Finite Group Databasebeta

← Group #72243820

Character table — Group #72243820

Order 2916.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111669999999999991218182727272727272727272727273636363636545454545454818181818181818181108108162162162162162162
order1333322666699999933318181818181818181818181833333669999266181818181818336618181818
χ1111111111111111111111111111111111111111111111111111111111111
χ211111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321111111−1+i32−1+i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32
χ311111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321111111−1−i32−1−i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32
χ4111111-111-1-1111111111111-1-1-1111-1-1-1111111-11111-1-1-1-1-1-1-1-1-1111-11-11-1
χ5111111-111-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i321−i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i32111111-1−1+i32−1+i32−1−i32−1−i32-1-1-11−i321−i321−i321+i321+i321+i32−1+i32−1−i321-1−1+i321−i32−1−i321+i32
χ6111111-111-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i321+i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i32111111-1−1−i32−1−i32−1+i32−1+i32-1-1-11+i321+i321+i321−i321−i321−i32−1−i32−1+i321-1−1−i321+i32−1+i321−i32
χ711111-11-1-111111111111-1-1-1111-1-1-111111111-111111-1-1-1-1-1-1-1-1-111-11-11-11
χ811111-11-1-111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111−i321−i321−i32−1+i32−1+i32−1+i321+i321+i321+i32−1−i32−1−i32−1−i3211111-11−1+i32−1+i32−1−i32−1−i32-1-1-11−i321−i321−i321+i321+i321+i32−1+i32−1−i32-111−i32−1+i321+i32−1−i32
χ911111-11-1-111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111+i321+i321+i32−1−i32−1−i32−1−i321−i321−i321−i32−1+i32−1+i32−1+i3211111-11−1−i32−1−i32−1+i32−1+i32-1-1-11+i321+i321+i321−i321−i321−i32−1−i32−1+i32-111+i32−1−i321−i32−1+i32
χ1011111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111111111111111-1-1-1-1-1-1
χ1111111-1-1-1-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i3211111-1-1−1+i32−1+i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+i32
χ1211111-1-1-1-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i3211111-1-1−1−i32−1−i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i32
χ132222202002222222222-10002220002222-1-1-1-1022-12-1000000000-1-10-10-10-1
χ1422222020022−1+i3−1+i3−1+i3−1−i3−1−i3−1−i322-1000−1+i3−1+i3−1+i3000−1−i3−1−i3−1−i32-1-1-1-102−1+i31−i32−1−i31+i320000000001−i321+i320-101−i3201+i32
χ1522222020022−1−i3−1−i3−1−i3−1+i3−1+i3−1+i322-1000−1−i3−1−i3−1−i3000−1+i3−1+i3−1+i32-1-1-1-102−1−i31+i32−1+i31−i320000000001+i321−i320-101+i3201−i32
χ16222220-200-2-222222222-1000-2-2-2000-2-2-22-1-1-1-10-22-12-1000000000-1-1010101
χ17222220-200-2-2−1+i3−1+i3−1+i3−1−i3−1−i3−1−i322-10001−i31−i31−i30001+i31+i31+i32-1-1-1-10-2−1+i31−i32−1−i31+i320000000001−i321+i32010−1+i320−1−i32
χ18222220-200-2-2−1−i3−1−i3−1−i3−1+i3−1+i3−1+i322-10001+i31+i31+i30001−i31−i31−i32-1-1-1-10-2−1−i31+i32−1+i31−i320000000001+i321−i32010−1−i320−1+i32
χ19222222022002222222-12222000222000-12-1-1-120-12-12000000000-1-1-10-10-10
χ2022222202200−1+i3−1+i3−1+i3−1−i3−1−i3−1−i32-12−1+i3−1+i3−1+i3000−1−i3−1−i3−1−i3000-12-1-1-1201−i32−1+i31+i32−1−i30000000001−i321+i32-101−i3201+i320
χ2122222202200−1−i3−1−i3−1−i3−1+i3−1+i3−1+i32-12−1−i3−1−i3−1−i3000−1+i3−1+i3−1+i3000-12-1-1-1201+i32−1−i31−i32−1+i30000000001+i321−i32-101+i3201−i320
χ2222222-20-2-2002222222-12-2-2-2000-2-2-2000-12-1-1-1-20-12-12000000000-1-1101010
χ2322222-20-2-200−1+i3−1+i3−1+i3−1−i3−1−i3−1−i32-121−i31−i31−i30001+i31+i31+i3000-12-1-1-1-201−i32−1+i31+i32−1−i30000000001−i321+i3210−1+i320−1−i320
χ2422222-20-2-200−1−i3−1−i3−1−i3−1+i3−1+i3−1+i32-121+i31+i31+i30001−i31−i31−i3000-12-1-1-1-201+i32−1−i31−i32−1+i30000000001+i321−i3210−1−i320−1+i320
χ25444440000004444444-2-2000000000000-2-211100-2-2-2-200000000011000000
χ2644444000000−2+2i3−2+2i3−2+2i3−2−2i3−2−2i3−2−2i34-2-2000000000000-2-2111001−i31−i31+i31+i3000000000−1+i32−1−i32000000
χ2744444000000−2−2i3−2−2i3−2−2i3−2+2i3−2+2i3−2+2i34-2-2000000000000-2-2111001+i31+i31−i31−i3000000000−1−i32−1+i32000000
χ286666-3060066000000-360000000000000-300000-3000000000000000000000
χ296666-30-600-6-6000000-360000000000000-3000003000000000000000000000
χ30666-36606600000000-3060000000000000-3000-30000000000000000000000
χ31666-36-60-6-600000000-3060000000000000-300030000000000000000000000
χ329−9+9i32−9−9i320033−3+3i32−3−3i32−3+3i32−3−3i32−3ζ−3ζ4−3ζ7−3ζ2−3ζ5−3ζ80002ζ+ζ4−ζ+ζ4−ζ−2ζ42ζ+ζ4−ζ+ζ4−ζ−2ζ4ζ2+2ζ5ζ2−ζ5−2ζ2−ζ5ζ2+2ζ5ζ2−ζ5−2ζ2−ζ5000000000001−1+i32−1−i32ζζ4ζ7ζ2ζ5ζ800000000
χ339−9+9i32−9−9i320033−3+3i32−3−3i32−3+3i32−3−3i32−3ζ4−3ζ7−3ζ−3ζ8−3ζ2−3ζ5000−ζ+ζ4−ζ−2ζ42ζ+ζ4−ζ+ζ4−ζ−2ζ42ζ+ζ4ζ2−ζ5−2ζ2−ζ5ζ2+2ζ5ζ2−ζ5−2ζ2−ζ5ζ2+2ζ5000000000001−1+i32−1−i32ζ4ζ7ζζ8ζ2ζ500000000
χ349−9+9i32−9−9i320033−3+3i32−3−3i32−3+3i32−3−3i32−3ζ7−3ζ−3ζ4−3ζ5−3ζ8−3ζ2000−ζ−2ζ42ζ+ζ4−ζ+ζ4−ζ−2ζ42ζ+ζ4−ζ+ζ4−2ζ2−ζ5ζ2+2ζ5ζ2−ζ5−2ζ2−ζ5ζ2+2ζ5ζ2−ζ5000000000001−1+i32−1−i32ζ7ζζ4ζ5ζ8ζ200000000
χ359−9+9i32−9−9i32003-3−3+3i32−3−3i323−3i323+3i32−3ζ−3ζ4−3ζ7−3ζ2−3ζ5−3ζ80002ζ+ζ4−ζ+ζ4−ζ−2ζ4−2ζ−ζ4ζ−ζ4ζ+2ζ4ζ2+2ζ5ζ2−ζ5−2ζ2−ζ5−ζ2−2ζ5−ζ2+ζ52ζ2+ζ500000000000-11−i321+i32−ζ−ζ4−ζ7−ζ2−ζ5−ζ800000000
χ369−9+9i32−9−9i32003-3−3+3i32−3−3i323−3i323+3i32−3ζ4−3ζ7−3ζ−3ζ8−3ζ2−3ζ5000−ζ+ζ4−ζ−2ζ42ζ+ζ4ζ−ζ4ζ+2ζ4−2ζ−ζ4ζ2−ζ5−2ζ2−ζ5ζ2+2ζ5−ζ2+ζ52ζ2+ζ5−ζ2−2ζ500000000000-11−i321+i32−ζ4−ζ7−ζ−ζ8−ζ2−ζ500000000
χ379−9+9i32−9−9i32003-3−3+3i32−3−3i323−3i323+3i32−3ζ7−3ζ−3ζ4−3ζ5−3ζ8−3ζ2000−ζ−2ζ42ζ+ζ4−ζ+ζ4ζ+2ζ4−2ζ−ζ4ζ−ζ4−2ζ2−ζ5ζ2+2ζ5ζ2−ζ52ζ2+ζ5−ζ2−2ζ5−ζ2+ζ500000000000-11−i321+i32−ζ7−ζ−ζ4−ζ5−ζ8−ζ200000000
χ389−9+9i32−9−9i3200-333−3i323+3i32−3+3i32−3−3i32−3ζ−3ζ4−3ζ7−3ζ2−3ζ5−3ζ8000−2ζ−ζ4ζ−ζ4ζ+2ζ42ζ+ζ4−ζ+ζ4−ζ−2ζ4−ζ2−2ζ5−ζ2+ζ52ζ2+ζ5ζ2+2ζ5ζ2−ζ5−2ζ2−ζ500000000000-11−i321+i32−ζ−ζ4−ζ7−ζ2−ζ5−ζ800000000
χ399−9+9i32−9−9i3200-333−3i323+3i32−3+3i32−3−3i32−3ζ4−3ζ7−3ζ−3ζ8−3ζ2−3ζ5000ζ−ζ4ζ+2ζ4−2ζ−ζ4−ζ+ζ4−ζ−2ζ42ζ+ζ4−ζ2+ζ52ζ2+ζ5−ζ2−2ζ5ζ2−ζ5−2ζ2−ζ5ζ2+2ζ500000000000-11−i321+i32−ζ4−ζ7−ζ−ζ8−ζ2−ζ500000000
χ409−9+9i32−9−9i3200-333−3i323+3i32−3+3i32−3−3i32−3ζ7−3ζ−3ζ4−3ζ5−3ζ8−3ζ2000ζ+2ζ4−2ζ−ζ4ζ−ζ4−ζ−2ζ42ζ+ζ4−ζ+ζ42ζ2+ζ5−ζ2−2ζ5−ζ2+ζ5−2ζ2−ζ5ζ2+2ζ5ζ2−ζ500000000000-11−i321+i32−ζ7−ζ−ζ4−ζ5−ζ8−ζ200000000
χ419−9+9i32−9−9i3200-3-33−3i323+3i323−3i323+3i32−3ζ−3ζ4−3ζ7−3ζ2−3ζ5−3ζ8000−2ζ−ζ4ζ−ζ4ζ+2ζ4−2ζ−ζ4ζ−ζ4ζ+2ζ4−ζ2−2ζ5−ζ2+ζ52ζ2+ζ5−ζ2−2ζ5−ζ2+ζ52ζ2+ζ5000000000001−1+i32−1−i32ζζ4ζ7ζ2ζ5ζ800000000
χ429−9+9i32−9−9i3200-3-33−3i323+3i323−3i323+3i32−3ζ4−3ζ7−3ζ−3ζ8−3ζ2−3ζ5000ζ−ζ4ζ+2ζ4−2ζ−ζ4ζ−ζ4ζ+2ζ4−2ζ−ζ4−ζ2+ζ52ζ2+ζ5−ζ2−2ζ5−ζ2+ζ52ζ2+ζ5−ζ2−2ζ5000000000001−1+i32−1−i32ζ4ζ7ζζ8ζ2ζ500000000
χ439−9+9i32−9−9i3200-3-33−3i323+3i323−3i323+3i32−3ζ7−3ζ−3ζ4−3ζ5−3ζ8−3ζ2000ζ+2ζ4−2ζ−ζ4ζ−ζ4ζ+2ζ4−2ζ−ζ4ζ−ζ42ζ2+ζ5−ζ2−2ζ5−ζ2+ζ52ζ2+ζ5−ζ2−2ζ5−ζ2+ζ5000000000001−1+i32−1−i32ζ7ζζ4ζ5ζ8ζ200000000
χ449−9−9i32−9+9i320033−3−3i32−3+3i32−3−3i32−3+3i32−3ζ2−3ζ8−3ζ5−3ζ4−3ζ−3ζ7000ζ2−ζ5−2ζ2−ζ5ζ2+2ζ5ζ2−ζ5−2ζ2−ζ5ζ2+2ζ52ζ+ζ4−ζ+ζ4−ζ−2ζ42ζ+ζ4−ζ+ζ4−ζ−2ζ4000000000001−1−i32−1+i32ζ2ζ8ζ5ζ4ζζ700000000
χ459−9−9i32−9+9i320033−3−3i32−3+3i32−3−3i32−3+3i32−3ζ5−3ζ2−3ζ8−3ζ−3ζ7−3ζ4000ζ2+2ζ5ζ2−ζ5−2ζ2−ζ5ζ2+2ζ5ζ2−ζ5−2ζ2−ζ5−ζ−2ζ42ζ+ζ4−ζ+ζ4−ζ−2ζ42ζ+ζ4−ζ+ζ4000000000001−1−i32−1+i32ζ5ζ2ζ8ζζ7ζ400000000
χ469−9−9i32−9+9i320033−3−3i32−3+3i32−3−3i32−3+3i32−3ζ8−3ζ5−3ζ2−3ζ7−3ζ4−3ζ000−2ζ2−ζ5ζ2+2ζ5ζ2−ζ5−2ζ2−ζ5ζ2+2ζ5ζ2−ζ5−ζ+ζ4−ζ−2ζ42ζ+ζ4−ζ+ζ4−ζ−2ζ42ζ+ζ4000000000001−1−i32−1+i32ζ8ζ5ζ2ζ7ζ4ζ00000000
χ479−9−9i32−9+9i32003-3−3−3i32−3+3i323+3i323−3i32−3ζ2−3ζ8−3ζ5−3ζ4−3ζ−3ζ7000ζ2−ζ5−2ζ2−ζ5ζ2+2ζ5−ζ2+ζ52ζ2+ζ5−ζ2−2ζ52ζ+ζ4−ζ+ζ4−ζ−2ζ4−2ζ−ζ4ζ−ζ4ζ+2ζ400000000000-11+i321−i32−ζ2−ζ8−ζ5−ζ4−ζ−ζ700000000
χ489−9−9i32−9+9i32003-3−3−3i32−3+3i323+3i323−3i32−3ζ5−3ζ2−3ζ8−3ζ−3ζ7−3ζ4000ζ2+2ζ5ζ2−ζ5−2ζ2−ζ5−ζ2−2ζ5−ζ2+ζ52ζ2+ζ5−ζ−2ζ42ζ+ζ4−ζ+ζ4ζ+2ζ4−2ζ−ζ4ζ−ζ400000000000-11+i321−i32−ζ5−ζ2−ζ8−ζ−ζ7−ζ400000000
χ499−9−9i32−9+9i32003-3−3−3i32−3+3i323+3i323−3i32−3ζ8−3ζ5−3ζ2−3ζ7−3ζ4−3ζ000−2ζ2−ζ5ζ2+2ζ5ζ2−ζ52ζ2+ζ5−ζ2−2ζ5−ζ2+ζ5−ζ+ζ4−ζ−2ζ42ζ+ζ4ζ−ζ4ζ+2ζ4−2ζ−ζ400000000000-11+i321−i32−ζ8−ζ5−ζ2−ζ7−ζ4−ζ00000000
χ509−9−9i32−9+9i3200-333+3i323−3i32−3−3i32−3+3i32−3ζ2−3ζ8−3ζ5−3ζ4−3ζ−3ζ7000−ζ2+ζ52ζ2+ζ5−ζ2−2ζ5ζ2−ζ5−2ζ2−ζ5ζ2+2ζ5−2ζ−ζ4ζ−ζ4ζ+2ζ42ζ+ζ4−ζ+ζ4−ζ−2ζ400000000000-11+i321−i32−ζ2−ζ8−ζ5−ζ4−ζ−ζ700000000
χ519−9−9i32−9+9i3200-333+3i323−3i32−3−3i32−3+3i32−3ζ5−3ζ2−3ζ8−3ζ−3ζ7−3ζ4000−ζ2−2ζ5−ζ2+ζ52ζ2+ζ5ζ2+2ζ5ζ2−ζ5−2ζ2−ζ5ζ+2ζ4−2ζ−ζ4ζ−ζ4−ζ−2ζ42ζ+ζ4−ζ+ζ400000000000-11+i321−i32−ζ5−ζ2−ζ8−ζ−ζ7−ζ400000000
χ529−9−9i32−9+9i3200-333+3i323−3i32−3−3i32−3+3i32−3ζ8−3ζ5−3ζ2−3ζ7−3ζ4−3ζ0002ζ2+ζ5−ζ2−2ζ5−ζ2+ζ5−2ζ2−ζ5ζ2+2ζ5ζ2−ζ5ζ−ζ4ζ+2ζ4−2ζ−ζ4−ζ+ζ4−ζ−2ζ42ζ+ζ400000000000-11+i321−i32−ζ8−ζ5−ζ2−ζ7−ζ4−ζ00000000
χ539−9−9i32−9+9i3200-3-33+3i323−3i323+3i323−3i32−3ζ2−3ζ8−3ζ5−3ζ4−3ζ−3ζ7000−ζ2+ζ52ζ2+ζ5−ζ2−2ζ5−ζ2+ζ52ζ2+ζ5−ζ2−2ζ5−2ζ−ζ4ζ−ζ4ζ+2ζ4−2ζ−ζ4ζ−ζ4ζ+2ζ4000000000001−1−i32−1+i32ζ2ζ8ζ5ζ4ζζ700000000
χ549−9−9i32−9+9i3200-3-33+3i323−3i323+3i323−3i32−3ζ5−3ζ2−3ζ8−3ζ−3ζ7−3ζ4000−ζ2−2ζ5−ζ2+ζ52ζ2+ζ5−ζ2−2ζ5−ζ2+ζ52ζ2+ζ5ζ+2ζ4−2ζ−ζ4ζ−ζ4ζ+2ζ4−2ζ−ζ4ζ−ζ4000000000001−1−i32−1+i32ζ5ζ2ζ8ζζ7ζ400000000
χ559−9−9i32−9+9i3200-3-33+3i323−3i323+3i323−3i32−3ζ8−3ζ5−3ζ2−3ζ7−3ζ4−3ζ0002ζ2+ζ5−ζ2−2ζ5−ζ2+ζ52ζ2+ζ5−ζ2−2ζ5−ζ2+ζ5ζ−ζ4ζ+2ζ4−2ζ−ζ4ζ−ζ4ζ+2ζ4−2ζ−ζ4000000000001−1−i32−1+i32ζ8ζ5ζ2ζ7ζ4ζ00000000
χ5612121212-6000000000000-6-600000000000003000000000000000000000000000
χ57121212-612000000000000-60-60000000000000300000000000000000000000000
χ58121212-6-6000000000000300000000000000006-3-300000000000000000000000
χ59121212-6-600000000000030000000000000000-36-300000000000000000000000
χ60121212-6-600000000000030000000000000000-3-3600000000000000000000000

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