Finite Group Databasebeta

← Group #65342

Character table — Group #65342

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size11222222222224444444444444444888888888202020204040
order1222255101010101010244410101010202020202020202041010202020202020224444
χ111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1
χ3111111111111111-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1
χ4111111111111111-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111
χ51111111111111-1-111111111111111-1-1-1-1-1-1-1-1-11-11-11-1
χ61111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-11-11-11
χ71111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-11111-1-11-11-1-11
χ81111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-11111-1-1-11-111-1
χ922222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52000000
χ1022222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222-2-2−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+52-2−1+52−1−521−521−521+521+52−1+52−1−52000000
χ1122222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-222−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-21−521+521−521−521+521+521−521+52000000
χ1222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-2−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+5221−521+52−1+52−1+52−1−52−1−521−521+52000000
χ1322222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+522−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52000000
χ1422222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222-2-2−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−52-2−1−52−1+521+521+521−521−52−1−52−1+52000000
χ1522222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-222−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-21+521−521+521+521−521−521+521−52000000
χ1622222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-2-2-2−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−5221+521−52−1−52−1−52−1+52−1+521+521−52000000
χ17222-2-2222222222-200-2-2-2-2000000000220000-2-2000000
χ18222-2-222222222-2200-2-2-2-2000000000-2-2000022000000
χ19222-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522-2001−521−521+521+52ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ180−1+52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−521+52000000
χ20222-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522-2001−521−521+521+52−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ180−1+52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ181−521+52000000
χ21222-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-22001−521−521+521+52ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ1801−521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−1+52−1−52000000
χ22222-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-22001−521−521+521+52−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ1801−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−1+52−1−52000000
χ23222-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522-2001+521+521−521−52−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ140−1−52−1+52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ141+521−52000000
χ24222-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522-2001+521+521−521−52ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ140−1−52−1+52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ141+521−52000000
χ25222-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-22001+521+521−521−52−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ1401+521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−1−52−1+52000000
χ26222-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-22001+521+521−521−52ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ1401+521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−1−52−1+52000000
χ2722-22-222-2-2-2-22200002-22-200000000000000000020-200
χ2822-22-222-2-2-2-22200002-22-2000000000000000000-20200
χ2922-2-2222-2-2-2-2220000-22-220000000000000000020-2000
χ3022-2-2222-2-2-2-2220000-22-2200000000000000000-202000
χ3144-44-4−1+5−1−51−51−51+51+5−1+5−1−50000−1+51−5−1−51+500000000000000000000000
χ3244-44-4−1−5−1+51+51+51−51−5−1−5−1+50000−1−51+5−1+51−500000000000000000000000
χ3344-4-44−1+5−1−51−51−51+51+5−1+5−1−500001−5−1+51+5−1−500000000000000000000000
χ3444-4-44−1−5−1+51+51+51−51−5−1−5−1+500001+5−1−51−5−1+500000000000000000000000
χ354-4000440000-4-4002i−2i00002i−2i2i−2i2i−2i2i−2i000000000000000
χ364-4000440000-4-400−2i2i0000−2i2i−2i2i−2i2i−2i2i000000000000000
χ374-4000−1+5−1−52ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ181−51+5002i−2i0000−2ζ112ζ11−2ζ192ζ19−2ζ32ζ3−2ζ72ζ7000000000000000
χ384-4000−1+5−1−52ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ181−51+500−2i2i00002ζ11−2ζ112ζ19−2ζ192ζ3−2ζ32ζ7−2ζ7000000000000000
χ394-4000−1+5−1−5−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ181−51+5002i−2i0000−2ζ192ζ19−2ζ112ζ11−2ζ72ζ7−2ζ32ζ3000000000000000
χ404-4000−1+5−1−5−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ181−51+500−2i2i00002ζ19−2ζ192ζ11−2ζ112ζ7−2ζ72ζ3−2ζ3000000000000000
χ414-4000−1−5−1+5−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ141+51−5002i−2i0000−2ζ32ζ3−2ζ72ζ7−2ζ192ζ19−2ζ112ζ11000000000000000
χ424-4000−1−5−1+5−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ141+51−500−2i2i00002ζ3−2ζ32ζ7−2ζ72ζ19−2ζ192ζ11−2ζ11000000000000000
χ434-4000−1−5−1+52ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ141+51−5002i−2i0000−2ζ72ζ7−2ζ32ζ3−2ζ112ζ11−2ζ192ζ19000000000000000
χ444-4000−1−5−1+52ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ141+51−500−2i2i00002ζ7−2ζ72ζ3−2ζ32ζ11−2ζ112ζ19−2ζ19000000000000000

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