Finite Group Databasebeta

← Group #12083289

Character table — Group #12083289

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110
size1111222222222222222244444444444444444444444444488888888888888888888881010101010101010101016161616161616161616161620202020202020202020203232323280808080
order1222444455888810101010101022444888888202020202020202040404040404040401010101020202020202040404040404040404040404044444488882488404040404040404024444888888101020204488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-11-1-1-1-1111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1111111-1-1
χ611111111111111111111-1-1-1-11-1-1-1-1111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111
χ711111111111111111111-1-1-1-11-1-1-1-1111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-111
χ811111111111111111111-1-1-1-11-1-1-1-1111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-11111-1-11111-1-1-1-111-1-1
χ91111111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-11-11111-1-1-1-111111-1-1-1-1-1-111-1-11-11-1
χ101111111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11-11-1-1-1-1111111111-1-1-1-1-1-1-1-111-11-11
χ111111111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-11111-1-1-1-1-1-1-1-1-111111111-1-1-11-11
χ121111111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11-1-1-1-11111-1-1-1-1-1111111-1-1111-11-1
χ131111111111-1-1-1-1111111-1-1-1-111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-11-1-11-1-1-1-111111-1-1-1-1-1-1111111-1-11-1-11
χ141111111111-1-1-1-1111111-1-1-1-111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-111-11111-1-1-1-11-1-1-1-1-1-11111-1-111-111-1
χ151111111111-1-1-1-1111111-1-1-1-111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111-1-11-1-1-1-11111-1111111-1-1-1-111-1-1-111-1
χ161111111111-1-1-1-1111111-1-1-1-111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-111-11111-1-1-1-1-1111111-1-1-1-1-1-1111-1-11
χ1722222222−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−5222222222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200000000002222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000000−1+52−1−52−1+52−1−520000
χ1822222222−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−5222222222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−520000000000-2-2-2-21−521−521+521+521−521−521+521+52000000000001−521+521−521+520000
χ1922222222−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−52-2-2-2-22-2-2-2-222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+52000000000022-2-21−521−521+521+521−521−521+521+5200000000000−1+52−1−52−1+52−1−520000
χ2022222222−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−52-2-2-2-22-2-2-2-222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+520000000000-2-222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000001−521+521−521+520000
χ2122222222−1+52−1−52-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−5222222-2-2-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+5200000000002-22-2−1+52−1+52−1−52−1−521−521−521+521+5200000000000−1+52−1−521−521+520000
χ2222222222−1+52−1−52-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−5222222-2-2-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+520000000000-22-221−521−521+521+52−1+52−1+52−1−52−1−52000000000001−521+52−1+52−1−520000
χ2322222222−1+52−1−52-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52-2-2-2-222222-2-2−1+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+52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200000000002-2-221−521−521+521+52−1+52−1+52−1−52−1−5200000000000−1+52−1−521−521+520000
χ2422222222−1+52−1−52-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52-2-2-2-222222-2-2−1+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+52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−520000000000-222-2−1+52−1+52−1−52−1−521−521−521+521+52000000000001−521+52−1+52−1−520000
χ2522222222−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1+5222222222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200000000002222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000000000−1−52−1+52−1−52−1+520000
χ2622222222−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1+5222222222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+520000000000-2-2-2-21+521+521−521−521+521+521−521−52000000000001+521−521+521−520000
χ2722222222−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1+52-2-2-2-22-2-2-2-222−1−52−1+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+521+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−52000000000022-2-21+521+521−521−521+521+521−521−5200000000000−1−52−1+52−1−52−1+520000
χ2822222222−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1+52-2-2-2-22-2-2-2-222−1−52−1+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+521+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−520000000000-2-222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000001+521−521+521−520000
χ2922222222−1−52−1+52-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+5222222-2-2-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−5200000000002-22-2−1−52−1−52−1+52−1+521+521+521−521−5200000000000−1−52−1+521+521−520000
χ3022222222−1−52−1+52-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+5222222-2-2-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−520000000000-22-221+521+521−521−52−1−52−1−52−1+52−1+52000000000001+521−52−1−52−1+520000
χ3122222222−1−52−1+52-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52-2-2-2-222222-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−521+521+521−521−52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200000000002-2-221+521+521−521−52−1−52−1−52−1+52−1+5200000000000−1−52−1+521+521−520000
χ3222222222−1−52−1+52-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52-2-2-2-222222-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−521+521+521−521−52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+520000000000-222-2−1−52−1−52−1+52−1+521+521+521−521−52000000000001+521−52−1−52−1+520000
χ3322222-2-2222000022222222-2-2-200000022-2-2-2-222000000002222-2-2-2-2-2-200000000000022-2-2-2-20000000000000000222-2-200000000000000
χ3422222-2-2222000022222222-2-2-200000022-2-2-2-222000000002222-2-2-2-2-2-2000000000000-2-222220000000000000000-2-2-22200000000000000
χ3522222-2-22220000222222-2-222-200000022-2-2-2-22200000000-2-2-2-2-2-2222200000000000022-2-2-2-200000000000000002-2-22200000000000000
χ3622222-2-22220000222222-2-222-200000022-2-2-2-22200000000-2-2-2-2-2-22222000000000000-2-222220000000000000000-222-2-200000000000000
χ372222-222-22222222222220000-20000-2-2-2-22222-2-2222222220000-2-20000-2-2-2-20000000022-2-2222222000000000000-20000-2-2000000000000
χ382222-222-22222222222220000-20000-2-2-2-22222-2-2222222220000-2-20000-2-2-2-200000000-2-222-2-2-2-2-2-20000000000002000022000000000000
χ392222-222-222-2-2-2-22222220000-2000022-2-22222-2-2-2-2-2-2-2-2-2-20000-2-2000022220000000022-2-222-2-2-2-2000000000000-2000022000000000000
χ402222-222-222-2-2-2-22222220000-2000022-2-22222-2-2-2-2-2-2-2-2-2-20000-2-20000222200000000-2-222-2-2222200000000000020000-2-2000000000000
χ412222-2-2-2-2220000222222000022i2i−2i−2i00-2-2-2-2-2-2-2-200000000000022000000002i2i−2i−2i2i2i−2i−2i2222-2-20000000000000000-20000002i2i−2i−2i00000000
χ422222-2-2-2-2220000222222000022i2i−2i−2i00-2-2-2-2-2-2-2-200000000000022000000002i2i−2i−2i2i2i−2i−2i-2-2-2-22200000000000000002000000−2i−2i2i2i00000000
χ432222-2-2-2-222000022222200002−2i−2i2i2i00-2-2-2-2-2-2-2-20000000000002200000000−2i−2i2i2i−2i−2i2i2i2222-2-20000000000000000-2000000−2i−2i2i2i00000000
χ442222-2-2-2-222000022222200002−2i−2i2i2i00-2-2-2-2-2-2-2-20000000000002200000000−2i−2i2i2i−2i−2i2i2i-2-2-2-222000000000000000020000002i2i−2i−2i00000000
χ4522-2-2200-22222−2−2-2-2-2-2222-20002−22−22−2-2-200002222−2−222−2−22-22-20000002−22−22−22−22−22−2002i−2i2i−2ii2i2−i2−i20000000000000002i−2ii2−i2i2−i2i2−i200000000
χ4622-2-2200-22222−2−2-2-2-2-2222-20002−22−22−2-2-200002222−2−222−2−22-22-20000002−22−22−22−22−22−200−2i2i−2i2i−i2−i2i2i2000000000000000−2i2i−i2i2−i2i2−i2i200000000
χ4722-2-2200-22222−2−2-2-2-2-222-22000−22−222−2-2-200002222−2−222−2−2-22-220000002−22−2−22−22−22−22002i−2i2i−2ii2i2−i2−i2000000000000000−2i2ii2−i2−i2i2−i2i200000000
χ4822-2-2200-22222−2−2-2-2-2-222-22000−22−222−2-2-200002222−2−222−2−2-22-220000002−22−2−22−22−22−2200−2i2i−2i2i−i2−i2i2i20000000000000002i−2i−i2i2i2−i2i2−i200000000
χ4922-2-2200-222−2−222-2-2-2-2222-2000−22−22−22-2-2000022−2−222−2−2222-22-2000000−22−22−22−22−22−22002i−2i2i−2i−i2−i2i2i20000000000000002i−2i−i2i2−i2i2−i2i200000000
χ5022-2-2200-222−2−222-2-2-2-2222-2000−22−22−22-2-2000022−2−222−2−2222-22-2000000−22−22−22−22−22−2200−2i2i−2i2ii2i2−i2−i2000000000000000−2i2ii2−i2i2−i2i2−i200000000
χ5122-2-2200-222−2−222-2-2-2-222-220002−22−2−22-2-2000022−2−222−2−222-22-22000000−22−222−22−22−22−2002i−2i2i−2i−i2−i2i2i2000000000000000−2i2i−i2i2i2−i2i2−i200000000
χ5222-2-2200-222−2−222-2-2-2-222-220002−22−2−22-2-2000022−2−222−2−222-22-22000000−22−222−22−22−22−200−2i2i−2i2ii2i2−i2−i20000000000000002i−2ii2−i2−i2i2−i2i200000000
χ5322-2-2-20022222−2−2-2-2-2-222002i−2i0i2−i2−i2i2−22220000-2-222−2−222−2−20000002i−2i2i−2i−22−22i2−i2−i2i2i2−i2−i2i2002i−2i−2i2i−i2−i2i2i200000000000002-200i2−i2−222−200000000
χ5422-2-2-20022222−2−2-2-2-2-222002i−2i0i2−i2−i2i2−22220000-2-222−2−222−2−20000002i−2i2i−2i−22−22i2−i2−i2i2i2−i2−i2i200−2i2i2i−2ii2i2−i2−i20000000000000-2200−i2i22−2−2200000000
χ5522-2-2-20022222−2−2-2-2-2-22200−2i2i0−i2i2i2−i2−22220000-2-222−2−222−2−2000000−2i2i−2i2i−22−22−i2i2i2−i2−i2i2i2−i2002i−2i−2i2i−i2−i2i2i20000000000000-2200i2−i22−2−2200000000
χ5622-2-2-20022222−2−2-2-2-2-22200−2i2i0−i2i2i2−i2−22220000-2-222−2−222−2−2000000−2i2i−2i2i−22−22−i2i2i2−i2−i2i2i2−i200−2i2i2i−2ii2i2−i2−i200000000000002-200−i2i2−222−200000000
χ5722-2-2-200222−2−222-2-2-2-222002i−2i0−i2i2i2−i22−2220000-2-2−2−222−2−2220000002i−2i2i−2i2−22−2−i2i2i2−i2−i2i2i2−i2002i−2i−2i2ii2i2−i2−i200000000000002-200−i2i22−2−2200000000
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χ1014-4-440000442i2−2i2−2i22i244-4-4-4-400000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000004i−4i000022−22−22220000000000000000000000000000000
χ1024-4-440000442i2−2i2−2i22i244-4-4-4-400000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000−4i4i0000−222222−220000000000000000000000000000000
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χ1078-8-880000−2+25−2−254i2−4i2−4i24i2−2+25−2−252−252+252−252+2500000000000000000002ζ7+2ζ13+2ζ23+2ζ37−2ζ7−2ζ13−2ζ23−2ζ37−2ζ7−2ζ13−2ζ23−2ζ372ζ7+2ζ13+2ζ23+2ζ372ζ21+2ζ29+2ζ31+2ζ39−2ζ21−2ζ29−2ζ31−2ζ39−2ζ21−2ζ29−2ζ31−2ζ392ζ21+2ζ29+2ζ31+2ζ39000000000000000000000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.