Finite Group Databasebeta

← Group #66321

Character table — Group #66321

Order 324.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size11111133333333333366999999999999999999181818181818
order12336633333366666636441212121212121212121212121212121236991818
χ111111111111111111111111111111111111111111111
χ211111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ3111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1+i32
χ4111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i3211−1−i32−1+i32−1−i32−1+i32
χ5111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1−i32
χ6111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i3211−1+i32−1−i32−1+i32−1−i32
χ71-111-1-1111111-1-1-1-1-1-11-1i−iii−i−iiii−i−i−iiii−i−i−i1-111-1-1
χ81-111-1-1111111-1-1-1-1-1-11-1−ii−i−iii−i−i−iiii−i−i−iiii1-111-1-1
χ91-111-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321−i321−i321−i321-1i−iii−i−iζ11ζ11ζ11−ζ11−ζ11−ζ11ζ7ζ7ζ7−ζ7−ζ7−ζ71-1−1−i32−1+i321+i321−i32
χ101-111-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321−i321−i321−i321-1−ii−i−iii−ζ11−ζ11−ζ11ζ11ζ11ζ11−ζ7−ζ7−ζ7ζ7ζ7ζ71-1−1−i32−1+i321+i321−i32
χ111-111-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321+i321+i321+i321-1i−iii−i−iζ7ζ7ζ7−ζ7−ζ7−ζ7ζ11ζ11ζ11−ζ11−ζ11−ζ111-1−1+i32−1−i321−i321+i32
χ121-111-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321+i321+i321+i321-1−ii−i−iii−ζ7−ζ7−ζ7ζ7ζ7ζ7−ζ11−ζ11−ζ11ζ11ζ11ζ111-1−1+i32−1−i321−i321+i32
χ1322222222222222222222000000000000000000-1-1-1-1-1-1
χ14222222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i322000000000000000000-1-11+i321−i321+i321−i32
χ15222222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i322000000000000000000-1-11−i321+i321−i321+i32
χ162-222-2-2222222-2-2-2-2-2-22-2000000000000000000-11-1-111
χ172-222-2-2−1−i3−1−i3−1−i3−1+i3−1+i3−1+i31+i31+i31+i31−i31−i31−i32-2000000000000000000-111+i321−i32−1−i32−1+i32
χ182-222-2-2−1+i3−1+i3−1+i3−1−i3−1−i3−1−i31−i31−i31−i31+i31+i31+i32-2000000000000000000-111−i321+i32−1+i32−1−i32
χ1933−3−3i32−3+3i32−3−3i32−3+3i323+i32−i3−3+i323−i32i3−3−i323+i32−i3−3+i323−i32i3−3−i320011−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32000000
χ2033−3−3i32−3+3i32−3−3i32−3+3i323+i32−i3−3+i323−i32i3−3−i323+i32−i3−3+i323−i32i3−3−i3200-1-11+i321−i321+i321−i32-11+i321−i32-11+i321−i32-11+i321−i32-11+i321−i32000000
χ2133−3−3i32−3+3i32−3−3i32−3+3i32−i3−3+i323+i32i3−3−i323−i32−i3−3+i323+i32i3−3−i323−i320011−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1+i321−1−i32−1+i321−1−i32000000
χ2233−3−3i32−3+3i32−3−3i32−3+3i32−i3−3+i323+i32i3−3−i323−i32−i3−3+i323+i32i3−3−i323−i3200-1-11+i321−i321+i321−i321+i321−i32-11+i321−i32-11−i32-11+i321−i32-11+i32000000
χ2333−3−3i32−3+3i32−3−3i32−3+3i32−3+i323+i32−i3−3−i323−i32i3−3+i323+i32−i3−3−i323−i32i30011−1−i32−1+i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1−i32−1+i321−1−i32−1+i321000000
χ2433−3−3i32−3+3i32−3−3i32−3+3i32−3+i323+i32−i3−3−i323−i32i3−3+i323+i32−i3−3−i323−i32i300-1-11+i321−i321+i321−i321−i32-11+i321−i32-11+i321+i321−i32-11+i321−i32-1000000
χ2533−3+3i32−3−3i32−3+3i32−3−3i323−i32i3−3−i323+i32−i3−3+i323−i32i3−3−i323+i32−i3−3+i320011−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32000000
χ2633−3+3i32−3−3i32−3+3i32−3−3i323−i32i3−3−i323+i32−i3−3+i323−i32i3−3−i323+i32−i3−3+i3200-1-11−i321+i321−i321+i32-11−i321+i32-11−i321+i32-11−i321+i32-11−i321+i32000000
χ2733−3+3i32−3−3i32−3+3i32−3−3i32i3−3−i323−i32−i3−3+i323+i32i3−3−i323−i32−i3−3+i323+i320011−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1−i321−1+i32−1−i321−1+i32000000
χ2833−3+3i32−3−3i32−3+3i32−3−3i32i3−3−i323−i32−i3−3+i323+i32i3−3−i323−i32−i3−3+i323+i3200-1-11−i321+i321−i321+i321−i321+i32-11−i321+i32-11+i32-11−i321+i32-11−i32000000
χ2933−3+3i32−3−3i32−3+3i32−3−3i32−3−i323−i32i3−3+i323+i32−i3−3−i323−i32i3−3+i323+i32−i30011−1+i32−1−i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1+i32−1−i321−1+i32−1−i321000000
χ3033−3+3i32−3−3i32−3+3i32−3−3i32−3−i323−i32i3−3+i323+i32−i3−3−i323−i32i3−3+i323+i32−i300-1-11−i321+i321−i321+i321+i32-11−i321+i32-11−i321−i321+i32-11−i321+i32-1000000
χ313-3−3−3i32−3+3i323+3i323−3i323+i32−i3−3+i323−i32i3−3−i32−3−i32i33−i32−3+i32−i33+i3200i−iζ11ζ7−ζ11−ζ7iζ11ζ7−i−ζ11−ζ7iζ11ζ7−i−ζ11−ζ7000000
χ323-3−3−3i32−3+3i323+3i323−3i323+i32−i3−3+i323−i32i3−3−i32−3−i32i33−i32−3+i32−i33+i3200−ii−ζ11−ζ7ζ11ζ7−i−ζ11−ζ7iζ11ζ7−i−ζ11−ζ7iζ11ζ7000000
χ333-3−3−3i32−3+3i323+3i323−3i32−i3−3+i323+i32i3−3−i323−i32i33−i32−3−i32−i33+i32−3+i3200i−iζ11ζ7−ζ11−ζ7ζ11ζ7i−ζ11−ζ7−iζ7iζ11−ζ7−i−ζ11000000
χ343-3−3−3i32−3+3i323+3i323−3i32−i3−3+i323+i32i3−3−i323−i32i33−i32−3−i32−i33+i32−3+i3200−ii−ζ11−ζ7ζ11ζ7−ζ11−ζ7−iζ11ζ7i−ζ7−i−ζ11ζ7iζ11000000
χ353-3−3−3i32−3+3i323+3i323−3i32−3+i323+i32−i3−3−i323−i32i33−i32−3−i32i33+i32−3+i32−i300i−iζ11ζ7−ζ11−ζ7ζ7iζ11−ζ7−i−ζ11ζ11ζ7i−ζ11−ζ7−i000000
χ363-3−3−3i32−3+3i323+3i323−3i32−3+i323+i32−i3−3−i323−i32i33−i32−3−i32i33+i32−3+i32−i300−ii−ζ11−ζ7ζ11ζ7−ζ7−i−ζ11ζ7iζ11−ζ11−ζ7−iζ11ζ7i000000
χ373-3−3+3i32−3−3i323−3i323+3i323−i32i3−3−i323+i32−i3−3+i32−3+i32−i33+i32−3−i32i33−i3200i−iζ7ζ11−ζ7−ζ11iζ7ζ11−i−ζ7−ζ11iζ7ζ11−i−ζ7−ζ11000000
χ383-3−3+3i32−3−3i323−3i323+3i323−i32i3−3−i323+i32−i3−3+i32−3+i32−i33+i32−3−i32i33−i3200−ii−ζ7−ζ11ζ7ζ11−i−ζ7−ζ11iζ7ζ11−i−ζ7−ζ11iζ7ζ11000000
χ393-3−3+3i32−3−3i323−3i323+3i32i3−3−i323−i32−i3−3+i323+i32−i33+i32−3+i32i33−i32−3−i3200i−iζ7ζ11−ζ7−ζ11ζ7ζ11i−ζ7−ζ11−iζ11iζ7−ζ11−i−ζ7000000
χ403-3−3+3i32−3−3i323−3i323+3i32i3−3−i323−i32−i3−3+i323+i32−i33+i32−3+i32i33−i32−3−i3200−ii−ζ7−ζ11ζ7ζ11−ζ7−ζ11−iζ7ζ11i−ζ11−i−ζ7ζ11iζ7000000
χ413-3−3+3i32−3−3i323−3i323+3i32−3−i323−i32i3−3+i323+i32−i33+i32−3+i32−i33−i32−3−i32i300i−iζ7ζ11−ζ7−ζ11ζ11iζ7−ζ11−i−ζ7ζ7ζ11i−ζ7−ζ11−i000000
χ423-3−3+3i32−3−3i323−3i323+3i32−3−i323−i32i3−3+i323+i32−i33+i32−3+i32−i33−i32−3−i32i300−ii−ζ7−ζ11ζ7ζ11−ζ11−i−ζ7ζ11iζ7−ζ7−ζ11−iζ7ζ11i000000
χ43666666000000000000-3-3000000000000000000000000
χ446-666-6-6000000000000-33000000000000000000000000

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