Finite Group Databasebeta

← Group #12016608

Character table — Group #12016608

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11112222222222444444444444444444444488888888888888888888888888888888888888161616161616161616161616161620202020202020204040404080808080
order1222225510101010101022224444441010101020202020202020202244441010101010101010101010101010101020202020202020202020202020202020882020202040404040404040404444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ4111111111111111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111-1-1-1-1111111111111111-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ61111111111111111111-1-1-1-1111111111111111-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ71111111111111111111-1-1-1-11111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-111-1-1-1-111
χ81111111111111111111-1-1-1-11111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-11111-1-1
χ911-1-11-111-1-1-1-11111-1-1-111-1-11-1-111-1-1-1-111111-11-11-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-11111-1-1-1-1ii−i−iii−i−ii−ii−ii−ii−i
χ1011-1-11-111-1-1-1-11111-1-1-111-1-11-1-111-1-1-1-111111-11-11-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-11111-1-1-1-1−i−iii−i−iii−ii−ii−ii−ii
χ1111-1-11-111-1-1-1-11111-1-1-111-1-11-1-111-1-1-1-11111-111-1-111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1111-1-1-1-1-1-11111ii−i−iii−i−ii−ii−i−ii−ii
χ1211-1-11-111-1-1-1-11111-1-1-111-1-11-1-111-1-1-1-11111-111-1-111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1111-1-1-1-1-1-11111−i−iii−i−iii−ii−iii−ii−i
χ1311-1-11-111-1-1-1-11111-1-1-1-1-1111-1-111-1-1-1-111111-1-111-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1-111-1-1-1-11111ii−i−i−i−iiii−i−iii−i−ii
χ1411-1-11-111-1-1-1-11111-1-1-1-1-1111-1-111-1-1-1-111111-1-111-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1-111-1-1-1-11111−i−iiiii−i−i−iii−i−iii−i
χ1511-1-11-111-1-1-1-11111-1-1-1-1-1111-1-111-1-1-1-11111-11-11-111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-1-1111111-1-1-1-1ii−i−i−i−iiii−i−ii−iii−i
χ1611-1-11-111-1-1-1-11111-1-1-1-1-1111-1-111-1-1-1-11111-11-11-111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-1-1111111-1-1-1-1−i−iiiii−i−i−iii−ii−i−ii
χ17222222222222222-22-2-20000-22222-2-2-2-2-2-2-2-200000022-2-222-2-2000000000000000000000000000000000000000000222200-2-20000
χ18222222222222222-22-2-20000-22222-2-2-2-2-2-2-2-200000022-2-222-2-2000000000000000000000000000000000000000000-2-2-2-200220000
χ1922222222222222-22-22-20000-22222-2-2-2-2-2-2-2-2000000-2-222-2-2220000000000000000000000000000000000000022220000-2-2000000
χ2022222222222222-22-22-20000-22222-2-2-2-2-2-2-2-2000000-2-222-2-22200000000000000000000000000000000000000-2-2-2-2000022000000
χ2122222222222222-2-2-2-222222222222222222200-2-200-2-2-2-2-2-2-2-200000000000000002222222200-2-2-2-2000000000000000000000000
χ2222222222222222-2-2-2-22-2-2-2-22222222222222002200-2-2-2-2-2-2-2-20000000000000000-2-2-2-2-2-2-2-2002222000000000000000000000000
χ23222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+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+52−1−52−1−520000000000000000
χ24222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-222-2-2−1+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+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+520000000000000000
χ25222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222222-2-2-2-22−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222-2-222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+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+52-2-21−521+521−521+521−521−521+521+521−521−521+521+520000000000000000
χ26222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222222-2-2-2-22−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-2-2-2-2−1+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+521−521−521+521+521−521−521+521+52221−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000000000000000
χ27222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-2222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200-2-2001−521+521−521+521−521+521−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52001−521+521−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ180000000000000000
χ28222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-2222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200-2-2001−521+521−521+521−521+521−521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52001−521+521−521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ180000000000000000
χ29222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-22-2-2-2-22−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520022001−521+521−521+521−521+521−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−521−521+521+521−521−521+521+5200−1+52−1−52−1+52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ180000000000000000
χ30222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-22-2-2-2-22−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520022001−521+521−521+521−521+521−521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ181−521−521+521+521−521−521+521+5200−1+52−1−52−1+52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ180000000000000000
χ31222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+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+520000000000000000
χ32222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-222-2-2−1−52−1+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+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−520000000000000000
χ33222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222222-2-2-2-22−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5222-2-222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52-2-21+521−521+521−521+521+521−521−521+521+521−521−520000000000000000
χ34222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222222-2-2-2-22−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-2-2-2-2−1−52−1+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+521−521−521+521+521−521−521+521+521−521−52221+521−521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000000000000000
χ35222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-2-2-2222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200-2-2001+521−521+521−521+521−521+521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52001+521−521+521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ140000000000000000
χ36222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-2-2-2222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200-2-2001+521−521+521−521+521−521+521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52001+521−521+521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ140000000000000000
χ37222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-2-2-22-2-2-2-22−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520022001+521−521+521−521+521−521+521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ141+521+521−521−521+521+521−521−5200−1−52−1+52−1−52−1+52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ140000000000000000
χ38222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-2-2-22-2-2-2-22−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520022001+521−521+521−521+521−521+521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ141+521+521−521−521+521+521−521−5200−1−52−1+52−1−52−1+52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ140000000000000000
χ3922-2-22-222-2-2-2-2222-2-2220000-2-2-2222222-2-2-2-200000022-2-2-2-2220000000000000000000000000000000000000000002i2i−2i−2i00−2i2i0000
χ4022-2-22-222-2-2-2-2222-2-2220000-2-2-2222222-2-2-2-200000022-2-2-2-222000000000000000000000000000000000000000000−2i−2i2i2i002i−2i0000
χ4122-2-22-222-2-2-2-222-222-220000-2-2-2222222-2-2-2-2000000-2-22222-2-2000000000000000000000000000000000000002i2i−2i−2i0000−2i2i000000
χ4222-2-22-222-2-2-2-222-222-220000-2-2-2222222-2-2-2-2000000-2-22222-2-200000000000000000000000000000000000000−2i−2i2i2i00002i−2i000000
χ4322-2-22-222-2-2-2-222-2-222-222-2-22-2-222-2-2-2-2222200-2200-2-2-2-2222200000000000000002222-2-2-2-200-2-222000000000000000000000000
χ4422-2-22-222-2-2-2-222-2-222-2-2-2222-2-222-2-2-2-22222002-200-2-2-2-222220000000000000000-2-2-2-222220022-2-2000000000000000000000000
χ4522-2-22-2−1+52−1−521−521−521+521+52−1+52−1−5222-2-2-222-2-221−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−522-22-22-2−1+52−1−52−1+52−1−521−521+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+52−1+52−1+52−1−52−1−521−521−521+521+522-2−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+520000000000000000
χ4622-2-22-2−1+52−1−521−521−521+521+52−1+52−1−5222-2-2-222-2-221−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52-222-2-22−1+52−1−52−1+52−1−521−521+521−521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+52-22−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−520000000000000000
χ4722-2-22-2−1+52−1−521−521−521+521+52−1+52−1−5222-2-2-2-2-22221−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−522-2-222-2−1+52−1−52−1+52−1−521−521+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+521−521−521+521+52−1+52−1+52−1−52−1−52-221−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−520000000000000000
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χ1028-8-8800−2+25−2−252−25−2+252+25−2−252−252+2500000−4i4i4i−4i00000000000000000000000000000000000000000002ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7000000000000000000000000000000
χ1038-8-8800−2−25−2+252+25−2−252−25−2+252+252−25000004i−4i−4i4i0000000000000000000000000000000000000000000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ19000000000000000000000000000000
χ1048-8-8800−2−25−2+252+25−2−252−25−2+252+252−2500000−4i4i4i−4i00000000000000000000000000000000000000000002ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ19−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19000000000000000000000000000000

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