Finite Group Databasebeta

← Group #72209605

Character table — Group #72209605

Order 3840.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28
size116610101515120120120120120120120120192192192192192192192192320320320320
order124444228888888855101020202020361212
χ11111111111111111111111111111
χ222-2-2-2-22200000000−1+52−1−52−1+52−1−521−521−521+521+52-1-111
χ322-2-2-2-22200000000−1−52−1+52−1−52−1+521+521+521−521−52-1-111
χ433333333-1-1-1-1-1-1-1-11−521+521−521+521−521−521+521+520000
χ533333333-1-1-1-1-1-1-1-11+521−521+521−521+521+521−521−520000
χ64444444400000000-1-1-1-1-1-1-1-11111
χ744-4-4-4-44400000000-1-1-1-1111111-1-1
χ8555555551111111100000000-1-1-1-1
χ966-6-6-6-666000000001111-1-1-1-10000
χ106-64i−4i002-2i2i2−i2−i222−2−211-1-1i−ii−i0000
χ116-64i−4i002-2−i2−i2i2i2−2−22211-1-1i−ii−i0000
χ126-6−4i4i002-2i2i2−i2−i2−2−22211-1-1−ii−ii0000
χ136-6−4i4i002-2−i2−i2i2i222−2−211-1-1−ii−ii0000
χ1410-10004i−4i-222−2−22i2−i2i2−i2000000001-1i−i
χ1510-10004i−4i-22−222−2−i2i2−i2i2000000001-1i−i
χ1610-1000−4i4i-222−2−22−i2i2−i2i2000000001-1−ii
χ1710-1000−4i4i-22−222−2i2−i2i2−i2000000001-1−ii
χ1812-128i−8i004-400000000−1+52−1−521−521+52−ζ22−ζ38ζ22+ζ38−ζ6−ζ14ζ6+ζ140000
χ1912-128i−8i004-400000000−1−52−1+521+521−52−ζ6−ζ14ζ6+ζ14−ζ22−ζ38ζ22+ζ380000
χ2012-12−8i8i004-400000000−1+52−1−521−521+52ζ22+ζ38−ζ22−ζ38ζ6+ζ14−ζ6−ζ140000
χ2112-12−8i8i004-400000000−1−52−1+521+521−52ζ6+ζ14−ζ6−ζ14ζ22+ζ38−ζ22−ζ380000
χ221515-5-533-1-11111−1+2i−1−2i−1−2i−1+2i000000000000
χ231515-5-533-1-11111−1−2i−1+2i−1+2i−1−2i000000000000
χ241515-5-533-1-1−1+2i−1−2i−1+2i−1−2i1111000000000000
χ251515-5-533-1-1−1−2i−1+2i−1−2i−1+2i1111000000000000
χ2620-20008i−8i-440000000000000000-11−ii
χ2720-2000−8i8i-440000000000000000-11i−i
χ2830301010-6-6-2-200000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.