Finite Group Databasebeta

← Group #13180072

Character table — Group #13180072

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111333333333999999999999999999484848484848484848484848484848484848484848484848192192
order13322266666622222266666666666633333366666666666666666633
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111−1+i32−1+i32−1−i32−1−i32111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i32
χ311111111111111111111111111111111−1−i32−1−i32−1+i32−1+i32111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i32
χ4111111111111111111111111111111−1+i32−1−i321−1+i321−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1−i32−1+i32
χ5111111111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211
χ6111111111111111111111111111111−1+i32−1−i32−1−i321−1+i321−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32111−1+i32−1−i32
χ7111111111111111111111111111111−1−i32−1+i321−1−i321−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1+i32−1−i32
χ8111111111111111111111111111111−1−i32−1+i32−1+i321−1−i321−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32111−1−i32−1+i32
χ9111111111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211
χ1033333-13333-1-13-1-1-1-1-133-1-1-1-1-1-1-1-1-1-1000303000000000-1-1-1000-1-1-100
χ1133333-13333-1-13-1-1-1-1-133-1-1-1-1-1-1-1-1-1-1000−3+3i320−3−3i320000000001−i321−i321−i320001+i321+i321+i3200
χ1233333-13333-1-13-1-1-1-1-133-1-1-1-1-1-1-1-1-1-1000−3−3i320−3+3i320000000001+i321+i321+i320001−i321−i321−i3200
χ133333-1333-1-133-13-1-1-1-1-1-133-1-1-1-1-1-1-1-1003030000000-1-1-1000-1-1-100000
χ143333-1333-1-133-13-1-1-1-1-1-133-1-1-1-1-1-1-1-100−3+3i320−3−3i3200000001−i321−i321−i320001+i321+i321+i3200000
χ153333-1333-1-133-13-1-1-1-1-1-133-1-1-1-1-1-1-1-100−3−3i320−3+3i3200000001+i321+i321+i320001−i321−i321−i3200000
χ16333-133-1-13333-1-13-1-1-1-1-1-1-133-1-1-1-1-1-1330000-1-1-1-1-1-100000000000000
χ17333-133-1-13333-1-13-1-1-1-1-1-1-133-1-1-1-1-1-1−3+3i32−3−3i3200001−i321−i321−i321+i321+i321+i3200000000000000
χ18333-133-1-13333-1-13-1-1-1-1-1-1-133-1-1-1-1-1-1−3−3i32−3+3i3200001+i321+i321+i321−i321−i321−i3200000000000000
χ193−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32333333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i3200000000000000000000000000
χ203−3+3i32−3−3i3233-1−3+3i32−3−3i32−3+3i32−3−3i321−i321+i323-1-1-1-1-1−3+3i32−3−3i321−i321+i321−i321+i321−i321−i321−i321+i321+i321+i320000000000000002−1+i3−1−i30002−1+i3−1−i300
χ213−3+3i32−3−3i3233-1−3+3i32−3−3i32−3+3i32−3−3i321−i321+i323-1-1-1-1-1−3+3i32−3−3i321−i321+i321−i321+i321−i321−i321−i321+i321+i321+i32000000000000000−1+i3−1−i32000−1−i32−1+i300
χ223−3+3i32−3−3i3233-1−3+3i32−3−3i32−3+3i32−3−3i321−i321+i323-1-1-1-1-1−3+3i32−3−3i321−i321+i321−i321+i321−i321−i321−i321+i321+i321+i32000000000000000−1−i32−1+i3000−1+i3−1−i3200
χ233−3+3i32−3−3i323-13−3+3i32−3−3i321−i321+i32−3+3i32−3−3i32-13-1-1-1-11−i321+i32−3+3i32−3−3i321−i321+i321−i321−i321−i321+i321+i321+i320000000000002−1+i3−1−i30002−1+i3−1−i300000
χ243−3+3i32−3−3i323-13−3+3i32−3−3i321−i321+i32−3+3i32−3−3i32-13-1-1-1-11−i321+i32−3+3i32−3−3i321−i321+i321−i321−i321−i321+i321+i321+i32000000000000−1+i3−1−i32000−1−i32−1+i300000
χ253−3+3i32−3−3i323-13−3+3i32−3−3i321−i321+i32−3+3i32−3−3i32-13-1-1-1-11−i321+i32−3+3i32−3−3i321−i321+i321−i321−i321−i321+i321+i321+i32000000000000−1−i32−1+i3000−1+i3−1−i3200000
χ263−3+3i32−3−3i32-1331−i321+i32−3+3i32−3−3i32−3+3i32−3−3i32-1-13-1-1-11−i321+i321−i321+i32−3+3i32−3−3i321−i321−i321−i321+i321+i321+i320000002−1+i3−1−i32−1+i3−1−i300000000000000
χ273−3+3i32−3−3i32-1331−i321+i32−3+3i32−3−3i32−3+3i32−3−3i32-1-13-1-1-11−i321+i321−i321+i32−3+3i32−3−3i321−i321−i321−i321+i321+i321+i32000000−1+i3−1−i32−1−i32−1+i300000000000000
χ283−3+3i32−3−3i32-1331−i321+i32−3+3i32−3−3i32−3+3i32−3−3i32-1-13-1-1-11−i321+i321−i321+i32−3+3i32−3−3i321−i321−i321−i321+i321+i321+i32000000−1−i32−1+i3−1+i3−1−i3200000000000000
χ293−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i3200000000000000000000000000
χ303−3−3i32−3+3i3233-1−3−3i32−3+3i32−3−3i32−3+3i321+i321−i323-1-1-1-1-1−3−3i32−3+3i321+i321−i321+i321−i321+i321+i321+i321−i321−i321−i320000000000000002−1−i3−1+i30002−1−i3−1+i300
χ313−3−3i32−3+3i3233-1−3−3i32−3+3i32−3−3i32−3+3i321+i321−i323-1-1-1-1-1−3−3i32−3+3i321+i321−i321+i321−i321+i321+i321+i321−i321−i321−i32000000000000000−1+i32−1−i3000−1−i3−1+i3200
χ323−3−3i32−3+3i3233-1−3−3i32−3+3i32−3−3i32−3+3i321+i321−i323-1-1-1-1-1−3−3i32−3+3i321+i321−i321+i321−i321+i321+i321+i321−i321−i321−i32000000000000000−1−i3−1+i32000−1+i32−1−i300
χ333−3−3i32−3+3i323-13−3−3i32−3+3i321+i321−i32−3−3i32−3+3i32-13-1-1-1-11+i321−i32−3−3i32−3+3i321+i321−i321+i321+i321+i321−i321−i321−i320000000000002−1−i3−1+i30002−1−i3−1+i300000
χ343−3−3i32−3+3i323-13−3−3i32−3+3i321+i321−i32−3−3i32−3+3i32-13-1-1-1-11+i321−i32−3−3i32−3+3i321+i321−i321+i321+i321+i321−i321−i321−i32000000000000−1+i32−1−i3000−1−i3−1+i3200000
χ353−3−3i32−3+3i323-13−3−3i32−3+3i321+i321−i32−3−3i32−3+3i32-13-1-1-1-11+i321−i32−3−3i32−3+3i321+i321−i321+i321+i321+i321−i321−i321−i32000000000000−1−i3−1+i32000−1+i32−1−i300000
χ363−3−3i32−3+3i32-1331+i321−i32−3−3i32−3+3i32−3−3i32−3+3i32-1-13-1-1-11+i321−i321+i321−i32−3−3i32−3+3i321+i321+i321+i321−i321−i321−i320000002−1−i3−1+i32−1−i3−1+i300000000000000
χ373−3−3i32−3+3i32-1331+i321−i32−3−3i32−3+3i32−3−3i32−3+3i32-1-13-1-1-11+i321−i321+i321−i32−3−3i32−3+3i321+i321+i321+i321−i321−i321−i32000000−1+i32−1−i3−1−i3−1+i3200000000000000
χ383−3−3i32−3+3i32-1331+i321−i32−3−3i32−3+3i32−3−3i32−3+3i32-1-13-1-1-11+i321−i321+i321−i32−3−3i32−3+3i321+i321+i321+i321−i321−i321−i32000000−1−i3−1+i32−1+i32−1−i300000000000000
χ399999-3-399-3-3-3-3-3-31111-3-3-3-31111111100000000000000000000000000
χ40999-39-3-3-399-3-3-31-3111-3-311-3-311111100000000000000000000000000
χ41999-3-39-3-3-3-3991-3-311111-3-3-3-311111100000000000000000000000000
χ42999-3-3-3-3-3-3-3-3-31115-3-31111115-3-35-3-300000000000000000000000000
χ43999-3-3-3-3-3-3-3-3-3111-35-3111111-35-3-35-300000000000000000000000000
χ44999-3-3-3-3-3-3-3-3-3111-3-35111111-3-35-3-3500000000000000000000000000
χ459−9+9i32−9−9i329-3-3−9+9i32−9−9i323−3i323+3i323−3i323+3i32-3-311113−3i323+3i323−3i323+3i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3200000000000000000000000000
χ469−9+9i32−9−9i32-39-33−3i323+3i32−9+9i32−9−9i323−3i323+3i32-31-31113−3i323+3i32−1+i32−1−i323−3i323+3i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3200000000000000000000000000
χ479−9+9i32−9−9i32-3-393−3i323+3i323−3i323+3i32−9+9i32−9−9i321-3-3111−1+i32−1−i323−3i323+3i323−3i323+3i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3200000000000000000000000000
χ489−9+9i32−9−9i32-3-3-33−3i323+3i323−3i323+3i323−3i323+3i321115-3-3−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−5+5i323−3i323−3i32−5−5i323+3i323+3i3200000000000000000000000000
χ499−9+9i32−9−9i32-3-3-33−3i323+3i323−3i323+3i323−3i323+3i32111-35-3−1+i32−1−i32−1+i32−1−i32−1+i32−1−i323−3i32−5+5i323−3i323+3i32−5−5i323+3i3200000000000000000000000000
χ509−9+9i32−9−9i32-3-3-33−3i323+3i323−3i323+3i323−3i323+3i32111-3-35−1+i32−1−i32−1+i32−1−i32−1+i32−1−i323−3i323−3i32−5+5i323+3i323+3i32−5−5i3200000000000000000000000000
χ519−9−9i32−9+9i329-3-3−9−9i32−9+9i323+3i323−3i323+3i323−3i32-3-311113+3i323−3i323+3i323−3i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3200000000000000000000000000
χ529−9−9i32−9+9i32-39-33+3i323−3i32−9−9i32−9+9i323+3i323−3i32-31-31113+3i323−3i32−1−i32−1+i323+3i323−3i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3200000000000000000000000000
χ539−9−9i32−9+9i32-3-393+3i323−3i323+3i323−3i32−9−9i32−9+9i321-3-3111−1−i32−1+i323+3i323−3i323+3i323−3i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3200000000000000000000000000
χ549−9−9i32−9+9i32-3-3-33+3i323−3i323+3i323−3i323+3i323−3i321115-3-3−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−5−5i323+3i323+3i32−5+5i323−3i323−3i3200000000000000000000000000
χ559−9−9i32−9+9i32-3-3-33+3i323−3i323+3i323−3i323+3i323−3i32111-35-3−1−i32−1+i32−1−i32−1+i32−1−i32−1+i323+3i32−5−5i323+3i323−3i32−5+5i323−3i3200000000000000000000000000
χ569−9−9i32−9+9i32-3-3-33+3i323−3i323+3i323−3i323+3i323−3i32111-3-35−1−i32−1+i32−1−i32−1+i32−1−i32−1+i323+3i323+3i32−5−5i323−3i323−3i32−5+5i3200000000000000000000000000

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