Finite Group Databasebeta

← Group #13049278

Character table — Group #13049278

Order 1296.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size123336666888991818182424242424242424545454545454123336666888991818182424242424242424545454545454
order13233333699966666999999992466121226266666618181866666181818181818181824661212
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111-1-1-1-1-1-11111111111111111111111111-1-1-1-1-1-1
χ3111−1+i32−1−i321−1+i32−1−i321111−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i321−1+i32−1−i321111−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1−i32
χ4111−1+i32−1−i321−1+i32−1−i321111−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-11−i321+i321−i321+i32111−1+i32−1−i321−1+i32−1−i321111−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-11−i321+i321−i321+i32
χ5111−1−i32−1+i321−1−i32−1+i321111−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i321−1−i32−1+i321111−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1+i32
χ6111−1−i32−1+i321−1−i32−1+i321111−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-11+i321−i321+i321−i32111−1−i32−1+i321−1−i32−1+i321111−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-11+i321−i321+i321−i32
χ7222222222-1-1-122222-1-1-1-1-1-1-1-1000000222222222-1-1-122222-1-1-1-1-1-1-1-1000000
χ822222-1-1-1222222-1-1-1-1-12-1-12-1-100000022222-1-1-1222222-1-1-1-1-12-1-12-1-1000000
χ922222-1-1-12-1-1-122-1-1-12-1-12-1-12-100000022222-1-1-12-1-1-122-1-1-12-1-12-1-12-1000000
χ1022222-1-1-12-1-1-122-1-1-1-12-1-12-1-1200000022222-1-1-12-1-1-122-1-1-1-12-1-12-1-12000000
χ11222−1+i3−1−i32−1+i3−1−i32-1-1-1−1+i3−1−i32−1+i3−1−i3-1-11−i321−i321−i321+i321+i321+i32000000222−1+i3−1−i32−1+i3−1−i32-1-1-1−1+i3−1−i32−1+i3−1−i3-1-11−i321−i321−i321+i321+i321+i32000000
χ12222−1+i3−1−i3-11−i321+i322222−1+i3−1−i3-11−i321+i32-1-1−1+i31−i321−i32−1−i31+i321+i32000000222−1+i3−1−i3-11−i321+i322222−1+i3−1−i3-11−i321+i32-1-1−1+i31−i321−i32−1−i31+i321+i32000000
χ13222−1+i3−1−i3-11−i321+i322-1-1-1−1+i3−1−i3-11−i321+i322-11−i32−1+i31−i321+i32−1−i31+i32000000222−1+i3−1−i3-11−i321+i322-1-1-1−1+i3−1−i3-11−i321+i322-11−i32−1+i31−i321+i32−1−i31+i32000000
χ14222−1+i3−1−i3-11−i321+i322-1-1-1−1+i3−1−i3-11−i321+i32-121−i321−i32−1+i31+i321+i32−1−i3000000222−1+i3−1−i3-11−i321+i322-1-1-1−1+i3−1−i3-11−i321+i32-121−i321−i32−1+i31+i321+i32−1−i3000000
χ15222−1−i3−1+i32−1−i3−1+i32-1-1-1−1−i3−1+i32−1−i3−1+i3-1-11+i321+i321+i321−i321−i321−i32000000222−1−i3−1+i32−1−i3−1+i32-1-1-1−1−i3−1+i32−1−i3−1+i3-1-11+i321+i321+i321−i321−i321−i32000000
χ16222−1−i3−1+i3-11+i321−i322222−1−i3−1+i3-11+i321−i32-1-1−1−i31+i321+i32−1+i31−i321−i32000000222−1−i3−1+i3-11+i321−i322222−1−i3−1+i3-11+i321−i32-1-1−1−i31+i321+i32−1+i31−i321−i32000000
χ17222−1−i3−1+i3-11+i321−i322-1-1-1−1−i3−1+i3-11+i321−i322-11+i32−1−i31+i321−i32−1+i31−i32000000222−1−i3−1+i3-11+i321−i322-1-1-1−1−i3−1+i3-11+i321−i322-11+i32−1−i31+i321−i32−1+i31−i32000000
χ18222−1−i3−1+i3-11+i321−i322-1-1-1−1−i3−1+i3-11+i321−i32-121+i321+i32−1−i31−i321−i32−1+i3000000222−1−i3−1+i3-11+i321−i322-1-1-1−1−i3−1+i3-11+i321−i32-121+i321+i32−1−i31−i321−i32−1+i3000000
χ1933-133333-1000-1-1-1-1-1000000001-111-1-133-133333-1000-1-1-1-1-1000000001-111-1-1
χ2033-133333-1000-1-1-1-1-100000000-11-1-11133-133333-1000-1-1-1-1-100000000-11-1-111
χ2133-1−3+3i32−3−3i323−3+3i32−3−3i32-10001−i321+i32-11−i321+i32000000001-1−1+i32−1−i321−i321+i3233-1−3+3i32−3−3i323−3+3i32−3−3i32-10001−i321+i32-11−i321+i32000000001-1−1+i32−1−i321−i321+i32
χ2233-1−3+3i32−3−3i323−3+3i32−3−3i32-10001−i321+i32-11−i321+i3200000000-111−i321+i32−1+i32−1−i3233-1−3+3i32−3−3i323−3+3i32−3−3i32-10001−i321+i32-11−i321+i3200000000-111−i321+i32−1+i32−1−i32
χ2333-1−3−3i32−3+3i323−3−3i32−3+3i32-10001+i321−i32-11+i321−i32000000001-1−1−i32−1+i321+i321−i3233-1−3−3i32−3+3i323−3−3i32−3+3i32-10001+i321−i32-11+i321−i32000000001-1−1−i32−1+i321+i321−i32
χ2433-1−3−3i32−3+3i323−3−3i32−3+3i32-10001+i321−i32-11+i321−i3200000000-111+i321−i32−1−i32−1+i3233-1−3−3i32−3+3i323−3−3i32−3+3i32-10001+i321−i32-11+i321−i3200000000-111+i321−i32−1−i32−1+i32
χ2566-266-3-3-3-2000-2-21110000000000000066-266-3-3-3-2000-2-211100000000000000
χ2666-2−3+3i3−3−3i3-33−3i323+3i32-20001−i31+i31−1+i32−1−i320000000000000066-2−3+3i3−3−3i3-33−3i323+3i32-20001−i31+i31−1+i32−1−i3200000000000000
χ2766-2−3−3i3−3+3i3-33+3i323−3i32-20001+i31−i31−1−i32−1+i320000000000000066-2−3−3i3−3+3i3-33+3i323−3i32-20001+i31−i31−1−i32−1+i3200000000000000
χ286-3600000-33ζ+3ζ83ζ2+3ζ73ζ4+3ζ500000000000000000006-3600000-33ζ+3ζ83ζ2+3ζ73ζ4+3ζ50000000000000000000
χ296-3600000-33ζ2+3ζ73ζ4+3ζ53ζ+3ζ800000000000000000006-3600000-33ζ2+3ζ73ζ4+3ζ53ζ+3ζ80000000000000000000
χ306-3600000-33ζ4+3ζ53ζ+3ζ83ζ2+3ζ700000000000000000006-3600000-33ζ4+3ζ53ζ+3ζ83ζ2+3ζ70000000000000000000
χ3118-9-6000003000000000000000000000018-9-60000030000000000000000000000
χ321111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ331111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ34111−1+i32−1−i321−1+i32−1−i321111−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1−i32-1-1-11−i321+i32-11−i321+i32-1-1-1-11−i321+i32-11−i321+i32-1-11−i321−i321−i321+i321+i321+i32-1-11−i321+i321−i321+i32
χ35111−1+i32−1−i321−1+i32−1−i321111−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-11−i321+i321−i321+i32-1-1-11−i321+i32-11−i321+i32-1-1-1-11−i321+i32-11−i321+i32-1-11−i321−i321−i321+i321+i321+i3211−1+i32−1−i32−1+i32−1−i32
χ36111−1−i32−1+i321−1−i32−1+i321111−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1+i32-1-1-11+i321−i32-11+i321−i32-1-1-1-11+i321−i32-11+i321−i32-1-11+i321+i321+i321−i321−i321−i32-1-11+i321−i321+i321−i32
χ37111−1−i32−1+i321−1−i32−1+i321111−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-11+i321−i321+i321−i32-1-1-11+i321−i32-11+i321−i32-1-1-1-11+i321−i32-11+i321−i32-1-11+i321+i321+i321−i321−i321−i3211−1−i32−1+i32−1−i32−1+i32
χ38222222222-1-1-122222-1-1-1-1-1-1-1-1000000-2-2-2-2-2-2-2-2-2111-2-2-2-2-211111111000000
χ3922222-1-1-1222222-1-1-1-1-12-1-12-1-1000000-2-2-2-2-2111-2-2-2-2-2-211111-211-211000000
χ4022222-1-1-12-1-1-122-1-1-12-1-12-1-12-1000000-2-2-2-2-2111-2111-2-2111-211-211-21000000
χ4122222-1-1-12-1-1-122-1-1-1-12-1-12-1-12000000-2-2-2-2-2111-2111-2-21111-211-211-2000000
χ42222−1+i3−1−i32−1+i3−1−i32-1-1-1−1+i3−1−i32−1+i3−1−i3-1-11−i321−i321−i321+i321+i321+i32000000-2-2-21−i31+i3-21−i31+i3-21111−i31+i3-21−i31+i311−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32000000
χ43222−1+i3−1−i3-11−i321+i322222−1+i3−1−i3-11−i321+i32-1-1−1+i31−i321−i32−1−i31+i321+i32000000-2-2-21−i31+i31−1+i32−1−i32-2-2-2-21−i31+i31−1+i32−1−i32111−i3−1+i32−1+i321+i3−1−i32−1−i32000000
χ44222−1+i3−1−i3-11−i321+i322-1-1-1−1+i3−1−i3-11−i321+i322-11−i32−1+i31−i321+i32−1−i31+i32000000-2-2-21−i31+i31−1+i32−1−i32-21111−i31+i31−1+i32−1−i32-21−1+i321−i3−1+i32−1−i321+i3−1−i32000000
χ45222−1+i3−1−i3-11−i321+i322-1-1-1−1+i3−1−i3-11−i321+i32-121−i321−i32−1+i31+i321+i32−1−i3000000-2-2-21−i31+i31−1+i32−1−i32-21111−i31+i31−1+i32−1−i321-2−1+i32−1+i321−i3−1−i32−1−i321+i3000000
χ46222−1−i3−1+i32−1−i3−1+i32-1-1-1−1−i3−1+i32−1−i3−1+i3-1-11+i321+i321+i321−i321−i321−i32000000-2-2-21+i31−i3-21+i31−i3-21111+i31−i3-21+i31−i311−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32000000
χ47222−1−i3−1+i3-11+i321−i322222−1−i3−1+i3-11+i321−i32-1-1−1−i31+i321+i32−1+i31−i321−i32000000-2-2-21+i31−i31−1−i32−1+i32-2-2-2-21+i31−i31−1−i32−1+i32111+i3−1−i32−1−i321−i3−1+i32−1+i32000000
χ48222−1−i3−1+i3-11+i321−i322-1-1-1−1−i3−1+i3-11+i321−i322-11+i32−1−i31+i321−i32−1+i31−i32000000-2-2-21+i31−i31−1−i32−1+i32-21111+i31−i31−1−i32−1+i32-21−1−i321+i3−1−i32−1+i321−i3−1+i32000000
χ49222−1−i3−1+i3-11+i321−i322-1-1-1−1−i3−1+i3-11+i321−i32-121+i321+i32−1−i31−i321−i32−1+i3000000-2-2-21+i31−i31−1−i32−1+i32-21111+i31−i31−1−i32−1+i321-2−1−i32−1−i321+i3−1+i32−1+i321−i3000000
χ5033-133333-1000-1-1-1-1-1000000001-111-1-1-3-31-3-3-3-3-310001111100000000-11-1-111
χ5133-133333-1000-1-1-1-1-100000000-11-1-111-3-31-3-3-3-3-3100011111000000001-111-1-1
χ5233-1−3+3i32−3−3i323−3+3i32−3−3i32-10001−i321+i32-11−i321+i32000000001-1−1+i32−1−i321−i321+i32-3-313−3i323+3i32-33−3i323+3i321000−1+i32−1−i321−1+i32−1−i3200000000-111−i321+i32−1+i32−1−i32
χ5333-1−3+3i32−3−3i323−3+3i32−3−3i32-10001−i321+i32-11−i321+i3200000000-111−i321+i32−1+i32−1−i32-3-313−3i323+3i32-33−3i323+3i321000−1+i32−1−i321−1+i32−1−i32000000001-1−1+i32−1−i321−i321+i32
χ5433-1−3−3i32−3+3i323−3−3i32−3+3i32-10001+i321−i32-11+i321−i32000000001-1−1−i32−1+i321+i321−i32-3-313+3i323−3i32-33+3i323−3i321000−1−i32−1+i321−1−i32−1+i3200000000-111+i321−i32−1−i32−1+i32
χ5533-1−3−3i32−3+3i323−3−3i32−3+3i32-10001+i321−i32-11+i321−i3200000000-111+i321−i32−1−i32−1+i32-3-313+3i323−3i32-33+3i323−3i321000−1−i32−1+i321−1−i32−1+i32000000001-1−1−i32−1+i321+i321−i32
χ5666-266-3-3-3-2000-2-211100000000000000-6-62-6-6333200022-1-1-100000000000000
χ5766-2−3+3i3−3−3i3-33−3i323+3i32-20001−i31+i31−1+i32−1−i3200000000000000-6-623−3i33+3i33−3+3i32−3−3i322000−1+i3−1−i3-11−i321+i3200000000000000
χ5866-2−3−3i3−3+3i3-33+3i323−3i32-20001+i31−i31−1−i32−1+i3200000000000000-6-623+3i33−3i33−3−3i32−3+3i322000−1−i3−1+i3-11+i321−i3200000000000000
χ596-3600000-33ζ+3ζ83ζ2+3ζ73ζ4+3ζ50000000000000000000-63-6000003−3ζ−3ζ8−3ζ2−3ζ7−3ζ4−3ζ50000000000000000000
χ606-3600000-33ζ2+3ζ73ζ4+3ζ53ζ+3ζ80000000000000000000-63-6000003−3ζ2−3ζ7−3ζ4−3ζ5−3ζ−3ζ80000000000000000000
χ616-3600000-33ζ4+3ζ53ζ+3ζ83ζ2+3ζ70000000000000000000-63-6000003−3ζ4−3ζ5−3ζ−3ζ8−3ζ2−3ζ70000000000000000000
χ6218-9-60000030000000000000000000000-189600000-30000000000000000000000

Here ζ is a primitive root of unity of order 9 (ζ9 = 1); i = ζ2.