Finite Group Databasebeta

← Group #12016334

Character table — Group #12016334

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111122222222222222444444444444444444444444888888888888888888888888888816161616161616161616161616161616161620202020404040404040404040408080
order124422244455101020202020888810101010101020202020202040404040404040404444161616164040404080808080808080808080808080808080442020202020202020202020202020202022444444881616161624
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ6111111111111111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ7111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111
χ8111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1
χ911-1-1-11-11-111111-1-1-1-111-1-1-1-111-1-111-1-1111111-1-1-1-1ii−i−iii−i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−i1-1iiii−i−i−i−i1111-1-1-1-11-11-1ii−i−i1-1ii−i−i1-1
χ1011-1-1-11-11-111111-1-1-1-111-1-1-1-111-1-111-1-1111111-1-1-1-1ii−i−iii−i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−i1-1iiii−i−i−i−i1111-1-1-1-1-11-11−i−iii-11−i−iii-11
χ1111-1-1-11-11-111111-1-1-1-111-1-1-1-111-1-111-1-1111111-1-1-1-1ii−i−i−i−iii11-1-1−i−i−i−i−i−i−i−iiiiiiiii-11iiii−i−i−i−i-1-1-1-111111-11-1ii−i−i1-1−i−iii-11
χ1211-1-1-11-11-111111-1-1-1-111-1-1-1-111-1-111-1-1111111-1-1-1-1ii−i−i−i−iii11-1-1−i−i−i−i−i−i−i−iiiiiiiii-11iiii−i−i−i−i-1-1-1-11111-11-11−i−iii-11ii−i−i1-1
χ1311-1-1-11-11-111111-1-1-1-111-1-1-1-111-1-111-1-1111111-1-1-1-1−i−iiiii−i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−i-11−i−i−i−iiiii-1-1-1-111111-11-1−i−iii1-1ii−i−i-11
χ1411-1-1-11-11-111111-1-1-1-111-1-1-1-111-1-111-1-1111111-1-1-1-1−i−iiiii−i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−i-11−i−i−i−iiiii-1-1-1-11111-11-11ii−i−i-11−i−iii1-1
χ1511-1-1-11-11-111111-1-1-1-111-1-1-1-111-1-111-1-1111111-1-1-1-1−i−iii−i−iii11-1-1−i−i−i−i−i−i−i−iiiiiiiii1-1−i−i−i−iiiii1111-1-1-1-11-11-1−i−iii1-1−i−iii1-1
χ1611-1-1-11-11-111111-1-1-1-111-1-1-1-111-1-111-1-1111111-1-1-1-1−i−iii−i−iii11-1-1−i−i−i−i−i−i−i−iiiiiiiii1-1−i−i−i−iiiii1111-1-1-1-1-11-11ii−i−i-11ii−i−i-11
χ17222222222222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-200000000-2-2-2-2000000000000000000000000000000000022220000-2-2000000
χ18222222222222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-200000000-2-2-2-20000000000000000000000000000000000-2-2-2-2000022000000
χ192222222222−1+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+52−1−52−1−5222222222−1+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+52−1−52−1−52−1−52−1−5222−1+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+52−1−52−1−520000000000000000
χ202222222222−1+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+52−1−52−1−522222-2-2-2-2−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+52-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+520000000000000000
χ212222222222−1+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+52−1−52−1−52-2-2-2-22222−1+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+52−1−52−1−52−1−52−1−52-2-21−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+520000000000000000
χ222222222222−1+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+52−1−52−1−52-2-2-2-2-2-2-2-2−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+52221−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000000000000000
χ232222222222−1−52−1+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+5222222222−1−52−1+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+5222−1−52−1−52−1+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+520000000000000000
χ242222222222−1−52−1+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+522222-2-2-2-2−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−52-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−520000000000000000
χ252222222222−1−52−1+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+52-2-2-2-22222−1−52−1+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+52-2-21+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−520000000000000000
χ262222222222−1−52−1+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+52-2-2-2-2-2-2-2-2−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−52221+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000000000000000
χ2722222-2-2-2-22222222222-22-222-2-2-2-2-2-2-2-222222222222i−2i2i−2i0000-2-2-2-20000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ2822222-2-2-2-22222222222-22-222-2-2-2-2-2-2-2-22222222222−2i2i−2i2i0000-2-2-2-2000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ2922222-2-2-2-2222222222-22-2222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2000000002222000000000000000000000000000000000000002i−2i2i−2i00000000
χ3022222-2-2-2-2222222222-22-2222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-200000000222200000000000000000000000000000000000000−2i2i−2i2i00000000
χ3122222-2-2-2-22−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522-22-2−1+52−1−521−521+521−521+521−521+521−521+52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522i−2i2i−2i00001−521+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−ζ3600−ζ22−ζ38ζ22+ζ38−ζ6−ζ14ζ6+ζ14−ζ22−ζ38ζ22+ζ38−ζ6−ζ14ζ6+ζ14−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ140000000000000000
χ3222222-2-2-2-22−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522-22-2−1+52−1−521−521+521−521+521−521+521−521+52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522i−2i2i−2i00001−521+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+ζ3600−ζ22−ζ38ζ22+ζ38−ζ6−ζ14ζ6+ζ14−ζ22−ζ38ζ22+ζ38−ζ6−ζ14ζ6+ζ14ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ140000000000000000
χ3322222-2-2-2-22−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522-22-2−1+52−1−521−521+521−521+521−521+521−521+52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−2i2i−2i2i00001−521+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−ζ3600ζ22+ζ38−ζ22−ζ38ζ6+ζ14−ζ6−ζ14ζ22+ζ38−ζ22−ζ38ζ6+ζ14−ζ6−ζ14ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ140000000000000000
χ3422222-2-2-2-22−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522-22-2−1+52−1−521−521+521−521+521−521+521−521+52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−2i2i−2i2i00001−521+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+ζ3600ζ22+ζ38−ζ22−ζ38ζ6+ζ14−ζ6−ζ14ζ22+ζ38−ζ22−ζ38ζ6+ζ14−ζ6−ζ14−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ140000000000000000
χ3522222-2-2-2-22−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522-22-2−1−52−1+521+521−521+521−521+521−521+521−52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522i−2i2i−2i00001+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−ζ2800−ζ6−ζ14ζ6+ζ14−ζ22−ζ38ζ22+ζ38−ζ6−ζ14ζ6+ζ14−ζ22−ζ38ζ22+ζ38−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ380000000000000000
χ3622222-2-2-2-22−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522-22-2−1−52−1+521+521−521+521−521+521−521+521−52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522i−2i2i−2i00001+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+ζ2800−ζ6−ζ14ζ6+ζ14−ζ22−ζ38ζ22+ζ38−ζ6−ζ14ζ6+ζ14−ζ22−ζ38ζ22+ζ38ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ380000000000000000
χ3722222-2-2-2-22−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522-22-2−1−52−1+521+521−521+521−521+521−521+521−52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−2i2i−2i2i00001+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−ζ2800ζ6+ζ14−ζ6−ζ14ζ22+ζ38−ζ22−ζ38ζ6+ζ14−ζ6−ζ14ζ22+ζ38−ζ22−ζ38ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ380000000000000000
χ3822222-2-2-2-22−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522-22-2−1−52−1+521+521−521+521−521+521−521+521−52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−2i2i−2i2i00001+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+ζ2800ζ6+ζ14−ζ6−ζ14ζ22+ζ38−ζ22−ζ38ζ6+ζ14−ζ6−ζ14ζ22+ζ38−ζ22−ζ38−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ380000000000000000
χ392222-22-2-22-2222222220000-2-222-2-2-2-222-2-2000000000000i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000002-2-22000000i2−i2i2−i200
χ402222-22-2-22-2222222220000-2-222-2-2-2-222-2-2000000000000i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000000000-222-2000000−i2i2−i2i200
χ412222-22-2-22-2222222220000-2-222-2-2-2-222-2-2000000000000−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000002-2-22000000−i2i2−i2i200
χ422222-22-2-22-2222222220000-2-222-2-2-2-222-2-2000000000000−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000000000-222-2000000i2−i2i2−i200
χ4322-2-2222-2-2-22222-2-2-2-20000222222-2-2-2-2-2-20000000000002−2−2200002−22−22−22−2−22−22−22−2200000000000000000022-2-20000002−2−2200
χ4422-2-2222-2-2-22222-2-2-2-20000222222-2-2-2-2-2-20000000000002−2−2200002−22−22−22−2−22−22−22−22000000000000000000-2-222000000−222−200
χ4522-2-2222-2-2-22222-2-2-2-20000222222-2-2-2-2-2-2000000000000−222−20000−22−22−22−222−22−22−22−200000000000000000022-2-2000000−222−200
χ4622-2-2222-2-2-22222-2-2-2-20000222222-2-2-2-2-2-2000000000000−222−20000−22−22−22−222−22−22−22−2000000000000000000-2-2220000002−2−2200
χ4722-2-2-22-22-222222-2-2-2-2-2-222-2-222-2-222-2-222-2-2-2-2222200000000-2-22200000000000000000000000000000000002-22-20000-22000000
χ4822-2-2-22-22-222222-2-2-2-2-2-222-2-222-2-222-2-222-2-2-2-2222200000000-2-2220000000000000000000000000000000000-22-2200002-2000000
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Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.