Finite Group Databasebeta

← Group #88604

Character table — Group #88604

Order 432.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38
size11223333333333666666181818181818181818181818242424242424
order1236223366666666666644441212121212121212333666
χ111111111111111111111111111111111111111
χ211111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ3111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i32
χ4111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321−1−i32−1+i321−1−i32−1+i32
χ5111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i32
χ6111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321−1+i32−1−i321−1+i32−1−i32
χ71-11-11-11111-1-1-1-11-11-11-1i−ii−iii−i−iii−i−i111-1-1-1
χ81-11-11-11111-1-1-1-11-11-11-1−ii−ii−i−iii−i−iii111-1-1-1
χ91-11-11-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321-1−1−i321+i32−1+i321−i32i−ii−iζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ71−1−i32−1+i32-11+i321−i32
χ101-11-11-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321-1−1−i321+i32−1+i321−i32−ii−ii−ζ11−ζ11ζ11ζ11−ζ7−ζ7ζ7ζ71−1−i32−1+i32-11+i321−i32
χ111-11-11-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321-1−1+i321−i32−1−i321+i32i−ii−iζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ111−1+i32−1−i32-11−i321+i32
χ121-11-11-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321-1−1+i321−i32−1−i321+i32−ii−ii−ζ7−ζ7ζ7ζ7−ζ11−ζ11ζ11ζ111−1+i32−1−i32-11−i321+i32
χ1322222222222222222222000000000000-1-1-1-1-1-1
χ14222222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i322−1−i3−1−i3−1+i3−1+i3000000000000-11+i321−i32-11+i321−i32
χ15222222−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i322−1+i3−1+i3−1−i3−1−i3000000000000-11−i321+i32-11−i321+i32
χ162-22-22-22222-2-2-2-22-22-22-2000000000000-1-1-1111
χ172-22-22-2−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i32-2−1−i31+i3−1+i31−i3000000000000-11+i321−i321−1−i32−1+i32
χ182-22-22-2−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i32-2−1+i31−i3−1−i31+i3000000000000-11−i321+i321−1+i32−1−i32
χ193333-1-133-1-13-13-1-1-1-1-1-1-111-1-11-11-11-11-1000000
χ203333-1-133-1-13-13-1-1-1-1-1-1-1-1-111-11-11-11-11000000
χ213333-1-1−3−3i32−3+3i321+i321−i32−3−3i321+i32−3+3i321−i32-1-11+i321+i321−i321−i3211-1-1−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32000000
χ223333-1-1−3−3i32−3+3i321+i321−i32−3−3i321+i32−3+3i321−i32-1-11+i321+i321−i321−i32-1-1111+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i32000000
χ233333-1-1−3+3i32−3−3i321−i321+i32−3+3i321−i32−3−3i321+i32-1-11−i321−i321+i321+i3211-1-1−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32000000
χ243333-1-1−3+3i32−3−3i321−i321+i32−3+3i321−i32−3−3i321+i32-1-11−i321−i321+i321+i32-1-1111−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i32000000
χ253-33-3-1133-1-1-31-31-11-11-11i−i−iii−i−iii−i−ii000000
χ263-33-3-1133-1-1-31-31-11-11-11−iii−i−iii−i−iii−i000000
χ273-33-3-11−3−3i32−3+3i321+i321−i323+3i32−1−i323−3i32−1+i32-111+i32−1−i321−i32−1+i32i−i−iiζ11−ζ11−ζ11ζ11ζ7−ζ7−ζ7ζ7000000
χ283-33-3-11−3−3i32−3+3i321+i321−i323+3i32−1−i323−3i32−1+i32-111+i32−1−i321−i32−1+i32−iii−i−ζ11ζ11ζ11−ζ11−ζ7ζ7ζ7−ζ7000000
χ293-33-3-11−3+3i32−3−3i321−i321+i323−3i32−1+i323+3i32−1−i32-111−i32−1+i321+i32−1−i32i−i−iiζ7−ζ7−ζ7ζ7ζ11−ζ11−ζ11ζ11000000
χ303-33-3-11−3+3i32−3−3i321−i321+i323−3i32−1+i323+3i32−1−i32-111−i32−1+i321+i32−1−i32−iii−i−ζ7ζ7ζ7−ζ7−ζ11ζ11ζ11−ζ11000000
χ3166-3-36600000000-3-30000000000000000000000
χ3266-3-3-2-20044040411-2-2-2-2000000000000000000
χ3366-3-3-2-200−2−2i3−2+2i30−2−2i30−2+2i3111+i31+i31−i31−i3000000000000000000
χ3466-3-3-2-200−2+2i3−2−2i30−2+2i30−2−2i3111−i31−i31+i31+i3000000000000000000
χ356-6-336-600000000-330000000000000000000000
χ366-6-33-2200440-40-41-1-22-22000000000000000000
χ376-6-33-2200−2−2i3−2+2i302+2i302−2i31-11+i3−1−i31−i3−1+i3000000000000000000
χ386-6-33-2200−2+2i3−2−2i302−2i302+2i31-11−i3−1+i31+i3−1−i3000000000000000000

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