Finite Group Databasebeta

← Group #14514274

Character table — Group #14514274

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size1121515161616163032323232323232323232323232323232323232323232323232324040120120160160160160
order12222336625566101010101010151515153030303030303030303030302444661212
χ111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32111111−1+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−i321111−1+i32−1−i32−1+i32−1−i32
χ411111−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32111111−1+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−i32-1-1-1-11−i321+i321−i321+i32
χ511111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32111111−1−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+i321111−1−i32−1+i32−1−i32−1+i32
χ611111−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32111111−1−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+i32-1-1-1-11+i321−i321+i321−i32
χ711-1111111-111-1-111-1-1-1-1111111-1-1-1-111-1-1-1-11-11-111-1-1
χ811-1111111-111-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-11-11-1-111
χ911-111−1+i32−1−i32−1+i32−1−i32-1111−i321+i3211-1-1-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i321-11-1−1+i32−1−i321−i321+i32
χ1011-111−1+i32−1−i32−1+i32−1−i32-1111−i321+i3211-1-1-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32-11-111−i321+i32−1+i32−1−i32
χ1111-111−1−i32−1+i32−1−i32−1+i32-1111+i321−i3211-1-1-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i321-11-1−1−i32−1+i321+i321−i32
χ1211-111−1−i32−1+i32−1−i32−1+i32-1111+i321−i3211-1-1-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32-11-111+i321−i32−1−i32−1+i32
χ132222222222−1+52−1−5222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1−52−1−5200000000
χ142222222222−1−52−1+5222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+5200000000
χ1522222−1+i3−1−i3−1+i3−1−i32−1+52−1−52−1+i3−1−i3−1+52−1−52−1+52−1+52−1−52−1−52ζ2+ζ8ζ11+ζ14ζ7+ζ13ζ+ζ4ζ2+ζ8ζ11+ζ14ζ2+ζ8ζ2+ζ8ζ11+ζ14ζ11+ζ14ζ7+ζ13ζ+ζ4ζ7+ζ13ζ7+ζ13ζ+ζ4ζ+ζ400000000
χ1622222−1+i3−1−i3−1+i3−1−i32−1−52−1+52−1+i3−1−i3−1−52−1+52−1−52−1−52−1+52−1+52ζ11+ζ14ζ2+ζ8ζ+ζ4ζ7+ζ13ζ11+ζ14ζ2+ζ8ζ11+ζ14ζ11+ζ14ζ2+ζ8ζ2+ζ8ζ+ζ4ζ7+ζ13ζ+ζ4ζ+ζ4ζ7+ζ13ζ7+ζ1300000000
χ1722222−1−i3−1+i3−1−i3−1+i32−1+52−1−52−1−i3−1+i3−1+52−1−52−1+52−1+52−1−52−1−52ζ7+ζ13ζ+ζ4ζ2+ζ8ζ11+ζ14ζ7+ζ13ζ+ζ4ζ7+ζ13ζ7+ζ13ζ+ζ4ζ+ζ4ζ2+ζ8ζ11+ζ14ζ2+ζ8ζ2+ζ8ζ11+ζ14ζ11+ζ1400000000
χ1822222−1−i3−1+i3−1−i3−1+i32−1−52−1+52−1−i3−1+i3−1−52−1+52−1−52−1−52−1+52−1+52ζ+ζ4ζ7+ζ13ζ11+ζ14ζ2+ζ8ζ+ζ4ζ7+ζ13ζ+ζ4ζ+ζ4ζ7+ζ13ζ7+ζ13ζ11+ζ14ζ2+ζ8ζ11+ζ14ζ11+ζ14ζ2+ζ8ζ2+ζ800000000
χ1922-2222222-2−1+52−1−52-2-2−1+52−1−521−521−521+521+52−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1−521−521−521+521+5200000000
χ2022-2222222-2−1−52−1+52-2-2−1−52−1+521+521+521−521−52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−52−1−52−1+521+521+521−521−5200000000
χ2122-222−1+i3−1−i3−1+i3−1−i3-2−1+52−1−521−i31+i3−1+52−1−521−521−521+521+52ζ2+ζ8ζ11+ζ14ζ7+ζ13ζ+ζ4ζ2+ζ8ζ11+ζ14−ζ2−ζ8−ζ2−ζ8−ζ11−ζ14−ζ11−ζ14ζ7+ζ13ζ+ζ4−ζ7−ζ13−ζ7−ζ13−ζ−ζ4−ζ−ζ400000000
χ2222-222−1+i3−1−i3−1+i3−1−i3-2−1−52−1+521−i31+i3−1−52−1+521+521+521−521−52ζ11+ζ14ζ2+ζ8ζ+ζ4ζ7+ζ13ζ11+ζ14ζ2+ζ8−ζ11−ζ14−ζ11−ζ14−ζ2−ζ8−ζ2−ζ8ζ+ζ4ζ7+ζ13−ζ−ζ4−ζ−ζ4−ζ7−ζ13−ζ7−ζ1300000000
χ2322-222−1−i3−1+i3−1−i3−1+i3-2−1+52−1−521+i31−i3−1+52−1−521−521−521+521+52ζ7+ζ13ζ+ζ4ζ2+ζ8ζ11+ζ14ζ7+ζ13ζ+ζ4−ζ7−ζ13−ζ7−ζ13−ζ−ζ4−ζ−ζ4ζ2+ζ8ζ11+ζ14−ζ2−ζ8−ζ2−ζ8−ζ11−ζ14−ζ11−ζ1400000000
χ2422-222−1−i3−1+i3−1−i3−1+i3-2−1−52−1+521+i31−i3−1−52−1+521+521+521−521−52ζ+ζ4ζ7+ζ13ζ11+ζ14ζ2+ζ8ζ+ζ4ζ7+ζ13−ζ−ζ4−ζ−ζ4−ζ7−ζ13−ζ7−ζ13ζ11+ζ14ζ2+ζ8−ζ11−ζ14−ζ11−ζ14−ζ2−ζ8−ζ2−ζ800000000
χ252-202-222-2-202200-2-200002222-2-20000-2-2000000000000
χ262-202-222-2-20−1+52−1−52001−521+52ζ2+ζ7−ζ8−ζ13−ζ2−ζ7+ζ8+ζ13−ζ+ζ4−ζ11+ζ14ζ−ζ4+ζ11−ζ14−1+52−1−52−1+52−1−521−521+52ζ2+ζ7−ζ8−ζ13−ζ2−ζ7+ζ8+ζ13−ζ+ζ4−ζ11+ζ14ζ−ζ4+ζ11−ζ141−521+52ζ2+ζ7−ζ8−ζ13−ζ2−ζ7+ζ8+ζ13−ζ+ζ4−ζ11+ζ14ζ−ζ4+ζ11−ζ1400000000
χ272-202-222-2-20−1+52−1−52001−521+52−ζ2−ζ7+ζ8+ζ13ζ2+ζ7−ζ8−ζ13ζ−ζ4+ζ11−ζ14−ζ+ζ4−ζ11+ζ14−1+52−1−52−1+52−1−521−521+52−ζ2−ζ7+ζ8+ζ13ζ2+ζ7−ζ8−ζ13ζ−ζ4+ζ11−ζ14−ζ+ζ4−ζ11+ζ141−521+52−ζ2−ζ7+ζ8+ζ13ζ2+ζ7−ζ8−ζ13ζ−ζ4+ζ11−ζ14−ζ+ζ4−ζ11+ζ1400000000
χ282-202-222-2-20−1−52−1+52001+521−52−ζ+ζ4−ζ11+ζ14ζ−ζ4+ζ11−ζ14−ζ2−ζ7+ζ8+ζ13ζ2+ζ7−ζ8−ζ13−1−52−1+52−1−52−1+521+521−52−ζ+ζ4−ζ11+ζ14ζ−ζ4+ζ11−ζ14−ζ2−ζ7+ζ8+ζ13ζ2+ζ7−ζ8−ζ131+521−52−ζ+ζ4−ζ11+ζ14ζ−ζ4+ζ11−ζ14−ζ2−ζ7+ζ8+ζ13ζ2+ζ7−ζ8−ζ1300000000
χ292-202-222-2-20−1−52−1+52001+521−52ζ−ζ4+ζ11−ζ14−ζ+ζ4−ζ11+ζ14ζ2+ζ7−ζ8−ζ13−ζ2−ζ7+ζ8+ζ13−1−52−1+52−1−52−1+521+521−52ζ−ζ4+ζ11−ζ14−ζ+ζ4−ζ11+ζ14ζ2+ζ7−ζ8−ζ13−ζ2−ζ7+ζ8+ζ131+521−52ζ−ζ4+ζ11−ζ14−ζ+ζ4−ζ11+ζ14ζ2+ζ7−ζ8−ζ13−ζ2−ζ7+ζ8+ζ1300000000
χ302-202-2−1+i3−1−i31−i31+i302200-2-20000−1+i3−1+i3−1−i3−1−i31−i31−i300001+i31+i3000000000000
χ312-202-2−1+i3−1−i31−i31+i30−1+52−1−52001−521+52ζ2+ζ7−ζ8−ζ13−ζ2−ζ7+ζ8+ζ13−ζ+ζ4−ζ11+ζ14ζ−ζ4+ζ11−ζ14ζ2+ζ8ζ11+ζ14ζ7+ζ13ζ+ζ4−ζ2−ζ8−ζ11−ζ14−ζ2+ζ8ζ2−ζ8ζ11−ζ14−ζ11+ζ14−ζ7−ζ13−ζ−ζ4−ζ7+ζ13ζ7−ζ13ζ−ζ4−ζ+ζ400000000
χ322-202-2−1+i3−1−i31−i31+i30−1+52−1−52001−521+52−ζ2−ζ7+ζ8+ζ13ζ2+ζ7−ζ8−ζ13ζ−ζ4+ζ11−ζ14−ζ+ζ4−ζ11+ζ14ζ2+ζ8ζ11+ζ14ζ7+ζ13ζ+ζ4−ζ2−ζ8−ζ11−ζ14ζ2−ζ8−ζ2+ζ8−ζ11+ζ14ζ11−ζ14−ζ7−ζ13−ζ−ζ4ζ7−ζ13−ζ7+ζ13−ζ+ζ4ζ−ζ400000000
χ332-202-2−1+i3−1−i31−i31+i30−1−52−1+52001+521−52−ζ+ζ4−ζ11+ζ14ζ−ζ4+ζ11−ζ14−ζ2−ζ7+ζ8+ζ13ζ2+ζ7−ζ8−ζ13ζ11+ζ14ζ2+ζ8ζ+ζ4ζ7+ζ13−ζ11−ζ14−ζ2−ζ8ζ11−ζ14−ζ11+ζ14ζ2−ζ8−ζ2+ζ8−ζ−ζ4−ζ7−ζ13ζ−ζ4−ζ+ζ4ζ7−ζ13−ζ7+ζ1300000000
χ342-202-2−1+i3−1−i31−i31+i30−1−52−1+52001+521−52ζ−ζ4+ζ11−ζ14−ζ+ζ4−ζ11+ζ14ζ2+ζ7−ζ8−ζ13−ζ2−ζ7+ζ8+ζ13ζ11+ζ14ζ2+ζ8ζ+ζ4ζ7+ζ13−ζ11−ζ14−ζ2−ζ8−ζ11+ζ14ζ11−ζ14−ζ2+ζ8ζ2−ζ8−ζ−ζ4−ζ7−ζ13−ζ+ζ4ζ−ζ4−ζ7+ζ13ζ7−ζ1300000000
χ352-202-2−1−i3−1+i31+i31−i302200-2-20000−1−i3−1−i3−1+i3−1+i31+i31+i300001−i31−i3000000000000
χ362-202-2−1−i3−1+i31+i31−i30−1+52−1−52001−521+52ζ2+ζ7−ζ8−ζ13−ζ2−ζ7+ζ8+ζ13−ζ+ζ4−ζ11+ζ14ζ−ζ4+ζ11−ζ14ζ7+ζ13ζ+ζ4ζ2+ζ8ζ11+ζ14−ζ7−ζ13−ζ−ζ4−ζ7+ζ13ζ7−ζ13ζ−ζ4−ζ+ζ4−ζ2−ζ8−ζ11−ζ14−ζ2+ζ8ζ2−ζ8ζ11−ζ14−ζ11+ζ1400000000
χ372-202-2−1−i3−1+i31+i31−i30−1+52−1−52001−521+52−ζ2−ζ7+ζ8+ζ13ζ2+ζ7−ζ8−ζ13ζ−ζ4+ζ11−ζ14−ζ+ζ4−ζ11+ζ14ζ7+ζ13ζ+ζ4ζ2+ζ8ζ11+ζ14−ζ7−ζ13−ζ−ζ4ζ7−ζ13−ζ7+ζ13−ζ+ζ4ζ−ζ4−ζ2−ζ8−ζ11−ζ14ζ2−ζ8−ζ2+ζ8−ζ11+ζ14ζ11−ζ1400000000
χ382-202-2−1−i3−1+i31+i31−i30−1−52−1+52001+521−52−ζ+ζ4−ζ11+ζ14ζ−ζ4+ζ11−ζ14−ζ2−ζ7+ζ8+ζ13ζ2+ζ7−ζ8−ζ13ζ+ζ4ζ7+ζ13ζ11+ζ14ζ2+ζ8−ζ−ζ4−ζ7−ζ13ζ−ζ4−ζ+ζ4ζ7−ζ13−ζ7+ζ13−ζ11−ζ14−ζ2−ζ8ζ11−ζ14−ζ11+ζ14ζ2−ζ8−ζ2+ζ800000000
χ392-202-2−1−i3−1+i31+i31−i30−1−52−1+52001+521−52ζ−ζ4+ζ11−ζ14−ζ+ζ4−ζ11+ζ14ζ2+ζ7−ζ8−ζ13−ζ2−ζ7+ζ8+ζ13ζ+ζ4ζ7+ζ13ζ11+ζ14ζ2+ζ8−ζ−ζ4−ζ7−ζ13−ζ+ζ4ζ−ζ4−ζ7+ζ13ζ7−ζ13−ζ11−ζ14−ζ2−ζ8−ζ11+ζ14ζ11−ζ14−ζ2+ζ8ζ2−ζ800000000
χ40151515-1-10000-10000000000000000000000000033-1-10000
χ41151515-1-10000-100000000000000000000000000-3-3110000
χ421515-15-1-100001000000000000000000000000003-3-110000
χ431515-15-1-10000100000000000000000000000000-331-10000
χ4430-300-22000000000000000000000000000000000000000

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