Finite Group Databasebeta

← Group #13164557

Character table — Group #13164557

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111166666666666121212121212121212121212121212121212363636363636727272727272727272969696969696
order1233662223666666646666666661212121212121212226666444121212121212333666
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ322222222222222222222222222222222222000000000000000-1-1-1-1-1-1
χ4222222222-1222222-12-1-1-1-1-1-1-1-1-122-1-1-1-1-1-10000000000000002-1-12-1-1
χ5222222222-1222222-12-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1000000000000000-12-1-12-1
χ6222222222-1222222-12-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1000000000000000-1-12-1-12
χ73333333-1-1333-1-1-1-13-1333-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111-1-1-1-1000000
χ83333333-1-1333-1-1-1-13-1333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111000000
χ9333333-13-13-1-133-1-13-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1111111-11-1-1-111-1-1000000
χ10333333-13-13-1-133-1-13-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-111000000
χ11333333-1-133-1-1-1-1333-1-1-1-1-1-1-1333-1-1-1-1-1-1-1-1111111-1-11-1-1-1-111000000
χ12333333-1-133-1-1-1-1333-1-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-1000000
χ1333−3+3i32−3−3i32−3+3i32−3−3i323330−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3203000000000−3+3i32−3−3i3200000011−1+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+3i32−3−3i323330−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3203000000000−3+3i32−3−3i32000000-1-11−i321−i321+i321+i32-1-1-11−i321+i321−i321+i321−i321+i32000000
χ1533−3+3i32−3−3i32−3+3i32−3−3i323-1-10−3+3i32−3−3i321−i321+i321−i321+i320-10002−1+i3−1−i32−1+i3−1−i31−i321+i3222−1+i3−1+i3−1−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+3i32−3−3i323-1-10−3+3i32−3−3i321−i321+i321−i321+i320-10002−1+i3−1−i32−1+i3−1−i31−i321+i3222−1+i3−1+i3−1−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+3i32−3−3i32-13-101−i321+i32−3+3i32−3−3i321−i321+i320-12−1+i3−1−i30002−1+i3−1−i31−i321+i32−1+i3−1−i32−1−i32−1+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+3i32−3−3i32-13-101−i321+i32−3+3i32−3−3i321−i321+i320-12−1+i3−1−i30002−1+i3−1−i31−i321+i32−1+i3−1−i32−1−i32−1+i3-1-11−i321−i321+i321+i321-11−1+i32−1−i321−i321+i32−1+i32−1−i32000000
χ1933−3+3i32−3−3i32−3+3i32−3−3i32-1-1301−i321+i321−i321+i32−3+3i32−3−3i320-12−1+i3−1−i32−1+i3−1−i30001−i321+i32−1−i3−1+i3−1−i32−1+i3211−1+i32−1+i32−1−i32−1−i32-1-111−i321+i321−i321+i32−1+i32−1−i32000000
χ2033−3+3i32−3−3i32−3+3i32−3−3i32-1-1301−i321+i321−i321+i32−3+3i32−3−3i320-12−1+i3−1−i32−1+i3−1−i30001−i321+i32−1−i3−1+i3−1−i32−1+i32-1-11−i321−i321+i321+i3211-1−1+i32−1−i32−1+i32−1−i321−i321+i32000000
χ2133−3−3i32−3+3i32−3−3i32−3+3i323330−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3203000000000−3−3i32−3+3i3200000011−1−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+3i323330−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3203000000000−3−3i32−3+3i32000000-1-11+i321+i321−i321−i32-1-1-11+i321−i321+i321−i321+i321−i32000000
χ2333−3−3i32−3+3i32−3−3i32−3+3i323-1-10−3−3i32−3+3i321+i321−i321+i321−i320-10002−1−i3−1+i32−1−i3−1+i31+i321−i3222−1−i3−1−i3−1+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+3i323-1-10−3−3i32−3+3i321+i321−i321+i321−i320-10002−1−i3−1+i32−1−i3−1+i31+i321−i3222−1−i3−1−i3−1+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+3i32-13-101+i321−i32−3−3i32−3+3i321+i321−i320-12−1−i3−1+i30002−1−i3−1+i31+i321−i32−1−i3−1+i32−1+i32−1−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+3i32-13-101+i321−i32−3−3i32−3+3i321+i321−i320-12−1−i3−1+i30002−1−i3−1+i31+i321−i32−1−i3−1+i32−1+i32−1−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+3i32-1-1301+i321−i321+i321−i32−3−3i32−3+3i320-12−1−i3−1+i32−1−i3−1+i30001+i321−i32−1+i3−1−i3−1+i32−1−i3211−1−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+3i32-1-1301+i321−i321+i321−i32−3−3i32−3+3i320-12−1−i3−1+i32−1−i3−1+i30001+i321−i32−1+i3−1−i3−1+i32−1−i32-1-11+i321+i321−i321−i3211-1−1−i32−1+i32−1−i32−1+i321+i321−i32000000
χ294-444-4-40004000000-40000000000000000002-22-22-2000000000111-1-1-1
χ304-444-4-40004000000-4000000000000000000-22-22-22000000000111-1-1-1
χ316666666-2-2-366-2-2-2-2-3-2-3-3-3111111-2-2111111000000000000000000000
χ32666666-26-2-3-2-266-2-2-3-2111-3-3-3111-2-2111111000000000000000000000
χ33666666-2-26-3-2-2-2-266-3-2111111-3-3-3-2-2111111000000000000000000000
χ34666666-2-2-26-2-2-2-2-2-262-2-2-2-2-2-2-2-2-222222222000000000000000000000
χ35666666-2-2-2-3-2-2-2-2-2-2-3211111111122−1+2i3−1−2i3−1−2i3−1+2i3−1+2i3−1−2i3000000000000000000000
χ36666666-2-2-2-3-2-2-2-2-2-2-3211111111122−1−2i3−1+2i3−1+2i3−1−2i3−1−2i3−1+2i3000000000000000000000
χ3766−3+3i3−3−3i3−3+3i3−3−3i36-2-20−3+3i3−3−3i31−i31+i31−i31+i30-2000-21−i31+i3-21−i31+i31−i31+i3-2-21−i31−i31+i31+i3000000000000000000000
χ3866−3+3i3−3−3i3−3+3i3−3−3i3-26-201−i31+i3−3+3i3−3−3i31−i31+i30-2-21−i31+i3000-21−i31+i31−i31+i31−i31+i3-21+i3-21−i3000000000000000000000
χ3966−3+3i3−3−3i3−3+3i3−3−3i3-2-2601−i31+i31−i31+i3−3+3i3−3−3i30-2-21−i31+i3-21−i31+i30001−i31+i31+i31−i31+i3-21−i3-2000000000000000000000
χ4066−3+3i3−3−3i3−3+3i3−3−3i3-2-2-201−i31+i31−i31+i31−i31+i3024−2+2i3−2−2i3-21−i31+i3-21−i31+i3−1+i3−1−i322−1+i3−1+i3−1−i3−1−i3000000000000000000000
χ4166−3+3i3−3−3i3−3+3i3−3−3i3-2-2-201−i31+i31−i31+i31−i31+i302-21−i31+i34−2+2i3−2−2i3-21−i31+i3−1+i3−1−i3−1+i3−1−i32−1−i32−1+i3000000000000000000000
χ4266−3+3i3−3−3i3−3+3i3−3−3i3-2-2-201−i31+i31−i31+i31−i31+i302-21−i31+i3-21−i31+i34−2+2i3−2−2i3−1+i3−1−i3−1−i3−1+i3−1−i32−1+i32000000000000000000000
χ4366−3−3i3−3+3i3−3−3i3−3+3i36-2-20−3−3i3−3+3i31+i31−i31+i31−i30-2000-21+i31−i3-21+i31−i31+i31−i3-2-21+i31+i31−i31−i3000000000000000000000
χ4466−3−3i3−3+3i3−3−3i3−3+3i3-26-201+i31−i3−3−3i3−3+3i31+i31−i30-2-21+i31−i3000-21+i31−i31+i31−i31+i31−i3-21−i3-21+i3000000000000000000000
χ4566−3−3i3−3+3i3−3−3i3−3+3i3-2-2601+i31−i31+i31−i3−3−3i3−3+3i30-2-21+i31−i3-21+i31−i30001+i31−i31−i31+i31−i3-21+i3-2000000000000000000000
χ4666−3−3i3−3+3i3−3−3i3−3+3i3-2-2-201+i31−i31+i31−i31+i31−i3024−2−2i3−2+2i3-21+i31−i3-21+i31−i3−1−i3−1+i322−1−i3−1−i3−1+i3−1+i3000000000000000000000
χ4766−3−3i3−3+3i3−3−3i3−3+3i3-2-2-201+i31−i31+i31−i31+i31−i302-21+i31−i34−2−2i3−2+2i3-21+i31−i3−1−i3−1+i3−1−i3−1+i32−1+i32−1−i3000000000000000000000
χ4866−3−3i3−3+3i3−3−3i3−3+3i3-2-2-201+i31−i31+i31−i31+i31−i302-21+i31−i3-21+i31−i34−2−2i3−2+2i3−1−i3−1+i3−1+i3−1−i3−1+i32−1−i32000000000000000000000
χ498-888-8-80008000000-8000000000000000000000000000000000-1-1-1111
χ508-888-8-8000-400000040000000000000000000000000000000002-1-1-211
χ518-888-8-8000-40000004000000000000000000000000000000000-12-11-21
χ528-888-8-8000-40000004000000000000000000000000000000000-1-1211-2
χ5312-12−6+6i3−6−6i36−6i36+6i3000000000000000000000000000002-2−1+i31−i3−1−i31+i3000000000000000
χ5412-12−6+6i3−6−6i36−6i36+6i300000000000000000000000000000-221−i3−1+i31+i3−1−i3000000000000000
χ5512-12−6−6i3−6+6i36+6i36−6i3000000000000000000000000000002-2−1−i31+i3−1+i31−i3000000000000000
χ5612-12−6−6i3−6+6i36+6i36−6i300000000000000000000000000000-221+i3−1−i31−i3−1+i3000000000000000

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