Finite Group Databasebeta

← Group #72276160

Character table — Group #72276160

Order 7776.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size111111181818181818242424244848484848484848818181818181162162162162162162162162162162162162216216216216324324324324324324324324324324324324
order1233664412121212336633336666226666444412121212121212121212121244441212121212121212
χ11111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111
χ5111111-1-1-1-1-1-111111111111111111111-1-11111-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ6111111-1-1-1-1-1-111111111111111111111-1-11111-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ7111111-1-1-1-1-1-1111111111111111111-1-111-1-1-1-11111-1-1-1-11-1-1111-1-1-1-111
χ8111111-1-1-1-1-1-1111111111111111111-1-111-1-1-1-11111-1-1-1-1-111-1-1-11111-1-1
χ92222222-222-2-2222222222222-2-2-2-2-2-200000000000022-2-2000000000000
χ10222222-22-2-222222222222222-2-2-2-2-2-2000000000000-2-222000000000000
χ112-222-2-200000022-2-22222-2-2-2-22-222-2-22-20022-2-200000000000000000000
χ122-222-2-200000022-2-22222-2-2-2-22-222-2-2-2200-2-22200000000000000000000
χ132-222-2-200000022-2-22222-2-2-2-2-22-2-222002-2000022-2-20000000000000000
χ142-222-2-200000022-2-22222-2-2-2-2-22-2-22200-220000-2-2220000000000000000
χ158888880800888-18-1-1-1-1-1-1-1-1-100000000000000000000-1-1000000000000
χ168888880-800-8-88-18-1-1-1-1-1-1-1-1-10000000000000000000011000000000000
χ17888888808800-18-18-1-1-1-1-1-1-1-1000000000000000000-1-100000000000000
χ18888888-80-8-800-18-18-1-1-1-1-1-1-1-10000000000000000001100000000000000
χ198-888-8-80000008-1-81-1-1-1-11111000000000000000000003i−3i000000000000
χ208-888-8-80000008-1-81-1-1-1-1111100000000000000000000−3i3i000000000000
χ218-888-8-8000000-181-8-1-1-1-111110000000000000000003i−3i00000000000000
χ228-888-8-8000000-181-8-1-1-1-11111000000000000000000−3i3i00000000000000
χ2399−9−9i32−9+9i32−9−9i32−9+9i3233−3−3i32−3+3i32−3−3i32−3+3i3200000000000011−1−i32−1+i32−1−i32−1+i3211-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i3200001-11-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32
χ2499−9−9i32−9+9i32−9−9i32−9+9i3233−3−3i32−3+3i32−3−3i32−3+3i3200000000000011−1−i32−1+i32−1−i32−1+i3211-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i320000-11-111+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32
χ2599−9−9i32−9+9i32−9−9i32−9+9i3233−3−3i32−3+3i32−3−3i32−3+3i3200000000000011−1−i32−1+i32−1−i32−1+i32-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i3200001-1-11−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32
χ2699−9−9i32−9+9i32−9−9i32−9+9i3233−3−3i32−3+3i32−3−3i32−3+3i3200000000000011−1−i32−1+i32−1−i32−1+i32-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i320000-111-11+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i32
χ2799−9−9i32−9+9i32−9−9i32−9+9i32-3-33+3i323−3i323+3i323−3i3200000000000011−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3200001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ2899−9−9i32−9+9i32−9−9i32−9+9i32-3-33+3i323−3i323+3i323−3i3200000000000011−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i320000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32
χ2999−9−9i32−9+9i32−9−9i32−9+9i32-3-33+3i323−3i323+3i323−3i3200000000000011−1−i32−1+i32−1−i32−1+i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32000011-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32
χ3099−9−9i32−9+9i32−9−9i32−9+9i32-3-33+3i323−3i323+3i323−3i3200000000000011−1−i32−1+i32−1−i32−1+i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i320000-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32
χ3199−9+9i32−9−9i32−9+9i32−9−9i3233−3+3i32−3−3i32−3+3i32−3−3i3200000000000011−1+i32−1−i32−1+i32−1−i3211-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i3200001-11-1−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32
χ3299−9+9i32−9−9i32−9+9i32−9−9i3233−3+3i32−3−3i32−3+3i32−3−3i3200000000000011−1+i32−1−i32−1+i32−1−i3211-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i320000-11-111−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32
χ3399−9+9i32−9−9i32−9+9i32−9−9i3233−3+3i32−3−3i32−3+3i32−3−3i3200000000000011−1+i32−1−i32−1+i32−1−i32-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i3200001-1-11−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32
χ3499−9+9i32−9−9i32−9+9i32−9−9i3233−3+3i32−3−3i32−3+3i32−3−3i3200000000000011−1+i32−1−i32−1+i32−1−i32-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i320000-111-11−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i32
χ3599−9+9i32−9−9i32−9+9i32−9−9i32-3-33−3i323+3i323−3i323+3i3200000000000011−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3200001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32
χ3699−9+9i32−9−9i32−9+9i32−9−9i32-3-33−3i323+3i323−3i323+3i3200000000000011−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i320000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32
χ3799−9+9i32−9−9i32−9+9i32−9−9i32-3-33−3i323+3i323−3i323+3i3200000000000011−1+i32−1−i32−1+i32−1−i32-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32000011-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32
χ3899−9+9i32−9−9i32−9+9i32−9−9i32-3-33−3i323+3i323−3i323+3i3200000000000011−1+i32−1−i32−1+i32−1−i32-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i320000-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32
χ39161616161616000000-2-2-2-27-2-2-27-2-2-20000000000000000000000000000000000
χ40161616161616000000-2-2-2-2-27-2-2-27-2-20000000000000000000000000000000000
χ41161616161616000000-2-2-2-2-2-27-2-2-27-20000000000000000000000000000000000
χ42161616161616000000-2-2-2-2-2-2-27-2-2-270000000000000000000000000000000000
χ4316-161616-16-16000000-2-2227-2-2-2-72220000000000000000000000000000000000
χ4416-161616-16-16000000-2-222-27-2-22-7220000000000000000000000000000000000
χ4516-161616-16-16000000-2-222-2-27-222-720000000000000000000000000000000000
χ4616-161616-16-16000000-2-222-2-2-27222-70000000000000000000000000000000000
χ471818−9−9i3−9+9i3−9−9i3−9+9i36-6−3−3i3−3+3i33+3i33−3i3000000000000-2-21+i31−i31+i31−i30000000000000000000000000000
χ481818−9−9i3−9+9i3−9−9i3−9+9i3-663+3i33−3i3−3−3i3−3+3i3000000000000-2-21+i31−i31+i31−i30000000000000000000000000000
χ491818−9+9i3−9−9i3−9+9i3−9−9i36-6−3+3i3−3−3i33−3i33+3i3000000000000-2-21−i31+i31−i31+i30000000000000000000000000000
χ501818−9+9i3−9−9i3−9+9i3−9−9i3-663−3i33+3i3−3+3i3−3−3i3000000000000-2-21−i31+i31−i31+i30000000000000000000000000000
χ5118-18−9−9i3−9+9i39+9i39−9i30000000000000000002-2−1−i3−1+i31+i31−i32-200−1−i3−1+i31+i31−i300000000000000000000
χ5218-18−9−9i3−9+9i39+9i39−9i30000000000000000002-2−1−i3−1+i31+i31−i3-22001+i31−i3−1−i3−1+i300000000000000000000
χ5318-18−9−9i3−9+9i39+9i39−9i3000000000000000000-221+i31−i3−1−i3−1+i3002-20000−1−i3−1+i31+i31−i30000000000000000
χ5418-18−9−9i3−9+9i39+9i39−9i3000000000000000000-221+i31−i3−1−i3−1+i300-2200001+i31−i3−1−i3−1+i30000000000000000
χ5518-18−9+9i3−9−9i39−9i39+9i30000000000000000002-2−1+i3−1−i31−i31+i32-200−1+i3−1−i31−i31+i300000000000000000000
χ5618-18−9+9i3−9−9i39−9i39+9i30000000000000000002-2−1+i3−1−i31−i31+i3-22001−i31+i3−1+i3−1−i300000000000000000000
χ5718-18−9+9i3−9−9i39−9i39+9i3000000000000000000-221−i31+i3−1+i3−1−i3002-20000−1+i3−1−i31−i31+i30000000000000000
χ5818-18−9+9i3−9−9i39−9i39+9i3000000000000000000-221−i31+i3−1+i3−1−i300-2200001−i31+i3−1+i3−1−i30000000000000000

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