Finite Group Databasebeta

← Group #12157356

Character table — Group #12157356

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110
size111111112222222222222222222244444444448888888888888888888888888888888888816161616161616161616161616161616162020202020202020202040404040404040404080
order1222222244445510101010101010101010101010104420202020202020204444444888820202020202020204040404040404040404040404040404042020202020202020202020202020202022444444444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1111-1-1-1-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111111
χ5111111111111111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-111111-1-1-1-1-1-11
χ6111111111111111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1111111-1
χ7111111111111111111111111111111111111111-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11-1-11111-1
χ8111111111111111111111111111111111111111-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-111-1-1-1-11
χ91111111111111111111111111111-1-111111111-111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-11111-1-1-1
χ101111111111111111111111111111-1-111111111-111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11-1-1-1-1111
χ111111111111111111111111111111-1-111111111-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1111
χ121111111111111111111111111111-1-111111111-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-11111-1-1-1-1111111111-1-111-1-1-1
χ131111111111111111111111111111-1-111111111-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11111-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1-111-1
χ141111111111111111111111111111-1-111111111-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-11
χ151111111111111111111111111111-1-111111111-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-111-1-11
χ161111111111111111111111111111-1-111111111-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-111-1
χ17222222222222−1+52−1−52−1+52−1+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+52−1−52−1−5222222222222−1+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+52−1−52−1−52−1−52−1−522−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000000000000000
χ18222222222222−1+52−1−52−1+52−1+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+52−1−52−1−5222222-2-2-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+52-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+5200000000000000000000
χ19222222222222−1+52−1−52−1+52−1+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+52−1−52−1−522-2-2-2-222-2-2-2-2−1+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+5221−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000000000000000
χ20222222222222−1+52−1−52−1+52−1+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+52−1−52−1−522-2-2-2-2-2-22222−1+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+52−1−52−1−52−1−52−1−52-21−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+5200000000000000000000
χ21222222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-222-2-22222-2-21−521−521+521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+52-21−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+5200000000000000000000
χ22222222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-222-2-2-2-2-2-2221−521−521+521+521−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5221−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−5200000000000000000000
χ23222222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-22222-2-2221−521−521+521+521−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+5200000000000000000000
χ24222222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-222-2-222-2-21−521−521+521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+522−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−5200000000000000000000
χ25222222222222−1−52−1+52−1−52−1−52−1+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+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+522−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000000000000000000
χ26222222222222−1−52−1+52−1−52−1−52−1+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+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+521−521−521−521−521+521+521+521+521−521−521−521−52-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−5200000000000000000000
χ27222222222222−1−52−1+52−1−52−1−52−1+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+522-2-2-2-222-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−5221+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000000000000000000
χ28222222222222−1−52−1+52−1−52−1−52−1+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+522-2-2-2-2-2-22222−1−52−1−52−1+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+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-21+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−5200000000000000000000
χ29222222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-222-2-22222-2-21+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+521−521−521−521−52-21+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−5200000000000000000000
χ30222222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-222-2-2-2-2-2-2221+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+5221+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+5200000000000000000000
χ31222222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-22222-2-2221+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+52-2−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−5200000000000000000000
χ32222222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-222-2-222-2-21+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+521−521−521−521−522−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+5200000000000000000000
χ3322222222-2-2-2-2222222222222222222-2-2-2-2-2-2-2-2-200000000002222-2-2-2-200000000000000000000000000000000022-2-200002200-20000000
χ3422222222-2-2-2-2222222222222222222-2-2-2-2-2-2-2-2-200000000002222-2-2-2-2000000000000000000000000000000000-2-2220000-2-20020000000
χ3522222222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-220000000000-2-2-2-2222200000000000000000000000000000000022-2-20000-2-20020000000
χ3622222222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-220000000000-2-2-2-22222000000000000000000000000000000000-2-22200002200-20000000
χ3722-22-22-2-222-2-2222-22-22-22-222-2-2-2-2002222-2-2-2-20002-200000000000000000000000000000002-22-20000000000002-22-222-2-2000000000000
χ3822-22-22-2-222-2-2222-22-22-22-222-2-2-2-2002222-2-2-2-20002-200000000000000000000000000000002-22-2000000000000-22-22-2-222000000000000
χ3922-22-22-2-222-2-2222-22-22-22-222-2-2-2-2002222-2-2-2-2000-220000000000000000000000000000000-22-220000000000002-22-2-2-222000000000000
χ4022-22-22-2-222-2-2222-22-22-22-222-2-2-2-2002222-2-2-2-2000-220000000000000000000000000000000-22-22000000000000-22-2222-2-2000000000000
χ4122-22-22-2-2-2-222222-22-22-22-222-2-2-2-200-2-2-2-2222202i−2i00000000000000000000000000000000000002i−2i2i−2i000000002-2-220000000002i−2i00000
χ4222-22-22-2-2-2-222222-22-22-22-222-2-2-2-200-2-2-2-2222202i−2i00000000000000000000000000000000000002i−2i2i−2i00000000-222-2000000000−2i2i00000
χ4322-22-22-2-2-2-222222-22-22-22-222-2-2-2-200-2-2-2-222220−2i2i0000000000000000000000000000000000000−2i2i−2i2i000000002-2-22000000000−2i2i00000
χ4422-22-22-2-2-2-222222-22-22-22-222-2-2-2-200-2-2-2-222220−2i2i0000000000000000000000000000000000000−2i2i−2i2i00000000-222-20000000002i−2i00000
χ452-2222-2-2-22-2-2222-2-2-2-22222-2-222-2-2002-22-22-22-2000002i−2i00000000000000000000000000000000000002i−2i2i−2i000000002i−2i2i−2i0000000002-20
χ462-2222-2-2-22-2-2222-2-2-2-22222-2-222-2-2002-22-22-22-2000002i−2i00000000000000000000000000000000000002i−2i2i−2i00000000−2i2i−2i2i000000000-220
χ472-2222-2-2-22-2-2222-2-2-2-22222-2-222-2-2002-22-22-22-200000−2i2i0000000000000000000000000000000000000−2i2i−2i2i000000002i−2i2i−2i000000000-220
χ482-2222-2-2-22-2-2222-2-2-2-22222-2-222-2-2002-22-22-22-200000−2i2i0000000000000000000000000000000000000−2i2i−2i2i00000000−2i2i−2i2i0000000002-20
χ492-2-22-2-2222-22-222-22-222-22-2-2-2-2-222002-22-2-22-220000000002i−2i00000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000000002i−2i−2i2i002-200000000
χ502-2-22-2-2222-22-222-22-222-22-2-2-2-2-222002-22-2-22-220000000002i−2i00000000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000−2i2i2i−2i00-2200000000
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χ522-2-22-2-2222-22-222-22-222-22-2-2-2-2-222002-22-2-22-22000000000−2i2i0000000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000−2i2i2i−2i002-200000000
χ5344444444-4-4-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1+5−1−5−1−5−1+5−1−5−1+5−1−5−1+5−1−5441−51−51+51+51−51−51+51+5-40000000000−1+5−1+5−1−5−1−51−51−51+51+500000000000000000000000000000000000000000000000000000
χ5444444444-4-4-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1+5−1−5−1−5−1+5−1−5−1+5−1−5−1+5−1−5-4-41−51−51+51+51−51−51+51+5400000000001−51−51+51+5−1+5−1+5−1−5−1−500000000000000000000000000000000000000000000000000000
χ5544444444-4-4-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1−5−1+5−1+5−1−5−1+5−1−5−1+5−1−5−1+5441+51+51−51−51+51+51−51−5-40000000000−1−5−1−5−1+5−1+51+51+51−51−500000000000000000000000000000000000000000000000000000
χ5644444444-4-4-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1−5−1+5−1+5−1−5−1+5−1−5−1+5−1−5−1+5-4-41+51+51−51−51+51+51−51−5400000000001+51+51−51−5−1−5−1−5−1+5−1+500000000000000000000000000000000000000000000000000000
χ57444-4-4-4-440000444-44-4-4-4-4-4-4-4444400000000000000000000000000000000000000000000000000000000000000000000004i−4i0000000000
χ58444-4-4-4-440000444-44-4-4-4-4-4-4-444440000000000000000000000000000000000000000000000000000000000000000000000−4i4i0000000000
χ5944-44-44-4-444-4-4−1+5−1−5−1+51−5−1−51+5−1+51−5−1−51+5−1+5−1−51−51+51−51+500−1+5−1+5−1−5−1−51−51−51+51+50004-40000000000000000000000000000000−1+51−5−1−51+500000000000000000000000000000000
χ6044-44-44-4-444-4-4−1+5−1−5−1+51−5−1−51+5−1+51−5−1−51+5−1+5−1−51−51+51−51+500−1+5−1+5−1−5−1−51−51−51+51+5000-4400000000000000000000000000000001−5−1+51+5−1−500000000000000000000000000000000
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Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.