Finite Group Databasebeta

← Group #65310

Character table — Group #65310

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11112222222222222222222244444444444444444444444444444202020204040
order1222444455101010101010202020202020202044444202020202020202020202020202020202020202020202020888844
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1
χ3111111111111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ51111-1-11111111111-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11-1
χ61111-1-11111111111-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-11
χ71111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-11
χ81111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111-1
χ922222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5222222−1+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+52−1−52−1−52−1−52−1−52000000
χ1022222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-22-2-2−1+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+52000000
χ1122222222−1−52−1+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+5222222−1−52−1−52−1+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+52000000
χ1222222222−1−52−1+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+52-2-22-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−52000000
χ13222222-2-2222222222222222200-200-2-2-2-2-2-2-2-20000000000000000000000
χ14222222-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200-2001−521−521+521+521−521−521+521+52ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36000000
χ15222222-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200-2001−521−521+521+521−521−521+521+52−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36000000
χ16222222-2-2−1−52−1+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+5200-2001+521+521−521−521+521+521−521−52−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28000000
χ17222222-2-2−1−52−1+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+5200-2001+521+521−521−521+521+521−521−52ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28000000
χ182222-2-222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+5222-2-2-2−1+52−1+52−1−52−1−521−521−521+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+52000000
χ192222-2-222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+52-2-2-222−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52000000
χ202222-2-222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−5222-2-2-2−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−52000000
χ212222-2-222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−52-2-2-222−1−52−1−52−1+52−1+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+52000000
χ222222-2-2-2-222222222-2-2-2-2-2-2-2-200200-2-2-2-222220000000000000000000000
χ232222-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+52002001−521−521+521+52−1+52−1+52−1−52−1−52ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36000000
χ242222-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+52002001−521−521+521+52−1+52−1+52−1−52−1−52−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36000000
χ252222-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−52002001+521+521−521−52−1−52−1−52−1+52−1+52−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28000000
χ262222-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−52002001+521+521−521−52−1−52−1−52−1+52−1+52ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28000000
χ2722-2-22-2002222-2-2-2-222-2-222-2-2000000000000000000000000000002−22−200
χ2822-2-22-2002222-2-2-2-222-2-222-2-200000000000000000000000000000−22−2200
χ2922-2-2-22002222-2-2-2-2-2-222-2-222000000000000000000000000000002−2−2200
χ3022-2-2-22002222-2-2-2-2-2-222-2-22200000000000000000000000000000−222−200
χ312-22-2002-222-2-22-22-2000000002-20002-22-200002-22-22-22-200000000000000
χ322-22-2002-222-2-22-22-200000000-220002-22-20000-22-22-22-2200000000000000
χ332-22-2002-2−1+52−1−521−521+52−1+521−52−1−521+52−ζ22+ζ38ζ22−ζ38−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ142-2000−1+521−52−1−521+52−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14−1+521−52−1+521−52−1−521+52−1−521+52−ζ22+ζ38ζ22−ζ38−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14000000
χ342-22-2002-2−1+52−1−521−521+52−1+521−52−1−521+52−ζ22+ζ38ζ22−ζ38−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14-22000−1+521−52−1−521+52−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ141−52−1+521−52−1+521+52−1−521+52−1−52ζ22−ζ38−ζ22+ζ38ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14000000
χ352-22-2002-2−1+52−1−521−521+52−1+521−52−1−521+52ζ22−ζ38−ζ22+ζ38ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ142-2000−1+521−52−1−521+52ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14−1+521−52−1+521−52−1−521+52−1−521+52ζ22−ζ38−ζ22+ζ38ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14000000
χ362-22-2002-2−1+52−1−521−521+52−1+521−52−1−521+52ζ22−ζ38−ζ22+ζ38ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14-22000−1+521−52−1−521+52ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ141−52−1+521−52−1+521+52−1−521+52−1−52−ζ22+ζ38ζ22−ζ38−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14000000
χ372-22-2002-2−1−52−1+521+521−52−1−521+52−1+521−52ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38ζ22−ζ38−ζ22+ζ382-2000−1−521+52−1+521−52ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38−1−521+52−1−521+52−1+521−52−1+521−52ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38ζ22−ζ38−ζ22+ζ38000000
χ382-22-2002-2−1−52−1+521+521−52−1−521+52−1+521−52ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38ζ22−ζ38−ζ22+ζ38-22000−1−521+52−1+521−52ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ381+52−1−521+52−1−521−52−1+521−52−1+52−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38−ζ22+ζ38ζ22−ζ38000000
χ392-22-2002-2−1−52−1+521+521−52−1−521+52−1+521−52−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38−ζ22+ζ38ζ22−ζ382-2000−1−521+52−1+521−52−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38−1−521+52−1−521+52−1+521−52−1+521−52−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38−ζ22+ζ38ζ22−ζ38000000
χ402-22-2002-2−1−52−1+521+521−52−1−521+52−1+521−52−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38−ζ22+ζ38ζ22−ζ38-22000−1−521+52−1+521−52−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ381+52−1−521+52−1−521−52−1+521−52−1+52ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38ζ22−ζ38−ζ22+ζ38000000
χ412-22-200-2222-2-22-22-2000000000002i−2i-22-220000000000002i−2i−2i2i−2i2i2i−2i000000
χ422-22-200-2222-2-22-22-200000000000−2i2i-22-22000000000000−2i2i2i−2i2i−2i−2i2i000000
χ432-22-200-22−1+52−1−521−521+52−1+521−52−1−521+52−ζ22+ζ38ζ22−ζ38−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ140002i−2i1−52−1+521+52−1−52ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14−ζ12+ζ28ζ12−ζ28ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ4−ζ36−ζ22−ζ38ζ22+ζ38ζ22+ζ38−ζ22−ζ38ζ6+ζ14−ζ6−ζ14−ζ6−ζ14ζ6+ζ14000000
χ442-22-200-22−1+52−1−521−521+52−1+521−52−1−521+52−ζ22+ζ38ζ22−ζ38−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14000−2i2i1−52−1+521+52−1−52ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14ζ12−ζ28−ζ12+ζ28−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ4+ζ36ζ22+ζ38−ζ22−ζ38−ζ22−ζ38ζ22+ζ38−ζ6−ζ14ζ6+ζ14ζ6+ζ14−ζ6−ζ14000000
χ452-22-200-22−1+52−1−521−521+52−1+521−52−1−521+52ζ22−ζ38−ζ22+ζ38ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ140002i−2i1−52−1+521+52−1−52−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14ζ12−ζ28−ζ12+ζ28−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ22−ζ38ζ22+ζ38ζ22+ζ38−ζ22−ζ38ζ6+ζ14−ζ6−ζ14−ζ6−ζ14ζ6+ζ14000000
χ462-22-200-22−1+52−1−521−521+52−1+521−52−1−521+52ζ22−ζ38−ζ22+ζ38ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14000−2i2i1−52−1+521+52−1−52−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14−ζ12+ζ28ζ12−ζ28ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ22+ζ38−ζ22−ζ38−ζ22−ζ38ζ22+ζ38−ζ6−ζ14ζ6+ζ14ζ6+ζ14−ζ6−ζ14000000
χ472-22-200-22−1−52−1+521+521−52−1−521+52−1+521−52ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38ζ22−ζ38−ζ22+ζ380002i−2i1+52−1−521−52−1+52−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ6−ζ14ζ6+ζ14ζ6+ζ14−ζ6−ζ14ζ22+ζ38−ζ22−ζ38−ζ22−ζ38ζ22+ζ38000000
χ482-22-200-22−1−52−1+521+521−52−1−521+52−1+521−52ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38ζ22−ζ38−ζ22+ζ38000−2i2i1+52−1−521−52−1+52−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ6+ζ14−ζ6−ζ14−ζ6−ζ14ζ6+ζ14−ζ22−ζ38ζ22+ζ38ζ22+ζ38−ζ22−ζ38000000
χ492-22-200-22−1−52−1+521+521−52−1−521+52−1+521−52−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38−ζ22+ζ38ζ22−ζ380002i−2i1+52−1−521−52−1+52ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ12+ζ28ζ12−ζ28−ζ6−ζ14ζ6+ζ14ζ6+ζ14−ζ6−ζ14ζ22+ζ38−ζ22−ζ38−ζ22−ζ38ζ22+ζ38000000
χ502-22-200-22−1−52−1+521+521−52−1−521+52−1+521−52−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38−ζ22+ζ38ζ22−ζ38000−2i2i1+52−1−521−52−1+52ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ12−ζ28−ζ12+ζ28ζ6+ζ14−ζ6−ζ14−ζ6−ζ14ζ6+ζ14−ζ22−ζ38ζ22+ζ38ζ22+ζ38−ζ22−ζ38000000
χ5144-4-44-400−1+5−1−5−1+5−1−51−51−51+51+5−1+5−1+51−51−5−1−5−1−51+51+500000000000000000000000000000000000
χ5244-4-44-400−1−5−1+5−1−5−1+51+51+51−51−5−1−5−1−51+51+5−1+5−1+51−51−500000000000000000000000000000000000
χ5344-4-4-4400−1+5−1−5−1+5−1−51−51−51+51+51−51−5−1+5−1+51+51+5−1−5−1−500000000000000000000000000000000000
χ5444-4-4-4400−1−5−1+5−1−5−1+51+51+51−51−51+51+5−1−5−1−51−51−5−1+5−1+500000000000000000000000000000000000
χ554-4-44000044-4-4-44-440000000000000000000000000000000000000000000
χ564-4-440000−1+5−1−51−51+51−5−1+51+5−1−5−2ζ22+2ζ382ζ22−2ζ382ζ22−2ζ38−2ζ22+2ζ382ζ6−2ζ14−2ζ6+2ζ14−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000000000000000
χ574-4-440000−1+5−1−51−51+51−5−1+51+5−1−52ζ22−2ζ38−2ζ22+2ζ38−2ζ22+2ζ382ζ22−2ζ38−2ζ6+2ζ142ζ6−2ζ142ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000000000000000
χ584-4-440000−1−5−1+51+51−51+5−1−51−5−1+52ζ6−2ζ14−2ζ6+2ζ14−2ζ6+2ζ142ζ6−2ζ142ζ22−2ζ38−2ζ22+2ζ38−2ζ22+2ζ382ζ22−2ζ3800000000000000000000000000000000000
χ594-4-440000−1−5−1+51+51−51+5−1−51−5−1+5−2ζ6+2ζ142ζ6−2ζ142ζ6−2ζ14−2ζ6+2ζ14−2ζ22+2ζ382ζ22−2ζ382ζ22−2ζ38−2ζ22+2ζ3800000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.