Finite Group Databasebeta

← Group #10602885

Character table — Group #10602885

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67
size112222222222222224444444444448888888888888888888888888888884040404040404040
order1222244445510101010101010101010202020202020202022248810101010101010101010101020202020404040404040404044888888
χ11111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ41111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ511111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111
χ9222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1−52222222−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200000000
χ10222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1−5222-2-2-2-2−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521+521+521−521−521+521+521−521−521−521−521+521+521+521+5200000000
χ11222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1−52-2-222-2-21−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+5200000000
χ12222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1−52-2-2-2-2221−521−521−521−521+521+521+521+521−521−521+521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200000000
χ13222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1+52222222−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200000000
χ14222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1+5222-2-2-2-2−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521−521−521+521+521−521−521+521+521+521+521−521−521−521−5200000000
χ15222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1+52-2-222-2-21+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−5200000000
χ16222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1+52-2-2-2-2221+521+521+521+521−521−521−521−521+521+521−521−521+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200000000
χ1722222-2-2-2-2222222222222-2-2-2-2-2-2-2-200000000000000000000000000000000002i−2i00
χ1822222-2-2-2-2222222222222-2-2-2-2-2-2-2-20000000000000000000000000000000000−2i2i00
χ19222-2-222-2-222222222-2-2-2-222-222-2-2-20000000000000000000000000000000000002i−2i
χ20222-2-222-2-222222222-2-2-2-222-222-2-2-2000000000000000000000000000000000000−2i2i
χ21222-2-2-2-22222222222-2-2-2-2-2-22-2-2222002-200000000002222-2-2-2-20000000000000000
χ22222-2-2-2-22222222222-2-2-2-2-2-22-2-222200-220000000000-2-2-2-222220000000000000000
χ23222-2-2-2-222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521−521+521+521−521−52−1+521+521+52−1−52−1+52−1−52002-200ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−1+52−1+52−1−52−1−521−521−521+521+52ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ1800000000
χ24222-2-2-2-222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521−521+521+521−521−52−1+521+521+52−1−52−1+52−1−52002-200−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18−1+52−1+52−1−52−1−521−521−521+521+52−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ1800000000
χ25222-2-2-2-222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521−521+521+521−521−52−1+521+521+52−1−52−1+52−1−5200-2200ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ181−521−521+521+52−1+52−1+52−1−52−1−52−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ1800000000
χ26222-2-2-2-222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521−521+521+521−521−52−1+521+521+52−1−52−1+52−1−5200-2200−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ181−521−521+521+52−1+52−1+52−1−52−1−52ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ1800000000
χ27222-2-2-2-222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521−521−521+521+52−1−521−521−52−1+52−1−52−1+52002-200−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14−1−52−1−52−1+52−1+521+521+521−521−52−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ1400000000
χ28222-2-2-2-222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521−521−521+521+52−1−521−521−52−1+52−1−52−1+52002-200ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−1−52−1−52−1+52−1+521+521+521−521−52ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ1400000000
χ29222-2-2-2-222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521−521−521+521+52−1−521−521−52−1+52−1−52−1+5200-2200−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ141+521+521−521−52−1−52−1−52−1+52−1+52ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ1400000000
χ30222-2-2-2-222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521−521−521+521+52−1−521−521−52−1+52−1−52−1+5200-2200ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ141+521+521−521−52−1−52−1−52−1+52−1+52−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ1400000000
χ3122-22-22-22-222-2-2-2-2222-22-22-222-22-2-20000000000000000000000000000002i−2i000000
χ3222-22-22-22-222-2-2-2-2222-22-22-222-22-2-2000000000000000000000000000000−2i2i000000
χ3322-22-2-22-2222-2-2-2-2222-22-2-22-2-22-22200002-200000000000000002-22-22-22-200000000
χ3422-22-2-22-2222-2-2-2-2222-22-2-22-2-22-2220000-220000000000000000-22-22-22-2200000000
χ3522-22-2-22-22−1+52−1−521−521−521+521+52−1+52−1−52−1+521−52−1−521+521−52−1+521−521+52−1−521+52−1+52−1−5200002-2ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−1+521−52−1+521−52−1−521+52−1−521+5200000000
χ3622-22-2-22-22−1+52−1−521−521−521+521+52−1+52−1−52−1+521−52−1−521+521−52−1+521−521+52−1−521+52−1+52−1−5200002-2−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−1+521−52−1+521−52−1−521+52−1−521+5200000000
χ3722-22-2-22-22−1+52−1−521−521−521+521+52−1+52−1−52−1+521−52−1−521+521−52−1+521−521+52−1−521+52−1+52−1−520000-22ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ181−52−1+521−52−1+521+52−1−521+52−1−5200000000
χ3822-22-2-22-22−1+52−1−521−521−521+521+52−1+52−1−52−1+521−52−1−521+521−52−1+521−521+52−1−521+52−1+52−1−520000-22−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−52−1+521−52−1+521+52−1−521+52−1−5200000000
χ3922-22-2-22-22−1−52−1+521+521+521−521−52−1−52−1+52−1−521+52−1+521−521+52−1−521+521−52−1+521−52−1−52−1+5200002-2−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−1−521+52−1−521+52−1+521−52−1+521−5200000000
χ4022-22-2-22-22−1−52−1+521+521+521−521−52−1−52−1+52−1−521+52−1+521−521+52−1−521+521−52−1+521−52−1−52−1+5200002-2ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−1−521+52−1−521+52−1+521−52−1+521−5200000000
χ4122-22-2-22-22−1−52−1+521+521+521−521−52−1−52−1+52−1−521+52−1+521−521+52−1−521+521−52−1+521−52−1−52−1+520000-22−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ141+52−1−521+52−1−521−52−1+521−52−1+5200000000
χ4222-22-2-22-22−1−52−1+521+521+521−521−52−1−52−1+52−1−521+52−1+521−521+52−1−521+521−52−1+521−52−1−52−1+520000-22ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ141+52−1−521+52−1−521−52−1+521−52−1+5200000000
χ4322-2-222-2-2222-2-2-2-222-22-222-2-22-2-2222-200002-2-222-2-22000000000000000000000000
χ4422-2-222-2-2222-2-2-2-222-22-222-2-22-2-222-220000-222-2-222-2000000000000000000000000
χ4522-2-222-2-22−1+52−1−521−521−521+521+52−1+52−1−521−52−1+521+52−1−52−1+521−521−52−1−521+521+52−1+52−1−522-20000−1+521−521−52−1+52−1−521+521+52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ1800000000
χ4622-2-222-2-22−1+52−1−521−521−521+521+52−1+52−1−521−52−1+521+52−1−52−1+521−521−52−1−521+521+52−1+52−1−522-20000−1+521−521−52−1+52−1−521+521+52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ1800000000
χ4722-2-222-2-22−1+52−1−521−521−521+521+52−1+52−1−521−52−1+521+52−1−52−1+521−521−52−1−521+521+52−1+52−1−52-2200001−52−1+52−1+521−521+52−1−52−1−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ1800000000
χ4822-2-222-2-22−1+52−1−521−521−521+521+52−1+52−1−521−52−1+521+52−1−52−1+521−521−52−1−521+521+52−1+52−1−52-2200001−52−1+52−1+521−521+52−1−52−1−521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ1800000000
χ4922-2-222-2-22−1−52−1+521+521+521−521−52−1−52−1+521+52−1−521−52−1+52−1−521+521+52−1+521−521−52−1−52−1+522-20000−1−521+521+52−1−52−1+521−521−52−1+52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ1400000000
χ5022-2-222-2-22−1−52−1+521+521+521−521−52−1−52−1+521+52−1−521−52−1+52−1−521+521+52−1+521−521−52−1−52−1+522-20000−1−521+521+52−1−52−1+521−521−52−1+52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ1400000000
χ5122-2-222-2-22−1−52−1+521+521+521−521−52−1−52−1+521+52−1−521−52−1+52−1−521+521+52−1+521−521−52−1−52−1+52-2200001+52−1−52−1−521+521−52−1+52−1+521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ1400000000
χ5222-2-222-2-22−1−52−1+521+521+521−521−52−1−52−1+521+52−1−521−52−1+52−1−521+521+52−1+521−521−52−1−52−1+52-2200001+52−1−52−1−521+521−52−1+52−1+521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ1400000000
χ5322-2-22-222-222-2-2-2-222-22-22-222-222-2-2000000000000000000000000000000002-20000
χ5422-2-22-222-222-2-2-2-222-22-22-222-222-2-200000000000000000000000000000000-220000
χ5544444-4-4-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5−1+5−1+5−1−5−1−51−51−51−51+51+51+51−51+500000000000000000000000000000000000000
χ5644444-4-4-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5−1−5−1−5−1+5−1+51+51+51+51−51−51−51+51−500000000000000000000000000000000000000
χ57444-4-444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−51−51−51+51+5−1+5−1+51−5−1−5−1−51+51−51+500000000000000000000000000000000000000
χ58444-4-444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+51+51+51−51−5−1−5−1−51+5−1+5−1+51−51+51−500000000000000000000000000000000000000
χ5944-44-44-44-4−1+5−1−51−51−51+51+5−1+5−1−5−1+51−5−1−51+5−1+51−5−1+5−1−51+5−1−51−51+500000000000000000000000000000000000000
χ6044-44-44-44-4−1−5−1+51+51+51−51−5−1−5−1+5−1−51+5−1+51−5−1−51+5−1−5−1+51−5−1+51+51−500000000000000000000000000000000000000
χ6144-4-44-444-4−1+5−1−51−51−51+51+5−1+5−1−51−5−1+51+5−1−51−5−1+5−1+51+5−1−5−1−51−51+500000000000000000000000000000000000000
χ6244-4-44-444-4−1−5−1+51+51+51−51−5−1−5−1+51+5−1−51−5−1+51+5−1−5−1−51−5−1+5−1+51+51−500000000000000000000000000000000000000
χ638-80000000880000-8-800000000000000000000000000000000000000000000000000
χ648-80000000−2+25−2−254ζ6−4ζ14−4ζ6+4ζ14−4ζ2+4ζ184ζ2−4ζ182−252+2500000000000000000000000000000000000000000000000000
χ658-80000000−2+25−2−25−4ζ6+4ζ144ζ6−4ζ144ζ2−4ζ18−4ζ2+4ζ182−252+2500000000000000000000000000000000000000000000000000
χ668-80000000−2−25−2+25−4ζ2+4ζ184ζ2−4ζ18−4ζ6+4ζ144ζ6−4ζ142+252−2500000000000000000000000000000000000000000000000000
χ678-80000000−2−25−2+254ζ2−4ζ18−4ζ2+4ζ184ζ6−4ζ14−4ζ6+4ζ142+252−2500000000000000000000000000000000000000000000000000

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