Finite Group Databasebeta

← Group #72210652

Character table — Group #72210652

Order 6000.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22
size1242525256060150240240300300300300300300500500500500600750
order1524455255101020202020361212104
χ11111111111111111111111
χ2111-1-111-11111-1-1-1-111-1-1-11
χ322-22i−2i−1+52−1−520−1+52−1−521−521+52ζ3+ζ7−ζ3−ζ7−ζ11−ζ19ζ11+ζ19-11i−i00
χ422-22i−2i−1−52−1+520−1−52−1+521+521−52ζ11+ζ19−ζ11−ζ19−ζ3−ζ7ζ3+ζ7-11i−i00
χ522-2−2i2i−1+52−1−520−1+52−1−521−521+52−ζ3−ζ7ζ3+ζ7ζ11+ζ19−ζ11−ζ19-11−ii00
χ622-2−2i2i−1−52−1+520−1−52−1+521+521−52−ζ11−ζ19ζ11+ζ19ζ3+ζ7−ζ3−ζ7-11−ii00
χ7333331−521+52-11−521+521−521+521+521+521−521−520000-1-1
χ8333331+521−52-11+521−521+521−521−521−521+521+520000-1-1
χ9333-3-31−521+5211−521+521−521+52−1−52−1−52−1+52−1+5200001-1
χ10333-3-31+521−5211+521−521+521−52−1+52−1+52−1−52−1−5200001-1
χ1144444-1-10-1-1-1-1-1-1-1-1111100
χ12444-4-4-1-10-1-1-1-1111111-1-100
χ1344-44i−4i-1-10-1-111i−i−ii1-1−ii00
χ1444-4−4i4i-1-10-1-111−iii−i1-1i−i00
χ155555500100000000-1-1-1-111
χ16555-5-500-100000000-1-111-11
χ1766-66i−6i11011-1-1−iii−i000000
χ1866-6−6i6i11011-1-1i−i−ii000000
χ1924-1000444-1-10000000000-10
χ2024-100044-4-1-1000000000010
χ2148-2000−2+25−2−2501−521+52000000000000
χ2248-2000−2−25−2+2501+521−52000000000000

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