Finite Group Databasebeta

← Group #12015413

Character table — Group #12015413

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11222222222222222224444444444444444444444444448888888888888888888888161616161616161616161616161616161616161640404040404040404040404040404040
order122224444558810102020202044448881010101010102020202020204040404040404040882020202020202020404040404040404040404040448820202020202020204040404040404040222244441616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911-1-11-111-111-1-111111111-1-111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-11111-1-1-1-11111i−ii−iiiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ1011-1-11-111-111-1-111111111-1-111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-11111-1-1-1-11111i−ii−iiiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ1111-1-11-111-111-1-111111111-1-111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-11111-1-1-1-11111−ii−ii−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ1211-1-11-111-111-1-111111111-1-111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-11111-1-1-1-11111−ii−ii−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ1311-1-11-111-111-1-1111111-1-11111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111111111i−i−iiiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ1411-1-11-111-111-1-1111111-1-11111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111111111i−i−iiiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ1511-1-11-111-111-1-1111111-1-11111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111111111−iii−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ1611-1-11-111-111-1-1111111-1-11111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111111111−iii−i−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1722222222222-2-22222222222-2-2-2222222222222-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ1822222222222-2-2222222-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000
χ19222222222−1+52−1−5222−1+52−1−52−1+52−1+52−1−52−1−522222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+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+52−1−52−1−52−1+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+52−1−52−1−520000000000000000
χ20222222222−1+52−1−5222−1+52−1−52−1+52−1+52−1−52−1−522222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+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+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-2-21−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+520000000000000000
χ21222222222−1+52−1−5222−1+52−1−52−1+52−1+52−1−52−1−52-2-2-2-2222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+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+52−1+52−1+52−1−52−1−5222-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+520000000000000000
χ22222222222−1+52−1−5222−1+52−1−52−1+52−1+52−1−52−1−52-2-2-2-2222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+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+52−1+52−1+52−1−52−1−52-2-2221−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000000000000000
χ23222222222−1+52−1−52-2-2−1+52−1−52−1+52−1+52−1−52−1−522222-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521−521−521+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+521−521−521+521+520000ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ360000000000000000
χ24222222222−1+52−1−52-2-2−1+52−1−52−1+52−1+52−1−52−1−522222-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521−521−521+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+521−521−521+521+520000−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ360000000000000000
χ25222222222−1+52−1−52-2-2−1+52−1−52−1+52−1+52−1−52−1−52-2-2-2-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+52221−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+520000ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ360000000000000000
χ26222222222−1+52−1−52-2-2−1+52−1−52−1+52−1+52−1−52−1−52-2-2-2-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+52221−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+520000−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ360000000000000000
χ27222222222−1−52−1+5222−1−52−1+52−1−52−1−52−1+52−1+522222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+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+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+520000000000000000
χ28222222222−1−52−1+5222−1−52−1+52−1−52−1−52−1+52−1+522222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+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+52−1−52−1−52−1+52−1+52-2-2-2-21+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−520000000000000000
χ29222222222−1−52−1+5222−1−52−1+52−1−52−1−52−1+52−1+52-2-2-2-2222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+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+521−521−52−1−52−1−52−1+52−1+5222-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−520000000000000000
χ30222222222−1−52−1+5222−1−52−1+52−1−52−1−52−1+52−1+52-2-2-2-2222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+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+521−521−52−1−52−1−52−1+52−1+52-2-2221+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000000000000000
χ31222222222−1−52−1+52-2-2−1−52−1+52−1−52−1−52−1+52−1+522222-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+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+521−521−521+521+521−521−520000−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ280000000000000000
χ32222222222−1−52−1+52-2-2−1−52−1+52−1−52−1−52−1+52−1+522222-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+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+521−521−521+521+521−521−520000ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ280000000000000000
χ33222222222−1−52−1+52-2-2−1−52−1+52−1−52−1−52−1+52−1+52-2-2-2-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+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+521+521+521−521−520000−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ280000000000000000
χ34222222222−1−52−1+52-2-2−1−52−1+52−1−52−1−52−1+52−1+52-2-2-2-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+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+521+521+521−521−520000ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ280000000000000000
χ35222-2-222-2-2222222-2-2-2-200002-2-222-2-2-2-22222-2-222-2-222-2-20000000000000000002-22-20000000000000000000000002i−2i2i−2i00000000
χ36222-2-222-2-2222222-2-2-2-200002-2-222-2-2-2-22222-2-222-2-222-2-20000000000000000002-22-2000000000000000000000000−2i2i−2i2i00000000
χ37222-2-222-2-222-2-222-2-2-2-20000-22222-2-2-2-22222-2-2-2-222-2-222000000000000000000-22-22000000000000000000002-22-2000000000000
χ38222-2-222-2-222-2-222-2-2-2-20000-22222-2-2-2-22222-2-2-2-222-2-222000000000000000000-22-2200000000000000000000-22-22000000000000
χ39222-2-2-2-22222002222222i−2i2i−2i00022-2-2-2-2-2-2-2-22200000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000i2−i2i2−i22−22−2
χ40222-2-2-2-22222002222222i−2i2i−2i00022-2-2-2-2-2-2-2-22200000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000−i2i2−i2i2−22−22
χ41222-2-2-2-2222200222222−2i2i−2i2i00022-2-2-2-2-2-2-2-2220000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000i2−i2i2−i2−22−22
χ42222-2-2-2-2222200222222−2i2i−2i2i00022-2-2-2-2-2-2-2-2220000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000−i2i2−i2i22−22−2
χ4322-22-22-22-222002222222i−2i−2i2i000-2-2-2-22222-2-2-2-200000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000000000002−2−22−i2i2i2−i2
χ4422-22-22-22-222002222222i−2i−2i2i000-2-2-2-22222-2-2-2-200000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000−222−2i2−i2−i2i2
χ4522-22-22-22-22200222222−2i2i2i−2i000-2-2-2-22222-2-2-2-20000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000000000002−2−22i2−i2−i2i2
χ4622-22-22-22-22200222222−2i2i2i−2i000-2-2-2-22222-2-2-2-20000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000−222−2−i2i2i2−i2
χ4722-22-2-22-22222222-2-2-2-20000-22-2-2-2-2-222-2-2222222-2-222-2-2000000000000000000-22-22000000000000000000002-2-22000000000000
χ4822-22-2-22-22222222-2-2-2-20000-22-2-2-2-2-222-2-2222222-2-222-2-2000000000000000000-22-2200000000000000000000-222-2000000000000
χ4922-22-2-22-2222-2-222-2-2-2-200002-22-2-2-2-222-2-22222-2-222-2-2220000000000000000002-22-20000000000000000000000002i−2i−2i2i00000000
χ5022-22-2-22-2222-2-222-2-2-2-200002-22-2-2-2-222-2-22222-2-222-2-2220000000000000000002-22-2000000000000000000000000−2i2i2i−2i00000000
χ5122-2-22-222-2222222222222-2-2-2-22-2-222-2-2-2-222-2-222222222-222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ5222-2-22-222-22222222222-2-222-2-22-2-222-2-2-2-222-2-2222222222-2-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000
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χ1008-80000000−2+25−2−25−42422−252+254ζ22−4ζ38−4ζ22+4ζ38−4ζ6+4ζ144ζ6−4ζ1400000000000000000002ζ7−2ζ13+2ζ23−2ζ37−2ζ7+2ζ13−2ζ23+2ζ372ζ7−2ζ13−2ζ23+2ζ37−2ζ7+2ζ13+2ζ23−2ζ37−2ζ21−2ζ29+2ζ31+2ζ392ζ21+2ζ29−2ζ31−2ζ39−2ζ21+2ζ29−2ζ31+2ζ392ζ21−2ζ29+2ζ31−2ζ390000000000000000000000000000000000000000000000000000000000
χ1018-80000000−2−25−2+2542−422+252−254ζ6−4ζ14−4ζ6+4ζ144ζ22−4ζ38−4ζ22+4ζ3800000000000000000002ζ21+2ζ29−2ζ31−2ζ39−2ζ21−2ζ29+2ζ31+2ζ39−2ζ21+2ζ29−2ζ31+2ζ392ζ21−2ζ29+2ζ31−2ζ39−2ζ7+2ζ13−2ζ23+2ζ372ζ7−2ζ13+2ζ23−2ζ37−2ζ7+2ζ13+2ζ23−2ζ372ζ7−2ζ13−2ζ23+2ζ370000000000000000000000000000000000000000000000000000000000
χ1028-80000000−2−25−2+2542−422+252−25−4ζ6+4ζ144ζ6−4ζ14−4ζ22+4ζ384ζ22−4ζ3800000000000000000002ζ21+2ζ29−2ζ31−2ζ39−2ζ21−2ζ29+2ζ31+2ζ392ζ21−2ζ29+2ζ31−2ζ39−2ζ21+2ζ29−2ζ31+2ζ39−2ζ7+2ζ13−2ζ23+2ζ372ζ7−2ζ13+2ζ23−2ζ372ζ7−2ζ13−2ζ23+2ζ37−2ζ7+2ζ13+2ζ23−2ζ370000000000000000000000000000000000000000000000000000000000
χ1038-80000000−2−25−2+25−42422+252−254ζ6−4ζ14−4ζ6+4ζ144ζ22−4ζ38−4ζ22+4ζ380000000000000000000−2ζ21−2ζ29+2ζ31+2ζ392ζ21+2ζ29−2ζ31−2ζ392ζ21−2ζ29+2ζ31−2ζ39−2ζ21+2ζ29−2ζ31+2ζ392ζ7−2ζ13+2ζ23−2ζ37−2ζ7+2ζ13−2ζ23+2ζ372ζ7−2ζ13−2ζ23+2ζ37−2ζ7+2ζ13+2ζ23−2ζ370000000000000000000000000000000000000000000000000000000000
χ1048-80000000−2−25−2+25−42422+252−25−4ζ6+4ζ144ζ6−4ζ14−4ζ22+4ζ384ζ22−4ζ380000000000000000000−2ζ21−2ζ29+2ζ31+2ζ392ζ21+2ζ29−2ζ31−2ζ39−2ζ21+2ζ29−2ζ31+2ζ392ζ21−2ζ29+2ζ31−2ζ392ζ7−2ζ13+2ζ23−2ζ37−2ζ7+2ζ13−2ζ23+2ζ37−2ζ7+2ζ13+2ζ23−2ζ372ζ7−2ζ13−2ζ23+2ζ370000000000000000000000000000000000000000000000000000000000

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