Finite Group Databasebeta

← Group #65371

Character table — Group #65371

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size11112222222222444444444444448888888888202020204040
order1222445510101010101044202020202020202020202020442020202020202020888844
χ111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ511111111111111-1-1-1-1-1-1-1-1-1-111111-11111-1-1-1-111-1-11-1
χ611111111111111-1-1-1-1-1-1-1-1-1-111111-11111-1-1-1-1-1-111-11
χ711111111111111-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-1111111-1-1-11
χ811111111111111-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-11111-1-1111-1
χ9222222−1+52−1−52−1+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+52−1−52−1−5222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000
χ10222222−1+52−1−52−1+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+52−1−52−1−52-2-21−521−521+521+521−521−521+521+52000000
χ11222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-21−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−522-2−1+52−1+52−1−52−1−521−521−521+521+52000000
χ12222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-21−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−52-221−521−521+521+52−1+52−1+52−1−52−1−52000000
χ13222222−1−52−1+52−1−52−1−52−1+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+5222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000
χ14222222−1−52−1+52−1−52−1−52−1+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+52-2-21+521+521−521−521+521+521−521−52000000
χ15222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-21+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+522-2−1−52−1−52−1+52−1+521+521+521−521−52000000
χ16222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-21+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+52-221+521+521−521−52−1−52−1−52−1+52−1+52000000
χ172222-2-2222222222-222-2-222-2-2-2-2-2-20000000000000000
χ182222-2-222222222-22-2-222-2-222-2-2-2-20000000000000000
χ192222-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522-2−1+52−1+521−521−52−1−52−1−521+521+521−521−521+521+5200ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18000000
χ202222-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522-2−1+52−1+521−521−52−1−52−1−521+521+521−521−521+521+5200−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18000000
χ212222-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-221−521−52−1+52−1+521+521+52−1−52−1−521−521−521+521+5200ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18000000
χ222222-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-221−521−52−1+52−1+521+521+52−1−52−1−521−521−521+521+5200−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18000000
χ232222-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522-2−1−52−1−521+521+52−1+52−1+521−521−521+521+521−521−5200−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14000000
χ242222-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522-2−1−52−1−521+521+52−1+52−1+521−521−521+521+521−521−5200ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14000000
χ252222-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-221+521+52−1−52−1−521−521−52−1+52−1+521+521+521−521−5200−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14000000
χ262222-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-221+521+52−1−52−1−521−521−52−1+52−1+521+521+521−521−5200ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14000000
χ2722-2-22-222-2-2-2-22200000000002-22-20000000000002i−2i00
χ2822-2-22-222-2-2-2-22200000000002-22-2000000000000−2i2i00
χ2922-2-2-2222-2-2-2-2220000000000-22-2200000000002i−2i0000
χ3022-2-2-2222-2-2-2-2220000000000-22-220000000000−2i2i0000
χ3144-4-44-4−1+5−1−51−51−51+51+5−1+5−1−50000000000−1+51−5−1−51+50000000000000000
χ3244-4-44-4−1−5−1+51+51+51−51−5−1−5−1+50000000000−1−51+5−1+51−50000000000000000
χ3344-4-4-44−1+5−1−51−51−51+51+5−1+5−1−500000000001−5−1+51+5−1−50000000000000000
χ3444-4-4-44−1−5−1+51+51+51−51−5−1−5−1+500000000001+5−1−51−5−1+50000000000000000
χ354-44-400444-44-4-4-4000000000000000000000000000000
χ364-44-400−1+5−1−5−1+51−5−1−51+51−51+5002ζ6−2ζ14−2ζ6+2ζ1400−2ζ2+2ζ182ζ2−2ζ180000000000000000000000
χ374-44-400−1+5−1−5−1+51−5−1−51+51−51+500−2ζ6+2ζ142ζ6−2ζ14002ζ2−2ζ18−2ζ2+2ζ180000000000000000000000
χ384-44-400−1−5−1+5−1−51+5−1+51−51+51−500−2ζ2+2ζ182ζ2−2ζ1800−2ζ6+2ζ142ζ6−2ζ140000000000000000000000
χ394-44-400−1−5−1+5−1−51+5−1+51−51+51−5002ζ2−2ζ18−2ζ2+2ζ18002ζ6−2ζ14−2ζ6+2ζ140000000000000000000000
χ404-4-440044-44-44-4-4000000000000000000000000000000
χ414-4-4400−1+5−1−51−5−1+51+5−1−51−51+500002ζ6−2ζ14−2ζ6+2ζ1400−2ζ2+2ζ182ζ2−2ζ1800000000000000000000
χ424-4-4400−1+5−1−51−5−1+51+5−1−51−51+50000−2ζ6+2ζ142ζ6−2ζ14002ζ2−2ζ18−2ζ2+2ζ1800000000000000000000
χ434-4-4400−1−5−1+51+5−1−51−5−1+51+51−50000−2ζ2+2ζ182ζ2−2ζ1800−2ζ6+2ζ142ζ6−2ζ1400000000000000000000
χ444-4-4400−1−5−1+51+5−1−51−5−1+51+51−500002ζ2−2ζ18−2ζ2+2ζ18002ζ6−2ζ14−2ζ6+2ζ1400000000000000000000

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