Finite Group Databasebeta

← Group #65029

Character table — Group #65029

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size11222222244444444444455888888888888101010202020202020
order1222255101024444410101010101044101020202020202020202020444244444
χ111111111111111111111111111111111111111111111
χ2111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1
χ311111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111-1-1-1-1
χ411111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111-1-111-1-111111111-1-1-1-11111-1-1-1-1111-1-111-1-1
χ6111111111-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-111
χ7111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111-1-1-1-111
χ8111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-1
χ9111-1-111111-1i−ii−i11-1-1-1-11111-1-1ii−i−iii−i−i1-1-1-11i−ii−i
χ10111-1-111111-1i−ii−i11-1-1-1-1-1-111-1-1ii−i−iii−i−i-1111-1−ii−ii
χ11111-1-111111-1−ii−ii11-1-1-1-11111-1-1−i−iii−i−iii1-1-1-11−ii−ii
χ12111-1-111111-1−ii−ii11-1-1-1-1-1-111-1-1−i−iii−i−iii-1111-1i−ii−i
χ13111-1-11111-11i−i−ii11-1-1-1-111-1-111ii−i−i−i−iii1-1-11-1i−i−ii
χ14111-1-11111-11i−i−ii11-1-1-1-1-1-1-1-111ii−i−i−i−iii-111-11−iii−i
χ15111-1-11111-11−iii−i11-1-1-1-111-1-111−i−iiiii−i−i1-1-11-1−iii−i
χ16111-1-11111-11−iii−i11-1-1-1-1-1-1-1-111−i−iiiii−i−i-111-11i−i−ii
χ1722222−1+52−1−52−1+52−1−52222222−1+52−1−52−1+52−1+52−1−52−1−5200−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52000000000
χ1822222−1+52−1−52−1+52−1−5222-2-2-2-2−1+52−1−52−1+52−1+52−1−52−1−5200−1+52−1−52−1+52−1−521−521+521−521+521−521+521−521+52000000000
χ1922222−1+52−1−52−1+52−1−52-2-222-2-2−1+52−1−52−1+52−1+52−1−52−1−52001−521+521−521+52−1+52−1−52−1+52−1−521−521+521−521+52000000000
χ2022222−1+52−1−52−1+52−1−52-2-2-2-222−1+52−1−52−1+52−1+52−1−52−1−52001−521+521−521+521−521+521−521+52−1+52−1−52−1+52−1−52000000000
χ2122222−1−52−1+52−1−52−1+52222222−1−52−1+52−1−52−1−52−1+52−1+5200−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52000000000
χ2222222−1−52−1+52−1−52−1+5222-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+5200−1−52−1+52−1−52−1+521+521−521+521−521+521−521+521−52000000000
χ2322222−1−52−1+52−1−52−1+52-2-222-2-2−1−52−1+52−1−52−1−52−1+52−1+52001+521−521+521−52−1−52−1+52−1−52−1+521+521−521+521−52000000000
χ2422222−1−52−1+52−1−52−1+52-2-2-2-222−1−52−1+52−1−52−1−52−1+52−1+52001+521−521+521−521+521−521+521−52−1−52−1+52−1−52−1+52000000000
χ25222-2-2−1+52−1−52−1+52−1−522-22i−2i2i−2i−1+52−1−521−521−521+521+5200−1+52−1−521−521+52−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7000000000
χ26222-2-2−1+52−1−52−1+52−1−522-2−2i2i−2i2i−1+52−1−521−521−521+521+5200−1+52−1−521−521+52ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7000000000
χ27222-2-2−1+52−1−52−1+52−1−52-222i−2i−2i2i−1+52−1−521−521−521+521+52001−521+52−1+52−1−52−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7000000000
χ28222-2-2−1+52−1−52−1+52−1−52-22−2i2i2i−2i−1+52−1−521−521−521+521+52001−521+52−1+52−1−52ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7000000000
χ29222-2-2−1−52−1+52−1−52−1+522-22i−2i2i−2i−1−52−1+521+521+521−521−5200−1−52−1+521+521−52−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19000000000
χ30222-2-2−1−52−1+52−1−52−1+522-2−2i2i−2i2i−1−52−1+521+521+521−521−5200−1−52−1+521+521−52ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19000000000
χ31222-2-2−1−52−1+52−1−52−1+52-222i−2i−2i2i−1−52−1+521+521+521−521−52001+521−52−1−52−1+52−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19000000000
χ32222-2-2−1−52−1+52−1−52−1+52-22−2i2i2i−2i−1−52−1+521+521+521−521−52001+521−52−1−52−1+52ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19000000000
χ3322-22-22222000000-2-22-22-222000000000000-22-2000000
χ3422-22-22222000000-2-22-22-2-2-20000000000002-22000000
χ3522-2-222222000000-2-2-22-2222000000000000-2-22000000
χ3622-2-222222000000-2-2-22-22-2-200000000000022-2000000
χ3744-44-4−1+5−1−5−1+5−1−50000001−51+5−1+51−5−1−51+500000000000000000000000
χ3844-44-4−1−5−1+5−1−5−1+50000001+51−5−1−51+5−1+51−500000000000000000000000
χ3944-4-44−1+5−1−5−1+5−1−50000001−51+51−5−1+51+5−1−500000000000000000000000
χ4044-4-44−1−5−1+5−1−5−1+50000001+51−51+5−1−51−5−1+500000000000000000000000
χ414-400044-4-40000000000004i−4i000000000000000000000
χ424-400044-4-4000000000000−4i4i000000000000000000000
χ438-8000−2+25−2−252−252+2500000000000000000000000000000000000
χ448-8000−2−25−2+252+252−2500000000000000000000000000000000000

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