Finite Group Databasebeta

← Group #682

Character table — Group #682

Order 80.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32
size11222255112222551122225511222255
order1255101044442020202044221010101044442020202044
χ111111111111111111111111111111111
χ2111111-1-1111111-1-1111111-1-1111111-1-1
χ31-111-1-1i−i1-111-1-1i−i1-111-1-1i−i1-111-1-1i−i
χ41-111-1-1−ii1-111-1-1−ii1-111-1-1−ii1-111-1-1−ii
χ522−1+52−1−52−1+52−1−520022−1+52−1−52−1+52−1−520022−1+52−1−52−1+52−1−520022−1+52−1−52−1+52−1−5200
χ622−1−52−1+52−1−52−1+520022−1−52−1+52−1−52−1+520022−1−52−1+52−1−52−1+520022−1−52−1+52−1−52−1+5200
χ72-2−1+52−1−521−521+52002-2−1+52−1−521−521+52002-2−1+52−1−521−521+52002-2−1+52−1−521−521+5200
χ82-2−1−52−1+521+521−52002-2−1−52−1+521+521−52002-2−1−52−1+521+521−52002-2−1−52−1+521+521−5200
χ911111111iiiiiiii-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i
χ10111111-1-1iiiiii−i−i-1-1-1-1-1-111−i−i−i−i−i−iii
χ111-111-1-1i−ii−iii−i−i-11-11-1-111−ii−ii−i−iii1-1
χ121-111-1-1−iii−iii−i−i1-1-11-1-111i−i−ii−i−iii-11
χ1322−1+52−1−52−1+52−1−52002i2i−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ700-2-21−521+521−521+5200−2i−2iζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ700
χ1422−1−52−1+52−1−52−1+52002i2i−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ1900-2-21+521−521+521−5200−2i−2iζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ1900
χ152-2−1+52−1−521−521+52002i−2i−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ700-221−521+52−1+52−1−5200−2i2iζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ700
χ162-2−1−52−1+521+521−52002i−2i−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ1900-221+521−52−1−52−1+5200−2i2iζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ1900
χ1711111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ18111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ191-111-1-1i−i-11-1-111−ii1-111-1-1i−i-11-1-111−ii
χ201-111-1-1−ii-11-1-111i−i1-111-1-1−ii-11-1-111i−i
χ2122−1+52−1−52−1+52−1−5200-2-21−521+521−521+520022−1+52−1−52−1+52−1−5200-2-21−521+521−521+5200
χ2222−1−52−1+52−1−52−1+5200-2-21+521−521+521−520022−1−52−1+52−1−52−1+5200-2-21+521−521+521−5200
χ232-2−1+52−1−521−521+5200-221−521+52−1+52−1−52002-2−1+52−1−521−521+5200-221−521+52−1+52−1−5200
χ242-2−1−52−1+521+521−5200-221+521−52−1−52−1+52002-2−1−52−1+521+521−5200-221+521−52−1−52−1+5200
χ2511111111−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-1iiiiiiii
χ26111111-1-1−i−i−i−i−i−iii-1-1-1-1-1-111iiiiii−i−i
χ271-111-1-1i−i−ii−i−iii1-1-11-1-111−iii−iii−i−i-11
χ281-111-1-1−ii−ii−i−iii-11-11-1-111i−ii−iii−i−i1-1
χ2922−1+52−1−52−1+52−1−5200−2i−2iζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ700-2-21−521+521−521+52002i2i−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ700
χ3022−1−52−1+52−1−52−1+5200−2i−2iζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ1900-2-21+521−521+521−52002i2i−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ1900
χ312-2−1+52−1−521−521+5200−2i2iζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ700-221−521+52−1+52−1−52002i−2i−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ700
χ322-2−1−52−1+521+521−5200−2i2iζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ1900-221+521−52−1−52−1+52002i−2i−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ1900

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.