Finite Group Databasebeta

← Group #12072109

Character table — Group #12072109

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111122222222222222444444444444444444444444888888888888888888888888888816161616161616161616161616161616161620202020404040404040404040408080
order1222224444551010101010104444101010102020202020202020202020202020202044444444202020202020202020202020202020202020202088202020202020202040404040404040404444224444444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1
χ6111111111111111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ7111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-111
χ8111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111111-1-1
χ9111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111-11-111-1-1-1-1-1-1-1-1-1-1-1-111111111111-111-1-111-1-11111-1-1-1-111-1-11-11-11-111-1-11-1
χ10111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111-11-111-1-1-1-1-1-1-1-1-1-1-1-111111111111-111-1-111-1-11111-1-1-1-1-1-111-11-11-11-1-111-11
χ11111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-1-1-1111111-1-11-11-11-1-1-111-11
χ12111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-1-1-11111-1-111-11-11-1111-1-11-1
χ13111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1111-1-1-1-1-1-1-1-1-1-1-1-11111111111-11-1-111-1-111-1-1-1-1111111-1-1-111-1-1111-1-1-11
χ14111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1111-1-1-1-1-1-1-1-1-1-1-1-11111111111-11-1-111-1-111-1-1-1-11111-1-1111-1-111-1-1-1111-1
χ15111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11-1-111-1-11111111111-1-1-1-1-1-1-1-11-1-1-111-1-1111111-1-1-1-111-1-1-111-1-11-1-1111-1
χ16111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11-1-111-1-11111111111-1-1-1-1-1-1-1-11-1-1-111-1-1111111-1-1-1-1-1-1111-1-111-111-1-1-11
χ17222222222222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-200000000-2-200000000-2-20000000000000000000000000022-2-200-2200000000
χ18222222222222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-200000000-2-200000000-2-200000000000000000000000000-2-222002-200000000
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+52−1−521−521−521−521−521+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
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+52−1−521−521−521−521−521+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
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+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
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+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
χ27222222-2-2-2-22222222222-2-22222-2-2-2-2-2-2-2-22222-2-2-2-2000000002200000000-2-200000000000000000000000000222200-2-200000000
χ28222222-2-2-2-22222222222-2-22222-2-2-2-2-2-2-2-22222-2-2-2-2000000002200000000-2-200000000000000000000000000-2-2-2-2002200000000
χ29222222-2-2-2-2−1+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+52−1−52−1−522-22-222-2-21−521+521−521−521−521−521+521+521+521+52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522-2−1+52−1−521−521+52−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+520000000000000000
χ30222222-2-2-2-2−1+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+52−1−52−1−522-22-2-2-2221−521+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+52-22−1+52−1−521−521+52−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−520000000000000000
χ31222222-2-2-2-2−1+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+52−1−52−1−52-22-2222-2-21−521+521−521−521−521−521+521+521+521+52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-221−521+52−1+52−1−521−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−520000000000000000
χ32222222-2-2-2-2−1+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+52−1−52−1−52-22-22-2-2221−521+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+522-21−521+52−1+52−1−521−521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+520000000000000000
χ33222222-2-2-2-2−1−52−1+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+522-22-222-2-21+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+522-2−1−52−1+521+521−52−1−52−1+521+521−52−1−52−1−52−1+52−1+521+521+521−521−520000000000000000
χ34222222-2-2-2-2−1−52−1+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+522-22-2-2-2221+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+521−521−521−521−52-22−1−52−1+521+521−52−1−52−1+521+521−521+521+521−521−52−1−52−1−52−1+52−1+520000000000000000
χ35222222-2-2-2-2−1−52−1+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+52-22-2222-2-21+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+52-221+521−52−1−52−1+521+521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+520000000000000000
χ36222222-2-2-2-2−1−52−1+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+52-22-22-2-2221+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+521−521−521−521−522-21+521−52−1−52−1+521+521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−520000000000000000
χ372222-2-222-2-2222222222-22-2-2-2-2-222-2-222-2-2222222222-2-220000-2-200000000-2-2000000000022-2-2-2-222000000000000000000000000
χ382222-2-222-2-2222222222-22-2-2-2-2-222-2-222-2-222222222-222-20000-2-200000000-2-20000000000-2-22222-2-2000000000000000000000000
χ392222-2-222-2-222222222-22-22-2-2-2-222-2-222-2-2-2-2-2-2-2-2-2-2000000002200000000220000000000000000000000000000002-200-22000000
χ402222-2-222-2-222222222-22-22-2-2-2-222-2-222-2-2-2-2-2-2-2-2-2-200000000220000000022000000000000000000000000000000-22002-2000000
χ412222-2-222-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522-22-21−521−521+521+52−1+52−1+521−521−52−1−52−1−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522-2-2200001−521+52ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ181−521+52ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ1800−1+52−1−521−521+521−521+52−1+52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ180000000000000000
χ422222-2-222-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522-22-21−521−521+521+52−1+52−1+521−521−52−1−52−1−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522-2-2200001−521+52−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ181−521+52−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ1800−1+52−1−521−521+521−521+52−1+52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ180000000000000000
χ432222-2-222-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522-22-21−521−521+521+52−1+52−1+521−521−52−1−52−1−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-222-200001−521+52ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ181−521+52ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18001−521+52−1+52−1−52−1+52−1−521−521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ180000000000000000
χ442222-2-222-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522-22-21−521−521+521+52−1+52−1+521−521−52−1−52−1−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-222-200001−521+52−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ181−521+52−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18001−521+52−1+52−1−52−1+52−1−521−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ180000000000000000
χ452222-2-222-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522-22-21+521+521−521−52−1−52−1−521+521+52−1+52−1+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522-2-2200001+521−52−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ141+521−52−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ1400−1−52−1+521+521−521+521−52−1−52−1+52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ140000000000000000
χ462222-2-222-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522-22-21+521+521−521−52−1−52−1−521+521+52−1+52−1+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522-2-2200001+521−52ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ141+521−52ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ1400−1−52−1+521+521−521+521−52−1−52−1+52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ140000000000000000
χ472222-2-222-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522-22-21+521+521−521−52−1−52−1−521+521+52−1+52−1+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-222-200001+521−52−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ141+521−52−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14001+521−52−1−52−1+52−1−52−1+521+521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ140000000000000000
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χ1018-8-888-80000−2+25−2−252−25−2+252+25−2−252−252+250000−2+252−25−2−252+25000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1028-8-888-80000−2−25−2+252+25−2−252−25−2+252+252−250000−2−252+25−2+252−25000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1038-8-88-880000−2+25−2−252−25−2+252+25−2−252−252+2500002−25−2+252+25−2−25000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-880000−2−25−2+252+25−2−252−25−2+252+252−2500002+25−2−252−25−2+25000000000000000000000000000000000000000000000000000000000000000000000000000000

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