Finite Group Databasebeta

← Group #12072897

Character table — Group #12072897

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111122222222222222444444444444444444444444888888888888888888888888888816161616161616161616161616161616161640404040404040404040404040404040
order1222222244551010101010102444101010101010101020202020202020202020202044444444101020202020202020202020202020202020202088202020202020202040404040404040402244444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-11111
χ5111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-11-111-1-1-1-1-1-11111
χ8111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11-11-1-1111111-1-1-1-1
χ911111-1-11-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11-11111-1-1-1-11111-1-1-1-111-111-1-1-111-1-111-1-1
χ1011111-1-11-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11-11111-1-1-1-11111-1-1-1-1-1-11-1-1111-1-111-1-111
χ1111111-1-11-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111111-1-1-11-11111-1-1-1-111
χ1211111-1-11-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-11111-1111-11-1-1-1-11111-1-1
χ1311111-1-11-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-111111-1-1-1-1-1-1-1-1111111-111-1-1-1-1-111-1-111
χ1411111-1-11-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-111111-1-1-1-1-1-1-1-11111-1-11-1-111111-1-111-1-1
χ1511111-1-11-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-111111111-1-1-1-11-1-1-11-111-1-11111-1-1
χ1611111-1-11-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-111111111-1-1-1-1-1111-11-1-111-1-1-1-111
χ172222222222−1+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
χ182222222222−1+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+52−1+52−1+52−1−52−1−52−1−52−1−52−1+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
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+52−1−52−1−52-2-2-2-22222−1+52−1−521−521−521−521−521+521+521+521+52−1+52−1−521−521−521−521−521+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
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+52−1−52−1−52-2-2-2-2-2-2-2-2−1+52−1−521−521−521−521−521+521+521+521+52−1+52−1−521−521−521−521−521+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
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+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
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+522222-2-2-2-2−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+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
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+52-2-2-2-22222−1−52−1+521+521+521+521+521−521−521−521−52−1−52−1+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
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+52-2-2-2-2-2-2-2-2−1−52−1+521+521+521+521+521−521−521−521−52−1−52−1+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
χ2522222222-2-2222222222-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2000000002200000000-2-20000000000000000000000000020-20-220000000000
χ2622222222-2-2222222222-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2000000002200000000-2-200000000000000000000000000-20202-20000000000
χ2722222-2-222222222222-22-2-22222-2-2-2-222222222-2-2-2-200000000-2-200000000-2-2000000000000000000000000002020-2-20000000000
χ2822222-2-222222222222-22-2-22222-2-2-2-222222222-2-2-2-200000000-2-200000000-2-200000000000000000000000000-20-20220000000000
χ2922222-2-22-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-222−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−5222-2-222-2-21−521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+522-2−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+520000000000000000
χ3022222-2-22-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-222−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−5222-2-2-2-2221−521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+52-221−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−520000000000000000
χ3122222-2-22-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-222−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−52-2-22222-2-21−521+521−521−521−521−521+521+521+521+52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-22−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−520000000000000000
χ3222222-2-22-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-222−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−52-2-222-2-2221−521+521−521−521−521−521+521+521+521+52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522-21−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+520000000000000000
χ3322222-2-22-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-222−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+5222-2-222-2-21+521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−522-2−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−520000000000000000
χ3422222-2-22-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-222−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+5222-2-2-2-2221+521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−52-221+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+520000000000000000
χ3522222-2-22-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-222−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+52-2-22222-2-21+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+52−1+52−1+52-22−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+520000000000000000
χ3622222-2-22-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-222−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+52-2-222-2-2221+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+52−1+52−1+522-21+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−520000000000000000
χ372222-222-22222222222-2-2-22-2-2-2-2222222-2-222-2-2-2-2-2-200000000-2-2000000002200000000000000000000000000020-2002-200000000
χ382222-222-22222222222-2-2-22-2-2-2-2222222-2-222-2-2-2-2-2-200000000-2-20000000022000000000000000000000000000-20200-2200000000
χ392222-222-2-2-222222222-222-2-2-2-2-22222-2-222-2-222222200002-22-2-2-200000000-2-200000000002-22-22-22-2000000000000000000000000
χ402222-222-2-2-222222222-222-2-2-2-2-22222-2-222-2-22222220000-22-22-2-200000000-2-20000000000-22-22-22-22000000000000000000000000
χ412222-222-2-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-222-21−521−521+521+52−1+52−1+52−1−52−1−521−521−52−1+52−1+521+521+52−1−52−1−52−1+52−1+52−1−52−1−5200002-22-21−521+52ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ361−521+52ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ3600−1+521−52−1−521+52−1+521−52−1−521+52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ360000000000000000
χ422222-222-2-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-222-21−521−521+521+52−1+52−1+52−1−52−1−521−521−52−1+52−1+521+521+52−1−52−1−52−1+52−1+52−1−52−1−5200002-22-21−521+52−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ361−521+52−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ3600−1+521−52−1−521+52−1+521−52−1−521+52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ360000000000000000
χ432222-222-2-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-222-21−521−521+521+52−1+52−1+52−1−52−1−521−521−52−1+52−1+521+521+52−1−52−1−52−1+52−1+52−1−52−1−520000-22-221−521+52ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ361−521+52ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36001−52−1+521+52−1−521−52−1+521+52−1−52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ360000000000000000
χ442222-222-2-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-222-21−521−521+521+52−1+52−1+52−1−52−1−521−521−52−1+52−1+521+521+52−1−52−1−52−1+52−1+52−1−52−1−520000-22-221−521+52−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ361−521+52−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36001−52−1+521+52−1−521−52−1+521+52−1−52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ360000000000000000
χ452222-222-2-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-222-21+521+521−521−52−1−52−1−52−1+52−1+521+521+52−1−52−1−521−521−52−1+52−1+52−1−52−1−52−1+52−1+5200002-22-21+521−52−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ281+521−52−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ2800−1−521+52−1+521−52−1−521+52−1+521−52−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ280000000000000000
χ462222-222-2-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-222-21+521+521−521−52−1−52−1−52−1+52−1+521+521+52−1−52−1−521−521−52−1+52−1+52−1−52−1−52−1+52−1+5200002-22-21+521−52ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ281+521−52ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ2800−1−521+52−1+521−52−1−521+52−1+521−52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ280000000000000000
χ472222-222-2-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-222-21+521+521−521−52−1−52−1−52−1+52−1+521+521+52−1−52−1−521−521−52−1+52−1+52−1−52−1−52−1+52−1+520000-22-221+521−52−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ281+521−52−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28001+52−1−521−52−1+521+52−1−521−52−1+52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ280000000000000000
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χ1028-88-800008i−8i−2−25−2+252+252−25−2−252+25−2+252−25000000000000−4ζ6−4ζ144ζ6+4ζ1400−4ζ22−4ζ384ζ22+4ζ3800000000000000000000000000000000000000000000000000000000000000000000
χ1038-88-80000−8i8i−2+25−2−252−252+25−2+252−25−2−252+250000000000004ζ22+4ζ38−4ζ22−4ζ38004ζ6+4ζ14−4ζ6−4ζ1400000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-80000−8i8i−2−25−2+252+252−25−2−252+25−2+252−250000000000004ζ6+4ζ14−4ζ6−4ζ14004ζ22+4ζ38−4ζ22−4ζ3800000000000000000000000000000000000000000000000000000000000000000000

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