Finite Group Databasebeta

← Group #72272532

Character table — Group #72272532

Order 5120.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020256256256256256256256256256256256256256256256256
order12222222222222222224444444444444444444444444444444444445555101010101010101010101010
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111ζζ2ζ3ζ4ζζζζ2ζ2ζ2ζ3ζ3ζ3ζ4ζ4ζ4
χ31111111111111111111111111111111111111111111111111111111ζ2ζ4ζζ3ζ2ζ2ζ2ζ4ζ4ζ4ζζζζ3ζ3ζ3
χ41111111111111111111111111111111111111111111111111111111ζ3ζζ4ζ2ζ3ζ3ζ3ζζζζ4ζ4ζ4ζ2ζ2ζ2
χ51111111111111111111111111111111111111111111111111111111ζ4ζ3ζ2ζζ4ζ4ζ4ζ3ζ3ζ3ζ2ζ2ζ2ζζζ
χ6555511111111111111-3111111111111111111555-3-3-3-3-3-3-3-3-3-3-3-3-3-3-30000000000000000
χ7555511111111111111-311111155-3-3-3-3-3-3-3-3-3-311-311111111115-3-3-3-30000000000000000
χ8555511111111111111-35-3-3-3-3-31-3111115-3-3-3-31-31111115-3-3-3-3111110000000000000000
χ9555511111111111111-3-35-3-3-3-3-315-3-3-3-311111-3115-3-3-3-311111111110000000000000000
χ1055551111111115-3-3-3-3111111-31-3115-3-3111-3-31-31-311-3-3-311151111-30000000000000000
χ115555111111111-35-3-3-3111111-3-31-35111-3-3-311-3111-3-31115-3-311111-30000000000000000
χ1255551111115-3-3111-3-31111-3-3511-3-311-311-31111-31111-3-311-3-3-311510000000000000000
χ135555111111-3-3-31115-31-3-35111-3111-3-3111-3111-311111-31-3-31115-31-30000000000000000
χ145555111111-3-3-3-3-3511-31115-31-311111-3-3-31111-31-311-31111-311-35110000000000000000
χ15555511115-311-31-311-31-31-3-3111111-3111-351-3-311-31151111-31-311-3-30000000000000000
χ1655551111-3511-3-31-3-31-31-311-3111111-35-3111-3-3111111-31-3511-311-310000000000000000
χ1755551111-3-31151-311-311-311-3-31-311-311-3115111-315-31-3111-311-3-3110000000000000000
χ1855551111-3-3-3511-31-31-31-31-311-31111-311-311511-31-3511-3111-31111-30000000000000000
χ1955551111-3-3-3-31-31-31-31-31-31-311-3-3-31-311-31-315551111111111111110000000000000000
χ205555115-3111-311-3-3-31-3-3111-311-311-35111-31111-3-3-311111-351111-310000000000000000
χ21555511-35111-31-3111-311-3-3-3111-31111-3-3511111-31-31-351-3111111-3-30000000000000000
χ22555511-3-311151-3111-31-3111-3-3111111-311-3-35-311-315111-3111-3-3-3110000000000000000
χ23555511-3-311-315-311-31-3-311-31111-3-31111115-31-31151-3111-311-3111-30000000000000000
χ24555511-3-311-31-31-3-31-311-3-31-31551111111111-31111-3-31-31-31-3511110000000000000000
χ25555511-3-3-3-351111-311-311-3115-3111-311-311-311-31-31-3111-31111115-30000000000000000
χ265555151-3-3111111-31-31-3-31151-311-311-31111-31-311-3111111-3-31-31-350000000000000000
χ27555515-311-31-3-3111-31-311115-31-3-31-3111-3111-311111-31-3-311111-3150000000000000000
χ2855551-3151-311-31-3-311-3-31111-311-311-3115-3111-3111-3151111-3-3-31110000000000000000
χ2955551-31-31-311-3-311-3-31511111-311-31-315111111-3-31-3-315111111-3-310000000000000000
χ3055551-31-31-3-3-3151111-31-3-3111111-3511-31-311-3111-3111111-35-31-3110000000000000000
χ3155551-31-3-311111151-3111-351-311-31-3-311111-311-31-3111-3-3-311-315110000000000000000
χ3255551-31-3-31111-3-3151-3115-3111-3-3111-3111-31-31111-311-311-31151-310000000000000000
χ3355551-3511-3-3111111-31111-311-31-31151-311-3-3-311111-3-31-315-31-31110000000000000000
χ3455551-3-3115-3111111-31111-3111-31-3-3151-3-3111-31-3-3-311-315111-31110000000000000000
χ3555551-3-31511-31-31-311-31-3111-3-311-3111115-3111-31115-3-31-3111-31110000000000000000
χ3655551-3-31-311-311-31-3-311511111151111-3-31-311-315111111-31-3-31-3-310000000000000000
χ3755551-3-31-31-31-315111-3-31-31111-31511-31111-311-3-3111-31511-311-3110000000000000000
χ385555511-3-311-3-3111155111-31-31-31-31-31-31111-311-3111111-31-31-311-30000000000000000
χ39555551-311-3111-3-3115511-31-31-31-3111111-31-31-311-311-3-3111111-3-310000000000000000
χ4055555-31111-31111-3-355-3-311111111-31-31-31-3111-311-3-311-31-31-311110000000000000000
χ415555-3115-31-311111-3111111-31-311-3-311151-3-3-311-31115-31-3-3111-3110000000000000000
χ425555-311-3151-311-31111-31-311-3-31-31115111-3111-3111-31115-3-311-31-30000000000000000
χ435555-311-31-31-311511111-31-3-311115-3-31111-311-31111-31-35111-3-31-310000000000000000
χ445555-311-31-3-31-3-31-31111511111-35111111-31-311-351111-3-31-311-311-30000000000000000
χ455555-311-351-311111-3111111-311-3-311-3-3-315111-311-3-3511-311-311-3110000000000000000
χ465555-3151-3111-3-3111111-3-311-3111-315-31-31111-3111-311-31151-31-31-30000000000000000
χ475555-31-311-3111115-311-3-315111-31-311111-3-31-31111-31-31111-3115-3-30000000000000000
χ485555-31-311-311111-35111151-3-3111-3111-3-311-311-3-3-31-311111-3-351110000000000000000
χ495555-31-31-3111-3511111-311-3-31-31-315111-311111-311-3111-3-3151-31-310000000000000000
χ505555-31-31-31-3-311-3-311151111111-31-31-351111-3111-311-351111-3-311-30000000000000000
χ515555-351111-311-3-3111111-3-35111111-31-31-3-3111-3-31-31-311-311-311150000000000000000
χ525555-3-3111115-311-311111-31111-3-3-3-311-311151-31115-3-311-3-31111-310000000000000000
χ535555-3-311111-3511-311111-3111-31111-3-31-3-351-311-35111-3-311-3111-310000000000000000
χ545555-3-31111511-3-31111-3-311151-3111-311-311-3-3111-31-3111-3111-3-3510000000000000000
χ555555-3-311-3-31-31-311-311-311-31-35511111111111-31-3-311-31-31-31511110000000000000000
χ565555-3-3-3-31111-31-31-3111-31-31-3-3111-31-3-31-31-35551111111111111110000000000000000
χ571616-16-1600000000000000000000000000000000000000000000000000011111-1-11-1-11-1-11-1-1
χ581616-16-16000000000000000000000000000000000000000000000000000ζζ2ζ3ζ4ζ−ζ−ζζ2−ζ2−ζ2ζ3−ζ3−ζ3ζ4−ζ4−ζ4
χ591616-16-16000000000000000000000000000000000000000000000000000ζ2ζ4ζζ3ζ2−ζ2−ζ2ζ4−ζ4−ζ4ζ−ζ−ζζ3−ζ3−ζ3
χ601616-16-16000000000000000000000000000000000000000000000000000ζ3ζζ4ζ2ζ3−ζ3−ζ3ζ−ζ−ζζ4−ζ4−ζ4ζ2−ζ2−ζ2
χ611616-16-16000000000000000000000000000000000000000000000000000ζ4ζ3ζ2ζζ4−ζ4−ζ4ζ3−ζ3−ζ3ζ2−ζ2−ζ2ζ−ζ−ζ
χ6216-1616-160000000000000000000000000000000000000000000000000001111-11-1-11-1-11-1-11-1
χ6316-1616-16000000000000000000000000000000000000000000000000000ζζ2ζ3ζ4−ζζ−ζ−ζ2ζ2−ζ2−ζ3ζ3−ζ3−ζ4ζ4−ζ4
χ6416-1616-16000000000000000000000000000000000000000000000000000ζ2ζ4ζζ3−ζ2ζ2−ζ2−ζ4ζ4−ζ4−ζζ−ζ−ζ3ζ3−ζ3
χ6516-1616-16000000000000000000000000000000000000000000000000000ζ3ζζ4ζ2−ζ3ζ3−ζ3−ζζ−ζ−ζ4ζ4−ζ4−ζ2ζ2−ζ2
χ6616-1616-16000000000000000000000000000000000000000000000000000ζ4ζ3ζ2ζ−ζ4ζ4−ζ4−ζ3ζ3−ζ3−ζ2ζ2−ζ2−ζζ−ζ
χ6716-16-16160000000000000000000000000000000000000000000000000001111-1-11-1-11-1-11-1-11
χ6816-16-1616000000000000000000000000000000000000000000000000000ζζ2ζ3ζ4−ζ−ζζ−ζ2−ζ2ζ2−ζ3−ζ3ζ3−ζ4−ζ4ζ4
χ6916-16-1616000000000000000000000000000000000000000000000000000ζ2ζ4ζζ3−ζ2−ζ2ζ2−ζ4−ζ4ζ4−ζ−ζζ−ζ3−ζ3ζ3
χ7016-16-1616000000000000000000000000000000000000000000000000000ζ3ζζ4ζ2−ζ3−ζ3ζ3−ζ−ζζ−ζ4−ζ4ζ4−ζ2−ζ2ζ2
χ7116-16-1616000000000000000000000000000000000000000000000000000ζ4ζ3ζ2ζ−ζ4−ζ4ζ4−ζ3−ζ3ζ3−ζ2−ζ2ζ2−ζ−ζζ

Here ζ is a primitive root of unity of order 5 (ζ5 = 1).