−2ζ58−2ζ2+ζ34−2ζ38+ζ46−2ζ14+ζ22−2ζ26+ζ58−1−i152−1−i152−1+i152−1+i152000000000000000000
χ378-42-4−1+3i3−1−3i322-21−i151+i150−1−352−1+35211−2ζ14+ζ22−2ζ26+ζ58−2ζ2+ζ34−2ζ38+ζ46ζ14−2ζ22+ζ26−2ζ58ζ2−2ζ34+ζ38−2ζ46−1+i152−1+i152−1−i152−1−i152000000000000000000
χ388-42-4−1+3i3−1−3i322-21+i151−i150−1+352−1−35211−2ζ2+ζ34−2ζ38+ζ46−2ζ14+ζ22−2ζ26+ζ58ζ2−2ζ34+ζ38−2ζ46ζ14−2ζ22+ζ26−2ζ58−1−i152−1−i152−1+i152−1+i152000000000000000000
χ398-4-4222−1−3i3−1+3i3-21−i151+i15011−1+352−1−352−1+i152−1−i152−1+i152−1−i152ζ14−2ζ22+ζ26−2ζ58−2ζ14+ζ22−2ζ26+ζ58ζ2−2ζ34+ζ38−2ζ46−2ζ2+ζ34−2ζ38+ζ46000000000000000000
χ408-4-4222−1−3i3−1+3i3-21+i151−i15011−1−352−1+352−1−i152−1+i152−1−i152−1+i152ζ2−2ζ34+ζ38−2ζ46−2ζ2+ζ34−2ζ38+ζ46ζ14−2ζ22+ζ26−2ζ58−2ζ14+ζ22−2ζ26+ζ58000000000000000000
χ418-4-4222−1+3i3−1−3i3-21−i151+i15011−1−352−1+352−1+i152−1−i152−1+i152−1−i152−2ζ14+ζ22−2ζ26+ζ58ζ14−2ζ22+ζ26−2ζ58−2ζ2+ζ34−2ζ38+ζ46ζ2−2ζ34+ζ38−2ζ46000000000000000000
χ428-4-4222−1+3i3−1−3i3-21+i151−i15011−1+352−1−352−1−i152−1+i152−1−i152−1+i152−2ζ2+ζ34−2ζ38+ζ46ζ2−2ζ34+ζ38−2ζ46−2ζ14+ζ22−2ζ26+ζ58ζ14−2ζ22+ζ26−2ζ58000000000000000000

Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.