Finite Group Databasebeta

← Group #64693

Character table — Group #64693

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35
size1122222444444444888888888888882020404040
order1225510102241010101010104410102020202020202020202044444
χ111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1
χ31111111111111111-1-11111-1-1-1-1-1-1-1-1111-1-1
χ41111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-111
χ51111111-1-1111-1-1-1-1i−i-1-111iiii−i−i−i−i11-1i−i
χ61111111-1-1111-1-1-1-1i−i-1-111iiii−i−i−i−i-1-11−ii
χ71111111-1-1111-1-1-1-1−ii-1-111−i−i−i−iiiii11-1−ii
χ81111111-1-1111-1-1-1-1−ii-1-111−i−i−i−iiiii-1-11i−i
χ922222222-2-222222200-2-2-2-20000000000000
χ102222222-22-222-2-2-2-20022-2-20000000000000
χ11222−1+52−1−52−1+52−1−52222−1+52−1−52−1+52−1+52−1−52−1−5222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000
χ12222−1+52−1−52−1+52−1−52222−1+52−1−52−1+52−1+52−1−52−1−52-2-2−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+5200000
χ13222−1+52−1−52−1+52−1−522-2-2−1+52−1−52−1+52−1+52−1−52−1−52001−521+521−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ1800000
χ14222−1+52−1−52−1+52−1−522-2-2−1+52−1−52−1+52−1+52−1−52−1−52001−521+521−521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ1800000
χ15222−1+52−1−52−1+52−1−52-22-2−1+52−1−521−521−521+521+5200−1+52−1−521−521+52−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ700000
χ16222−1+52−1−52−1+52−1−52-22-2−1+52−1−521−521−521+521+5200−1+52−1−521−521+52ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ700000
χ17222−1+52−1−52−1+52−1−52-2-22−1+52−1−521−521−521+521+522i−2i1−521+52−1+52−1−52−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ700000
χ18222−1+52−1−52−1+52−1−52-2-22−1+52−1−521−521−521+521+52−2i2i1−521+52−1+52−1−52ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ700000
χ19222−1−52−1+52−1−52−1+52222−1−52−1+52−1−52−1−52−1+52−1+5222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000
χ20222−1−52−1+52−1−52−1+52222−1−52−1+52−1−52−1−52−1+52−1+52-2-2−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−5200000
χ21222−1−52−1+52−1−52−1+522-2-2−1−52−1+52−1−52−1−52−1+52−1+52001+521−521+521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ1400000
χ22222−1−52−1+52−1−52−1+522-2-2−1−52−1+52−1−52−1−52−1+52−1+52001+521−521+521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ1400000
χ23222−1−52−1+52−1−52−1+52-22-2−1−52−1+521+521+521−521−5200−1−52−1+521+521−52ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ1900000
χ24222−1−52−1+52−1−52−1+52-22-2−1−52−1+521+521+521−521−5200−1−52−1+521+521−52−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ1900000
χ25222−1−52−1+52−1−52−1+52-2-22−1−52−1+521+521+521−521−522i−2i1+521−52−1−52−1+52−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ1900000
χ26222−1−52−1+52−1−52−1+52-2-22−1−52−1+521+521+521−521−52−2i2i1+521−52−1−52−1+52ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ1900000
χ2744-44444000-4-400000000000000000000000
χ2844-4−1+5−1−5−1+5−1−50001−51+52ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ180000000000000000000
χ2944-4−1+5−1−5−1+5−1−50001−51+5−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ180000000000000000000
χ3044-4−1−5−1+5−1−5−1+50001+51−5−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ140000000000000000000
χ3144-4−1−5−1+5−1−5−1+50001+51−52ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ140000000000000000000
χ324-4044-4-4000000000000000000000002i−2i000
χ334-4044-4-400000000000000000000000−2i2i000
χ348-80−2+25−2−252−252+250000000000000000000000000000
χ358-80−2−25−2+252+252−250000000000000000000000000000

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