Finite Group Databasebeta

← Group #64749

Character table — Group #64749

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222222222224444444444444444444444444444101010101010101020202020
order1222222244445510101010101010101010101010104444202020202020202020202020202020202020202020202020888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111-1-11-1-11-1-11111111-1-1-1-1-1-111-1-1ii−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1ii−i−i
χ6111-1-11-1-11-1-11111111-1-1-1-1-1-111-1-1ii−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−iii
χ7111-1-11-1-11-1-11111111-1-1-1-1-1-111-1-1−i−iii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−iii
χ8111-1-11-1-11-1-11111111-1-1-1-1-1-111-1-1−i−iii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111ii−i−i
χ91-1-11-111-111-1-111-1-1-1-111-1-1-1-111111-11-111-1-111-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−ii−ii−i
χ101-1-11-111-111-1-111-1-1-1-111-1-1-1-111111-11-111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−ii−ii
χ111-1-11-111-111-1-111-1-1-1-111-1-1-1-11111-11-1111-1-111-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−ii−ii
χ121-1-11-111-111-1-111-1-1-1-111-1-1-1-11111-11-1111-1-111-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiii−ii−i
χ131-1-1-111-111-11-111-1-1-1-1-1-1111111-1-1i−i−ii11-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii-111-1
χ141-1-1-111-111-11-111-1-1-1-1-1-1111111-1-1i−i−ii11-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i1-1-11
χ151-1-1-111-111-11-111-1-1-1-1-1-1111111-1-1−iii−i11-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii1-1-11
χ161-1-1-111-111-11-111-1-1-1-1-1-1111111-1-1−iii−i11-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i-111-1
χ17222222222222−1+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+52−1−522222−1+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+52−1−52−1−52000000000000
χ18222222222222−1+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+52−1−52-2-2-2-2−1+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+52000000000000
χ19222222222222−1−52−1+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+522222−1−52−1+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+52000000000000
χ20222222222222−1−52−1+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+52-2-2-2-2−1−52−1+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+521−521−52000000000000
χ2122222222-2-2-2-222222222222222220000-2-2-2-2-2-2-2-20000000000000000000000000000
χ2222222222-2-2-2-2−1+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+52−1−5200001−521+521−521+521−521+521−521+52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36000000000000
χ2322222222-2-2-2-2−1+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+52−1−5200001−521+521−521+521−521+521−521+52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36000000000000
χ2422222222-2-2-2-2−1−52−1+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+5200001+521−521+521−521+521−521+521−52−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28000000000000
χ2522222222-2-2-2-2−1−52−1+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+5200001+521−521+521−521+521−521+521−52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28000000000000
χ26222-2-22-2-22-2-22−1+52−1−52−1+52−1+52−1−52−1−521−521+521−521−521+521+52−1+52−1−521−521+522i2i−2i−2i−1+52−1−52−1+52−1−521−521+521−521+52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14000000000000
χ27222-2-22-2-22-2-22−1+52−1−52−1+52−1+52−1−52−1−521−521+521−521−521+521+52−1+52−1−521−521+52−2i−2i2i2i−1+52−1−52−1+52−1−521−521+521−521+52ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14000000000000
χ28222-2-22-2-22-2-22−1−52−1+52−1−52−1−52−1+52−1+521+521−521+521+521−521−52−1−52−1+521+521−522i2i−2i−2i−1−52−1+52−1−52−1+521+521−521+521−52−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38000000000000
χ29222-2-22-2-22-2-22−1−52−1+52−1−52−1−52−1+52−1+521+521−521+521+521−521−52−1−52−1+521+521−52−2i−2i2i2i−1−52−1+52−1−52−1+521+521−521+521−52ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38000000000000
χ30222-2-22-2-2-222-2222222-2-2-2-2-2-222-2-20000-2-2-2-222220000000000000000000000000000
χ31222-2-22-2-2-222-2−1+52−1−52−1+52−1+52−1−52−1−521−521+521−521−521+521+52−1+52−1−521−521+5200001−521+521−521+52−1+52−1−52−1+52−1−52−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ14000000000000
χ32222-2-22-2-2-222-2−1+52−1−52−1+52−1+52−1−52−1−521−521+521−521−521+521+52−1+52−1−521−521+5200001−521+521−521+52−1+52−1−52−1+52−1−52ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ14000000000000
χ33222-2-22-2-2-222-2−1−52−1+52−1−52−1−52−1+52−1+521+521−521+521+521−521−52−1−52−1+521+521−5200001+521−521+521−52−1−52−1+52−1−52−1+52ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38000000000000
χ34222-2-22-2-2-222-2−1−52−1+52−1−52−1−52−1+52−1+521+521−521+521+521−521−52−1−52−1+521+521−5200001+521−521+521−52−1−52−1+52−1−52−1+52−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38000000000000
χ3522-222-2-2-20000222-22-2222-22-2-2-2-2-200000000000000000000000000002−22−22−22−20000
χ3622-222-2-2-20000222-22-2222-22-2-2-2-2-20000000000000000000000000000−22−22−22−220000
χ3722-2-2-2-2220000222-22-2-2-2-22-22-2-22200000000000000000000000000002−22−2−22−220000
χ3822-2-2-2-2220000222-22-2-2-2-22-22-2-2220000000000000000000000000000−22−222−22−20000
χ392-222-2-2-22000022-22-2222-22-22-2-2-2-20000000000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ402-222-2-2-22000022-22-2222-22-22-2-2-2-20000000000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ412-22-22-22-2000022-22-22-2-22-22-2-2-2220000000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ422-22-22-22-2000022-22-22-2-22-22-2-2-2220000000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ432-2-22-222-222-2-2−1+52−1−521−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1−52−1+52−1−522-22-2−1+52−1−521−521+52−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52000000000000
χ442-2-22-222-222-2-2−1+52−1−521−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1−52−1+52−1−52-22-22−1+52−1−521−521+52−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−52000000000000
χ452-2-22-222-222-2-2−1−52−1+521+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1+52−1−52−1+522-22-2−1−52−1+521+521−52−1−52−1+521+521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52000000000000
χ462-2-22-222-222-2-2−1−52−1+521+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1+52−1−52−1+52-22-22−1−52−1+521+521−52−1−52−1+521+521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+52000000000000
χ472-2-22-222-2-2-22222-2-2-2-222-2-2-2-222220000-2-222-2-2220000000000000000000000000000
χ482-2-22-222-2-2-222−1+52−1−521−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1−52−1+52−1−5200001−521+52−1+52−1−521−521+52−1+52−1−52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36000000000000
χ492-2-22-222-2-2-222−1+52−1−521−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1−52−1+52−1−5200001−521+52−1+52−1−521−521+52−1+52−1−52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36000000000000
χ502-2-22-222-2-2-222−1−52−1+521+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1+52−1−52−1+5200001+521−52−1−52−1+521+521−52−1−52−1+52−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28000000000000
χ512-2-22-222-2-2-222−1−52−1+521+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1+52−1−52−1+5200001+521−52−1−52−1+521+521−52−1−52−1+52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28000000000000
χ522-2-2-222-222-22-2−1+52−1−521−521−521+521+521−521+52−1+52−1+52−1−52−1−52−1+52−1−521−521+522i−2i−2i2i−1+52−1−521−521+521−521+52−1+52−1−52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14000000000000
χ532-2-2-222-222-22-2−1+52−1−521−521−521+521+521−521+52−1+52−1+52−1−52−1−52−1+52−1−521−521+52−2i2i2i−2i−1+52−1−521−521+521−521+52−1+52−1−52ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14000000000000
χ542-2-2-222-222-22-2−1−52−1+521+521+521−521−521+521−52−1−52−1−52−1+52−1+52−1−52−1+521+521−522i−2i−2i2i−1−52−1+521+521−521+521−52−1−52−1+52−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38000000000000
χ552-2-2-222-222-22-2−1−52−1+521+521+521−521−521+521−52−1−52−1−52−1+52−1+52−1−52−1+521+521−52−2i2i2i−2i−1−52−1+521+521−521+521−52−1−52−1+52ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38000000000000
χ562-2-2-222-22-22-2222-2-2-2-2-2-2222222-2-20000-2-22222-2-20000000000000000000000000000
χ572-2-2-222-22-22-22−1+52−1−521−521−521+521+521−521+52−1+52−1+52−1−52−1−52−1+52−1−521−521+5200001−521+52−1+52−1−52−1+52−1−521−521+52−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ14000000000000
χ582-2-2-222-22-22-22−1+52−1−521−521−521+521+521−521+52−1+52−1+52−1−52−1−52−1+52−1−521−521+5200001−521+52−1+52−1−52−1+52−1−521−521+52ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ14000000000000
χ592-2-2-222-22-22-22−1−52−1+521+521+521−521−521+521−52−1−52−1−52−1+52−1+52−1−52−1+521+521−5200001+521−52−1−52−1+52−1−52−1+521+521−52ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38000000000000
χ602-2-2-222-22-22-22−1−52−1+521+521+521−521−521+521−52−1−52−1−52−1+52−1+52−1−52−1+521+521−5200001+521−52−1−52−1+52−1−52−1+521+521−52−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38000000000000
χ6144-444-4-4-40000−1+5−1−5−1+51−5−1−51+5−1+5−1−5−1+51−5−1−51+51−51+51−51+50000000000000000000000000000000000000000
χ6244-444-4-4-40000−1−5−1+5−1−51+5−1+51−5−1−5−1+5−1−51+5−1+51−51+51−51+51−50000000000000000000000000000000000000000
χ6344-4-4-4-4440000−1+5−1−5−1+51−5−1−51+51−51+51−5−1+51+5−1−51−51+5−1+5−1−50000000000000000000000000000000000000000
χ6444-4-4-4-4440000−1−5−1+5−1−51+5−1+51−51+51−51+5−1−51−5−1+51+51−5−1−5−1+50000000000000000000000000000000000000000
χ654-444-4-4-440000−1+5−1−51−5−1+51+5−1−5−1+5−1−51−5−1+51+5−1−51−51+51−51+50000000000000000000000000000000000000000
χ664-444-4-4-440000−1−5−1+51+5−1−51−5−1+5−1−5−1+51+5−1−51−5−1+51+51−51+51−50000000000000000000000000000000000000000
χ674-44-44-44-40000−1+5−1−51−5−1+51+5−1−51−51+5−1+51−5−1−51+51−51+5−1+5−1−50000000000000000000000000000000000000000
χ684-44-44-44-40000−1−5−1+51+5−1−51−5−1+51+51−5−1−51+5−1+51−51+51−5−1−5−1+50000000000000000000000000000000000000000

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