Finite Group Databasebeta

← Group #12128025

Character table — Group #12128025

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size112222222222244444444444444558888888888888810101010101010161616161616161616161616161616161616161616161616161616164040404040404040404040404040
order1222244445510101010101010102020202020202020444488888888888822224442020202040404040404040404040404040404040404040404040404022888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111-1-111-1-111-1-111-1-11111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-1
χ611111111111111111111111111111-1-111-1-1-1-111-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-1-111
χ711111111111111111111111111111-1-1-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ811111111111111111111111111111-1-1-1-111-1-11111-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1
χ9111111111111111111111111111-1-111111111111111-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ10111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ11111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ12111111111111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1
χ13111111111111111111111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111
χ14111111111111111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-111-1-1
χ15111111111111111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ16111111111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-111
χ17222222222−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−5200222222222222220000000−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000000000
χ18222222222−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−5200222222-2-2-2-2-2-2-2-20000000−1+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+521−521−521+521+521−521−521+521+5200000000000000
χ19222222222−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−520022-2-2-2-22222-2-2-2-20000000−1+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+52−1−52−1−521−521−521+521+521−521−521+521+5200000000000000
χ20222222222−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−520022-2-2-2-2-2-2-2-222220000000−1+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+52−1−52−1−5200000000000000
χ21222222222−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−5200-2-222-2-222-2-222-2-200000001−521−521+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+5200000000000000
χ22222222222−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−5200-2-222-2-2-2-222-2-22200000001−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−5200000000000000
χ23222222222−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−5200-2-2-2-22222-2-2-2-22200000001−521−521+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+52−1+52−1+52−1−52−1−5200000000000000
χ24222222222−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−5200-2-2-2-222-2-22222-2-200000001−521−521+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+5200000000000000
χ25222222222−1−52−1+52−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+5200222222222222220000000−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000000000000
χ26222222222−1−52−1+52−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+5200222222-2-2-2-2-2-2-2-20000000−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−5200000000000000
χ27222222222−1−52−1+52−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+520022-2-2-2-22222-2-2-2-20000000−1−52−1−52−1+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+521+521+521−521−521+521+521−521−5200000000000000
χ28222222222−1−52−1+52−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+520022-2-2-2-2-2-2-2-222220000000−1−52−1−52−1+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+5200000000000000
χ29222222222−1−52−1+52−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+5200-2-222-2-222-2-222-2-200000001+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+521−521−5200000000000000
χ30222222222−1−52−1+52−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+5200-2-222-2-2-2-222-2-22200000001+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+521+521+521−521−52−1−52−1−52−1+52−1+5200000000000000
χ31222222222−1−52−1+52−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+5200-2-2-2-22222-2-2-2-22200000001+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+521−521−52−1−52−1−52−1+52−1+5200000000000000
χ32222222222−1−52−1+52−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+5200-2-2-2-222-2-22222-2-200000001+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+521−521−5200000000000000
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χ7944-44-4-44-44−1−5−1+5−1−5−1+51+5−1−51+51−5−1+51−51+51−5−1−51+5−1−5−1+51−5−1+5000000004-40000000000000000000000000−1−51+5−1+51−500000000000000000000000000
χ8044-44-4-44-44−1−5−1+5−1−5−1+51+5−1−51+51−5−1+51−51+51−5−1−51+5−1−5−1+51−5−1+500000000-4400000000000000000000000001+5−1−51−5−1+500000000000000000000000000
χ8144-4-444-4-44−1+5−1−5−1+5−1−51−51−5−1+51+51+5−1−5−1+5−1−51−51−5−1+51+51+5−1−500004i−4i000000000000000000000−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ70000000000000000000000000000000000
χ8244-4-444-4-44−1+5−1−5−1+5−1−51−51−5−1+51+51+5−1−5−1+5−1−51−51−5−1+51+51+5−1−50000−4i4i0000000000000000000002ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ70000000000000000000000000000000000
χ8344-4-444-4-44−1−5−1+5−1−5−1+51+51+5−1−51−51−5−1+5−1−5−1+51+51+5−1−51−51−5−1+500004i−4i000000000000000000000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ190000000000000000000000000000000000
χ8444-4-444-4-44−1−5−1+5−1−5−1+51+51+5−1−51−51−5−1+5−1−5−1+51+51+5−1−51−51−5−1+50000−4i4i0000000000000000000002ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ190000000000000000000000000000000000
χ8544-4-44-444-4−1+5−1−5−1+5−1−51−51−5−1+51+51+5−1−51−51+5−1+5−1+51−5−1−5−1−51+50000004-400000000000000000000000−1+51−5−1−51+5000000000000000000000000000000
χ8644-4-44-444-4−1+5−1−5−1+5−1−51−51−5−1+51+51+5−1−51−51+5−1+5−1+51−5−1−5−1−51+5000000-44000000000000000000000001−5−1+51+5−1−5000000000000000000000000000000
χ8744-4-44-444-4−1−5−1+5−1−5−1+51+51+5−1−51−51−5−1+51+51−5−1−5−1−51+5−1+5−1+51−50000004-400000000000000000000000−1−51+5−1+51−5000000000000000000000000000000
χ8844-4-44-444-4−1−5−1+5−1−5−1+51+51+5−1−51−51−5−1+51+51−5−1−5−1−51+5−1+5−1+51−5000000-44000000000000000000000001+5−1−51−5−1+5000000000000000000000000000000
χ898-8000000088-8-8000000000000008i−8i000000000000000000000000000000000000000000000000000000000000000
χ908-8000000088-8-800000000000000−8i8i000000000000000000000000000000000000000000000000000000000000000
χ9116-160000000−4+45−4−454−454+450000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9216-160000000−4−45−4+454+454−450000000000000000000000000000000000000000000000000000000000000000000000000000000

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