Finite Group Databasebeta

← Group #780

Character table — Group #780

Order 90.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27
size122222221512222222151222222215
order1355151515152331515151515156331515151515156
χ1111111111111111111111111111
χ211111111-111111111-111111111-1
χ322−1+52−1−52−1+52−1+52−1−52−1−52022−1+52−1−52−1+52−1+52−1−52−1−52022−1+52−1−52−1+52−1+52−1−52−1−520
χ422−1−52−1+52−1−52−1−52−1+52−1+52022−1−52−1+52−1−52−1−52−1+52−1+52022−1−52−1+52−1−52−1−52−1+52−1+520
χ52-122-1-1-1-102-122-1-1-1-102-122-1-1-1-10
χ62-1−1+52−1−52ζ2+ζ13ζ7+ζ8ζ4+ζ11ζ+ζ1402-1−1+52−1−52ζ2+ζ13ζ7+ζ8ζ4+ζ11ζ+ζ1402-1−1+52−1−52ζ2+ζ13ζ7+ζ8ζ4+ζ11ζ+ζ140
χ72-1−1+52−1−52ζ7+ζ8ζ2+ζ13ζ+ζ14ζ4+ζ1102-1−1+52−1−52ζ7+ζ8ζ2+ζ13ζ+ζ14ζ4+ζ1102-1−1+52−1−52ζ7+ζ8ζ2+ζ13ζ+ζ14ζ4+ζ110
χ82-1−1−52−1+52ζ4+ζ11ζ+ζ14ζ7+ζ8ζ2+ζ1302-1−1−52−1+52ζ4+ζ11ζ+ζ14ζ7+ζ8ζ2+ζ1302-1−1−52−1+52ζ4+ζ11ζ+ζ14ζ7+ζ8ζ2+ζ130
χ92-1−1−52−1+52ζ+ζ14ζ4+ζ11ζ2+ζ13ζ7+ζ802-1−1−52−1+52ζ+ζ14ζ4+ζ11ζ2+ζ13ζ7+ζ802-1−1−52−1+52ζ+ζ14ζ4+ζ11ζ2+ζ13ζ7+ζ80
χ10111111111−1+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
χ1111111111-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32
χ1222−1+52−1−52−1+52−1+52−1−52−1−520−1+i3−1+i3ζ2+ζ8ζ11+ζ14ζ2+ζ8ζ2+ζ8ζ11+ζ14ζ11+ζ140−1−i3−1−i3ζ7+ζ13ζ+ζ4ζ7+ζ13ζ7+ζ13ζ+ζ4ζ+ζ40
χ1322−1−52−1+52−1−52−1−52−1+52−1+520−1+i3−1+i3ζ11+ζ14ζ2+ζ8ζ11+ζ14ζ11+ζ14ζ2+ζ8ζ2+ζ80−1−i3−1−i3ζ+ζ4ζ7+ζ13ζ+ζ4ζ+ζ4ζ7+ζ13ζ7+ζ130
χ142-122-1-1-1-10−1+i31−i32−1+i3−1+i31−i321−i321−i321−i320−1−i31+i32−1−i3−1−i31+i321+i321+i321+i320
χ152-1−1+52−1−52ζ2+ζ13ζ7+ζ8ζ4+ζ11ζ+ζ140−1+i31−i32ζ2+ζ8ζ11+ζ14ζ7−ζ8−ζ13−ζ2−ζ7+ζ13ζ−ζ4−ζ14−ζ+ζ4−ζ110−1−i31+i32ζ7+ζ13ζ+ζ4−ζ2−ζ7+ζ8ζ2−ζ8−ζ13−ζ−ζ11+ζ14−ζ4+ζ11−ζ140
χ162-1−1+52−1−52ζ7+ζ8ζ2+ζ13ζ+ζ14ζ4+ζ110−1+i31−i32ζ2+ζ8ζ11+ζ14−ζ2−ζ7+ζ13ζ7−ζ8−ζ13−ζ+ζ4−ζ11ζ−ζ4−ζ140−1−i31+i32ζ7+ζ13ζ+ζ4ζ2−ζ8−ζ13−ζ2−ζ7+ζ8−ζ4+ζ11−ζ14−ζ−ζ11+ζ140
χ172-1−1−52−1+52ζ4+ζ11ζ+ζ14ζ7+ζ8ζ2+ζ130−1+i31−i32ζ11+ζ14ζ2+ζ8ζ−ζ4−ζ14−ζ+ζ4−ζ11−ζ2−ζ7+ζ13ζ7−ζ8−ζ130−1−i31+i32ζ+ζ4ζ7+ζ13−ζ−ζ11+ζ14−ζ4+ζ11−ζ14ζ2−ζ8−ζ13−ζ2−ζ7+ζ80
χ182-1−1−52−1+52ζ+ζ14ζ4+ζ11ζ2+ζ13ζ7+ζ80−1+i31−i32ζ11+ζ14ζ2+ζ8−ζ+ζ4−ζ11ζ−ζ4−ζ14ζ7−ζ8−ζ13−ζ2−ζ7+ζ130−1−i31+i32ζ+ζ4ζ7+ζ13−ζ4+ζ11−ζ14−ζ−ζ11+ζ14−ζ2−ζ7+ζ8ζ2−ζ8−ζ130
χ19111111111−1−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
χ2011111111-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32
χ2122−1+52−1−52−1+52−1+52−1−52−1−520−1−i3−1−i3ζ7+ζ13ζ+ζ4ζ7+ζ13ζ7+ζ13ζ+ζ4ζ+ζ40−1+i3−1+i3ζ2+ζ8ζ11+ζ14ζ2+ζ8ζ2+ζ8ζ11+ζ14ζ11+ζ140
χ2222−1−52−1+52−1−52−1−52−1+52−1+520−1−i3−1−i3ζ+ζ4ζ7+ζ13ζ+ζ4ζ+ζ4ζ7+ζ13ζ7+ζ130−1+i3−1+i3ζ11+ζ14ζ2+ζ8ζ11+ζ14ζ11+ζ14ζ2+ζ8ζ2+ζ80
χ232-122-1-1-1-10−1−i31+i32−1−i3−1−i31+i321+i321+i321+i320−1+i31−i32−1+i3−1+i31−i321−i321−i321−i320
χ242-1−1+52−1−52ζ2+ζ13ζ7+ζ8ζ4+ζ11ζ+ζ140−1−i31+i32ζ7+ζ13ζ+ζ4−ζ2−ζ7+ζ8ζ2−ζ8−ζ13−ζ−ζ11+ζ14−ζ4+ζ11−ζ140−1+i31−i32ζ2+ζ8ζ11+ζ14ζ7−ζ8−ζ13−ζ2−ζ7+ζ13ζ−ζ4−ζ14−ζ+ζ4−ζ110
χ252-1−1+52−1−52ζ7+ζ8ζ2+ζ13ζ+ζ14ζ4+ζ110−1−i31+i32ζ7+ζ13ζ+ζ4ζ2−ζ8−ζ13−ζ2−ζ7+ζ8−ζ4+ζ11−ζ14−ζ−ζ11+ζ140−1+i31−i32ζ2+ζ8ζ11+ζ14−ζ2−ζ7+ζ13ζ7−ζ8−ζ13−ζ+ζ4−ζ11ζ−ζ4−ζ140
χ262-1−1−52−1+52ζ4+ζ11ζ+ζ14ζ7+ζ8ζ2+ζ130−1−i31+i32ζ+ζ4ζ7+ζ13−ζ−ζ11+ζ14−ζ4+ζ11−ζ14ζ2−ζ8−ζ13−ζ2−ζ7+ζ80−1+i31−i32ζ11+ζ14ζ2+ζ8ζ−ζ4−ζ14−ζ+ζ4−ζ11−ζ2−ζ7+ζ13ζ7−ζ8−ζ130
χ272-1−1−52−1+52ζ+ζ14ζ4+ζ11ζ2+ζ13ζ7+ζ80−1−i31+i32ζ+ζ4ζ7+ζ13−ζ4+ζ11−ζ14−ζ−ζ11+ζ14−ζ2−ζ7+ζ8ζ2−ζ8−ζ130−1+i31−i32ζ11+ζ14ζ2+ζ8−ζ+ζ4−ζ11ζ−ζ4−ζ14ζ7−ζ8−ζ13−ζ2−ζ7+ζ130

Here ζ is a primitive root of unity of order 15 (ζ15 = 1); i = ζ3.