Finite Group Databasebeta

← Group #72222243

Character table — Group #72222243

Order 6048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size1336778891818212121212424242424243232545656565663637272727296969696168168168168224224224224252252252252252252252252252252252252
order1227333321414666666212121213314333366424242422121212166663333244466121212121212
χ11111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111−1+i32−1−i3211111−1+i32−1+i32−1−i32−1−i32111111111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211111111−1+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−i32
χ41111−1+i32−1−i3211111−1+i32−1+i32−1−i32−1−i32111111111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321+i321−i321−i321+i321+i321−i321+i32
χ51111−1−i32−1+i3211111−1−i32−1−i32−1+i32−1+i32111111111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211111111−1−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+i32
χ61111−1−i32−1+i3211111−1−i32−1−i32−1+i32−1+i32111111111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321−i321+i321+i321−i321−i321+i321−i32
χ72222222-122222222-122-1-1-1-122-12-12222-1-1-1-1-1-12-12-1-1-1-1-1000000000000
χ8222222-122222222-12-1-122-1-12-12-1222-1-122-1-1-1-1-12-12-1-1-1-1000000000000
χ9222222-1-12222222-1-1-1-1-1-12-12-1-1-1-122-1-1-1-122-1-1-1-1-1-12-12-1000000000000
χ10222222-1-12222222-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-1-122-1-1-1-1-12-12000000000000
χ112222−1+i3−1−i32-1222−1+i3−1+i3−1−i3−1−i32-122-1-1-1-12−1+i31−i32−1−i31+i32−1+i3−1−i322-1-1-1-1-1-1−1+i31−i32−1−i31+i321−i321−i321+i321+i32000000000000
χ122222−1+i3−1−i3-12222−1+i3−1+i3−1−i3−1−i3-12-1-122-1-121−i32−1+i31+i32−1−i3−1+i3−1−i3-1-122-1-1-1-11−i32−1+i31+i32−1−i31−i321−i321+i321+i32000000000000
χ132222−1+i3−1−i3-1-1222−1+i3−1+i3−1−i3−1−i3-1-1-1-1-1-12-121−i321−i321+i321+i32−1+i3−1−i3-1-1-1-122-1-11−i321−i321+i321+i32−1+i31−i32−1−i31+i32000000000000
χ142222−1+i3−1−i3-1-1222−1+i3−1+i3−1−i3−1−i3-1-1-1-1-1-1-1221−i321−i321+i321+i32−1+i3−1−i3-1-1-1-1-1-1221−i321−i321+i321+i321−i32−1+i31+i32−1−i3000000000000
χ152222−1−i3−1+i32-1222−1−i3−1−i3−1+i3−1+i32-122-1-1-1-12−1−i31+i32−1+i31−i32−1−i3−1+i322-1-1-1-1-1-1−1−i31+i32−1+i31−i321+i321+i321−i321−i32000000000000
χ162222−1−i3−1+i3-12222−1−i3−1−i3−1+i3−1+i3-12-1-122-1-121+i32−1−i31−i32−1+i3−1−i3−1+i3-1-122-1-1-1-11+i32−1−i31−i32−1+i31+i321+i321−i321−i32000000000000
χ172222−1−i3−1+i3-1-1222−1−i3−1−i3−1+i3−1+i3-1-1-1-1-1-12-121+i321+i321−i321−i32−1−i3−1+i3-1-1-1-122-1-11+i321+i321−i321−i32−1−i31+i32−1+i31−i32000000000000
χ182222−1−i3−1+i3-1-1222−1−i3−1−i3−1+i3−1+i3-1-1-1-1-1-1-1221+i321+i321−i321−i32−1−i3−1+i3-1-1-1-1-1-1221+i321+i321−i321−i321+i32−1−i31−i32−1+i3000000000000
χ1933-133303-13-13-13-10-1003300-10303-1-100-1-100000-10-1000011-1-1111-11-1-1-1
χ2033-133303-13-13-13-10-1003300-10303-1-100-1-100000-10-10000-1-111-1-1-11-1111
χ2133-13−3+3i32−3−3i3203-13-1−3+3i321−i32−3−3i321+i320-1003300-10−3+3i320−3−3i321−i321+i3200-1-1000001−i3201+i32000011-1-1−1+i32−1−i32−1+i321−i32−1−i321+i321−i321+i32
χ2233-13−3+3i32−3−3i3203-13-1−3+3i321−i32−3−3i321+i320-1003300-10−3+3i320−3−3i321−i321+i3200-1-1000001−i3201+i320000-1-1111−i321+i321−i32−1+i321+i32−1−i32−1+i32−1−i32
χ2333-13−3−3i32−3+3i3203-13-1−3−3i321+i32−3+3i321−i320-1003300-10−3−3i320−3+3i321+i321−i3200-1-1000001+i3201−i32000011-1-1−1−i32−1+i32−1−i321+i32−1+i321−i321+i321−i32
χ2433-13−3−3i32−3+3i3203-13-1−3−3i321+i32−3+3i321−i320-1003300-10−3−3i320−3+3i321+i321−i3200-1-1000001+i3201−i320000-1-1111+i321−i321+i32−1−i321−i32−1+i32−1−i32−1+i32
χ253-1333330-1-13-13-13-10330000-13030-1-1-1-1000000-10-1000001-11-111-11-11-1-1
χ263-1333330-1-13-13-13-10330000-13030-1-1-1-1000000-10-100000-11-11-1-11-11-111
χ273-133−3+3i32−3−3i3230-1-131−i32−3+3i321+i32−3−3i32-10330000-1−3+3i320−3−3i3201−i321+i32-1-10000001−i3201+i32000001-11-1−1+i32−1−i321−i32−1+i321+i32−1−i321−i321+i32
χ283-133−3+3i32−3−3i3230-1-131−i32−3+3i321+i32−3−3i32-10330000-1−3+3i320−3−3i3201−i321+i32-1-10000001−i3201+i3200000-11-111−i321+i32−1+i321−i32−1−i321+i32−1+i32−1−i32
χ293-133−3−3i32−3+3i3230-1-131+i32−3−3i321−i32−3+3i32-10330000-1−3−3i320−3+3i3201+i321−i32-1-10000001+i3201−i32000001-11-1−1−i32−1+i321+i32−1−i321−i32−1+i321+i321−i32
χ303-133−3−3i32−3+3i3230-1-131+i32−3−3i321−i32−3+3i32-10330000-1−3−3i320−3+3i3201+i321−i32-1-10000001+i3201−i3200000-11-111+i321−i32−1−i321+i32−1+i321−i32−1−i32−1+i32
χ31666-100666-1-1000066-1-1-1-166-1000000-1-1-1-1-1-1-1-100000000000000000000
χ32666-1006-36-1-100006-3-1-11−2121+212-3-3-1000000-1-11−2121+2121−2121+2121−2121+21200000000000000000000
χ33666-1006-36-1-100006-3-1-11+2121−212-3-3-1000000-1-11+2121−2121+2121−2121+2121−21200000000000000000000
χ34666-100-366-1-10000-361−2121+212-1-1-3-3-10000001−2121+212-1-11−2121+2121+2121−21200000000000000000000
χ35666-100-366-1-10000-361+2121−212-1-1-3-3-10000001+2121−212-1-11+2121−2121−2121+21200000000000000000000
χ36666-100-3-36-1-10000-3-31−2121+2121−2121+212-36-10000001−2121+2121−2121+2121+2121−212-1-100000000000000000000
χ37666-100-3-36-1-10000-3-31−2121+2121+2121−2126-3-10000001−2121+2121+2121−212-1-11−2121+21200000000000000000000
χ38666-100-3-36-1-10000-3-31+2121−2121−2121+2126-3-10000001+2121−2121−2121+212-1-11+2121−21200000000000000000000
χ39666-100-3-36-1-10000-3-31+2121−2121+2121−212-36-10000001+2121−2121+2121−2121−2121+212-1-100000000000000000000
χ4066-26660-3-26-26-26-20100-3-300-20-30-3-2-20011000001010000000000000000
χ4166-26−3+3i3−3−3i30-3-26-2−3+3i31−i3−3−3i31+i30100-3-300-203−3i3203+3i321−i31+i3001100000−1+i320−1−i320000000000000000
χ4266-26−3−3i3−3+3i30-3-26-2−3−3i31+i3−3+3i31−i30100-3-300-203+3i3203−3i321+i31−i3001100000−1−i320−1+i320000000000000000
χ436-26666-30-2-26-26-2610-3-30000-2-30-30-2-21100000010100000000000000000
χ446-266−3+3i3−3−3i3-30-2-261−i3−3+3i31+i3−3−3i310-3-30000-23−3i3203+3i3201−i31+i311000000−1+i320−1−i3200000000000000000
χ456-266−3−3i3−3+3i3-30-2-261+i3−3−3i31−i3−3+3i310-3-30000-23+3i3203−3i3201+i31−i311000000−1−i320−1+i3200000000000000000
χ469-3-3999001-3-3-3-3-3-300000000100001100000000000000001-1-1111-1-1-1-111
χ479-3-3999001-3-3-3-3-3-30000000010000110000000000000000-111-1-1-11111-1-1
χ489-3-39−9+9i32−9−9i32001-3-33−3i323−3i323+3i323+3i320000000010000−1+i32−1−i3200000000000000001-1-11−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32
χ499-3-39−9+9i32−9−9i32001-3-33−3i323−3i323+3i323+3i320000000010000−1+i32−1−i320000000000000000-111-11−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i32
χ509-3-39−9−9i32−9+9i32001-3-33+3i323+3i323−3i323−3i320000000010000−1−i32−1+i3200000000000000001-1-11−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32
χ519-3-39−9−9i32−9+9i32001-3-33+3i323+3i323−3i323−3i320000000010000−1−i32−1+i320000000000000000-111-11+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i32
χ521818-6-300018-6-3100000-600-3-30010000000011000000000000000000000000
χ531818-6-3000-9-6-31000003003−32123+321200100000000−1+212−1−212000000000000000000000000
χ541818-6-3000-9-6-31000003003+32123−321200100000000−1−212−1+212000000000000000000000000
χ5518-618-300180-61-30000-60-3-3000010000001100000000000000000000000000
χ5618-618-300-90-61-30000303−32123+321200001000000−1+212−1−21200000000000000000000000000
χ5718-618-300-90-61-30000303+32123−321200001000000−1−212−1+21200000000000000000000000000
χ5854-18-18-90000633000000000000-10000000000000000000000000000000000

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