Finite Group Databasebeta

← Group #13164556

Character table — Group #13164556

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111166666666666121212121212121212121212121212121212363636363636727272727272727272969696969696
order1233662344666121212122666666666661212121212124412121212488121224242424333666
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ322222222222222222222222222222222222000000000000000-1-1-1-1-1-1
χ42222222-12222-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000002-1-12-1-1
χ52222222-12222-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000-12-1-12-1
χ62222222-12222-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000-1-12-1-12
χ733333333-1-1333-1-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111-1-1-1-1000000
χ833333333-1-1333-1-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111000000
χ9333333-133-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-1111111-11-1-1-111-1-1000000
χ10333333-133-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-11-1111-1-111000000
χ11333333-13-13-1-13-1-133-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1333111111-1-11-1-1-1-111000000
χ12333333-13-13-1-13-1-133-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-1-1-1-111-11111-1-1000000
χ1333−3−3i32−3+3i32−3−3i32−3+3i323033−3−3i32−3+3i320−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i3200000000000000011−1−i32−1−i32−1+i32−1+i32111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32000000
χ1433−3−3i32−3+3i32−3−3i32−3+3i323033−3−3i32−3+3i320−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32000000000000000-1-11+i321+i321−i321−i32-1-1-11+i321−i321+i321−i321+i321−i32000000
χ1533−3−3i32−3+3i32−3−3i32−3+3i3230-1-1−3−3i32−3+3i3201+i321−i321+i321−i32-11+i321−i3200022−1−i3−1−i3−1+i3−1+i32−1−i3−1+i32−1−i3−1+i311−1−i32−1−i32−1+i32−1+i321-1-1−1−i32−1+i321+i321−i321+i321−i32000000
χ1633−3−3i32−3+3i32−3−3i32−3+3i3230-1-1−3−3i32−3+3i3201+i321−i321+i321−i32-11+i321−i3200022−1−i3−1−i3−1+i3−1+i32−1−i3−1+i32−1−i3−1+i3-1-11+i321+i321−i321−i32-1111+i321−i32−1−i32−1+i32−1−i32−1+i32000000
χ1733−3−3i32−3+3i32−3−3i32−3+3i32-103-11+i321−i320−3−3i32−3+3i321+i321−i32-11+i321−i322−1−i3−1+i3−1−i3−1+i32−1+i32−1−i30002−1−i3−1+i311−1−i32−1−i32−1+i32−1+i32-11-11+i321−i32−1−i32−1+i321+i321−i32000000
χ1833−3−3i32−3+3i32−3−3i32−3+3i32-103-11+i321−i320−3−3i32−3+3i321+i321−i32-11+i321−i322−1−i3−1+i3−1−i3−1+i32−1+i32−1−i30002−1−i3−1+i3-1-11+i321+i321−i321−i321-11−1−i32−1+i321+i321−i32−1−i32−1+i32000000
χ1933−3−3i32−3+3i32−3−3i32−3+3i32-10-131+i321−i3201+i321−i32−3−3i32−3+3i32-11+i321−i322−1−i3−1+i3−1+i3−1−i3−1+i32−1−i322−1−i3−1+i300011−1−i32−1−i32−1+i32−1+i32-1-111+i321−i321+i321−i32−1−i32−1+i32000000
χ2033−3−3i32−3+3i32−3−3i32−3+3i32-10-131+i321−i3201+i321−i32−3−3i32−3+3i32-11+i321−i322−1−i3−1+i3−1+i3−1−i3−1+i32−1−i322−1−i3−1+i3000-1-11+i321+i321−i321−i3211-1−1−i32−1+i32−1−i32−1+i321+i321−i32000000
χ2133−3+3i32−3−3i32−3+3i32−3−3i323033−3+3i32−3−3i320−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i3200000000000000011−1+i32−1+i32−1−i32−1−i32111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32000000
χ2233−3+3i32−3−3i32−3+3i32−3−3i323033−3+3i32−3−3i320−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32000000000000000-1-11−i321−i321+i321+i32-1-1-11−i321+i321−i321+i321−i321+i32000000
χ2333−3+3i32−3−3i32−3+3i32−3−3i3230-1-1−3+3i32−3−3i3201−i321+i321−i321+i32-11−i321+i3200022−1+i3−1+i3−1−i3−1−i32−1+i3−1−i32−1+i3−1−i311−1+i32−1+i32−1−i32−1−i321-1-1−1+i32−1−i321−i321+i321−i321+i32000000
χ2433−3+3i32−3−3i32−3+3i32−3−3i3230-1-1−3+3i32−3−3i3201−i321+i321−i321+i32-11−i321+i3200022−1+i3−1+i3−1−i3−1−i32−1+i3−1−i32−1+i3−1−i3-1-11−i321−i321+i321+i32-1111−i321+i32−1+i32−1−i32−1+i32−1−i32000000
χ2533−3+3i32−3−3i32−3+3i32−3−3i32-103-11−i321+i320−3+3i32−3−3i321−i321+i32-11−i321+i322−1+i3−1−i3−1+i3−1−i32−1−i32−1+i30002−1+i3−1−i311−1+i32−1+i32−1−i32−1−i32-11-11−i321+i32−1+i32−1−i321−i321+i32000000
χ2633−3+3i32−3−3i32−3+3i32−3−3i32-103-11−i321+i320−3+3i32−3−3i321−i321+i32-11−i321+i322−1+i3−1−i3−1+i3−1−i32−1−i32−1+i30002−1+i3−1−i3-1-11−i321−i321+i321+i321-11−1+i32−1−i321−i321+i32−1+i32−1−i32000000
χ2733−3+3i32−3−3i32−3+3i32−3−3i32-10-131−i321+i3201−i321+i32−3+3i32−3−3i32-11−i321+i322−1+i3−1−i3−1−i3−1+i3−1−i32−1+i322−1+i3−1−i300011−1+i32−1+i32−1−i32−1−i32-1-111−i321+i321−i321+i32−1+i32−1−i32000000
χ2833−3+3i32−3−3i32−3+3i32−3−3i32-10-131−i321+i3201−i321+i32−3+3i32−3−3i32-11−i321+i322−1+i3−1−i3−1−i3−1+i3−1−i32−1+i322−1+i3−1−i3000-1-11−i321−i321+i321+i3211-1−1+i32−1−i32−1+i32−1−i321−i321+i32000000
χ294-444-4-4040000-400000000000000000000002i−2i2i−2i2i−2i000000000111-1-1-1
χ304-444-4-4040000-40000000000000000000000−2i2i−2i2i−2i2i000000000111-1-1-1
χ316666666-3-2-266-3-2-2-2-2-2-2-2-3-3-3111111111111000000000000000000000
χ32666666-26-2-2-2-26-2-2-2-2222-2-2-2222222-2-2-2-2-2-2000000000000000000000
χ33666666-2-36-2-2-2-366-2-2-2-2-2111111111-3-3-3111000000000000000000000
χ34666666-2-3-26-2-2-3-2-266-2-2-2111111111111-3-3-3000000000000000000000
χ35666666-2-3-2-2-2-2-3-2-2-2-2222111−1−2i3−1+2i3−1+2i3−1−2i3−1−2i3−1+2i3111111000000000000000000000
χ36666666-2-3-2-2-2-2-3-2-2-2-2222111−1+2i3−1−2i3−1−2i3−1+2i3−1+2i3−1−2i3111111000000000000000000000
χ3766−3−3i3−3+3i3−3−3i3−3+3i360-2-2−3−3i3−3+3i301+i31−i31+i31−i3-21+i31−i3000-2-21+i31+i31−i31−i3-21+i31−i3-21+i31−i3000000000000000000000
χ3866−3−3i3−3+3i3−3−3i3−3+3i3-206-21+i31−i30−3−3i3−3+3i31+i31−i3-21+i31−i3-21+i31−i31+i31−i3-21−i3-21+i3000-21+i31−i3000000000000000000000
χ3966−3−3i3−3+3i3−3−3i3−3+3i3-20-261+i31−i301+i31−i3−3−3i3−3+3i3-21+i31−i3-21+i31−i31−i31+i31−i3-21+i3-2-21+i31−i3000000000000000000000000
χ4066−3−3i3−3+3i3−3−3i3−3+3i3-20-2-21+i31−i301+i31−i31+i31−i32−1−i3−1+i34−2−2i3−2+2i322−1−i3−1−i3−1+i3−1+i3-21+i31−i3-21+i31−i3000000000000000000000
χ4166−3−3i3−3+3i3−3−3i3−3+3i3-20-2-21+i31−i301+i31−i31+i31−i32−1−i3−1+i3-21+i31−i3−1−i3−1+i32−1+i32−1−i34−2−2i3−2+2i3-21+i31−i3000000000000000000000
χ4266−3−3i3−3+3i3−3−3i3−3+3i3-20-2-21+i31−i301+i31−i31+i31−i32−1−i3−1+i3-21+i31−i3−1+i3−1−i3−1+i32−1−i32-21+i31−i34−2−2i3−2+2i3000000000000000000000
χ4366−3+3i3−3−3i3−3+3i3−3−3i360-2-2−3+3i3−3−3i301−i31+i31−i31+i3-21−i31+i3000-2-21−i31−i31+i31+i3-21−i31+i3-21−i31+i3000000000000000000000
χ4466−3+3i3−3−3i3−3+3i3−3−3i3-206-21−i31+i30−3+3i3−3−3i31−i31+i3-21−i31+i3-21−i31+i31−i31+i3-21+i3-21−i3000-21−i31+i3000000000000000000000
χ4566−3+3i3−3−3i3−3+3i3−3−3i3-20-261−i31+i301−i31+i3−3+3i3−3−3i3-21−i31+i3-21−i31+i31+i31−i31+i3-21−i3-2-21−i31+i3000000000000000000000000
χ4666−3+3i3−3−3i3−3+3i3−3−3i3-20-2-21−i31+i301−i31+i31−i31+i32−1+i3−1−i34−2+2i3−2−2i322−1+i3−1+i3−1−i3−1−i3-21−i31+i3-21−i31+i3000000000000000000000
χ4766−3+3i3−3−3i3−3+3i3−3−3i3-20-2-21−i31+i301−i31+i31−i31+i32−1+i3−1−i3-21−i31+i3−1−i3−1+i3−1−i32−1+i32-21−i31+i34−2+2i3−2−2i3000000000000000000000
χ4866−3+3i3−3−3i3−3+3i3−3−3i3-20-2-21−i31+i301−i31+i31−i31+i32−1+i3−1−i3-21−i31+i3−1+i3−1−i32−1−i32−1+i34−2+2i3−2−2i3-21−i31+i3000000000000000000000
χ498-888-8-8080000-80000000000000000000000000000000000000-1-1-1111
χ508-888-8-80-40000400000000000000000000000000000000000002-1-1-211
χ518-888-8-80-4000040000000000000000000000000000000000000-12-11-21
χ528-888-8-80-4000040000000000000000000000000000000000000-1-1211-2
χ5312-12−6−6i3−6+6i36+6i36−6i3000000000000000000000000000002i−2i2ζ11−2ζ112ζ7−2ζ7000000000000000
χ5412-12−6−6i3−6+6i36+6i36−6i300000000000000000000000000000−2i2i−2ζ112ζ11−2ζ72ζ7000000000000000
χ5512-12−6+6i3−6−6i36−6i36+6i3000000000000000000000000000002i−2i2ζ7−2ζ72ζ11−2ζ11000000000000000
χ5612-12−6+6i3−6−6i36−6i36+6i300000000000000000000000000000−2i2i−2ζ72ζ7−2ζ112ζ11000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.