Finite Group Databasebeta

← Group #6788

Character table — Group #6788

Order 240.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36
size11222226622444441212224444412125510101010103030
order1223666245101015303030102051010153030301020222666624
χ1111111111111111111111111111111111111
χ21111111-1-11111111-1-11111111-1-11111111-1-1
χ311-111-1-11-111-111-1-11-111-111-1-11-111-111-1-11-1
χ411-111-1-1-1111-111-1-1-1111-111-1-1-1111-111-1-1-11
χ5222-1-1-1-100222-1-1-1-100222-1-1-1-100222-1-1-1-100
χ622-2-1-1110022-2-1-1110022-2-1-1110022-2-1-11100
χ72-202-200002-202-200002-202-200002-202-20000
χ82-20-11i3−i3002-20-11i3−i3002-20-11i3−i3002-20-11i3−i300
χ92-20-11−i3i3002-20-11−i3i3002-20-11−i3i3002-20-11−i3i300
χ10111111111111111111111111111-1-1-1-1-1-1-1-1-1
χ111111111-1-11111111-1-11111111-1-1-1-1-1-1-1-1-111
χ1211-111-1-11-111-111-1-11-111-111-1-11-1-1-11-1-111-11
χ1311-111-1-1-1111-111-1-1-1111-111-1-1-11-1-11-1-1111-1
χ14222-1-1-1-100222-1-1-1-100222-1-1-1-100-2-2-2111100
χ1522-2-1-1110022-2-1-1110022-2-1-11100-2-2211-1-100
χ162-202-200002-202-200002-202-20000-220-220000
χ172-20-11i3−i3002-20-11i3−i3002-20-11i3−i300-2201-1−i3i300
χ182-20-11−i3i3002-20-11−i3i3002-20-11−i3i300-2201-1i3−i300
χ19222222222−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52000000000
χ202222222-2-2−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+52000000000
χ2122-222-2-22-2−1+52−1+521−52−1+52−1+521−521−52−1+521−52−1−52−1−521+52−1−52−1−521+521+52−1−521+52000000000
χ2222-222-2-2-22−1+52−1+521−52−1+52−1+521−521−521−52−1+52−1−52−1−521+52−1−52−1−521+521+521+52−1−52000000000
χ23444-2-2-2-200−1+5−1+5−1+51−521−521−521−5200−1−5−1−5−1−51+521+521+521+5200000000000
χ2444-4-2-22200−1+5−1+51−51−521−52−1+52−1+5200−1−5−1−51+51+521+52−1−52−1−5200000000000
χ254-404-40000−1+51−50−1+51−50000−1−51+50−1−51+50000000000000
χ264-40-222i3−2i300−1+51−501−52−1+52ζ2−ζ7+ζ8−ζ13−ζ2+ζ7−ζ8+ζ1300−1−51+501+52−1−52−ζ−ζ4+ζ11+ζ14ζ+ζ4−ζ11−ζ1400000000000
χ274-40-22−2i32i300−1+51−501−52−1+52−ζ2+ζ7−ζ8+ζ13ζ2−ζ7+ζ8−ζ1300−1−51+501+52−1−52ζ+ζ4−ζ11−ζ14−ζ−ζ4+ζ11+ζ1400000000000
χ28222222222−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52000000000
χ292222222-2-2−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−52000000000
χ3022-222-2-22-2−1−52−1−521+52−1−52−1−521+521+52−1−521+52−1+52−1+521−52−1+52−1+521−521−52−1+521−52000000000
χ3122-222-2-2-22−1−52−1−521+52−1−52−1−521+521+521+52−1−52−1+52−1+521−52−1+52−1+521−521−521−52−1+52000000000
χ32444-2-2-2-200−1−5−1−5−1−51+521+521+521+5200−1+5−1+5−1+51−521−521−521−5200000000000
χ3344-4-2-22200−1−5−1−51+51+521+52−1−52−1−5200−1+5−1+51−51−521−52−1+52−1+5200000000000
χ344-404-40000−1−51+50−1−51+50000−1+51−50−1+51−50000000000000
χ354-40-222i3−2i300−1−51+501+52−1−52−ζ−ζ4+ζ11+ζ14ζ+ζ4−ζ11−ζ1400−1+51−501−52−1+52ζ2−ζ7+ζ8−ζ13−ζ2+ζ7−ζ8+ζ1300000000000
χ364-40-22−2i32i300−1−51+501+52−1−52ζ+ζ4−ζ11−ζ14−ζ−ζ4+ζ11+ζ1400−1+51−501−52−1+52−ζ2+ζ7−ζ8+ζ13ζ2−ζ7+ζ8−ζ1300000000000

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