Finite Group Databasebeta

← Group #12016096

Character table — Group #12016096

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11112222222222444444444444448888888888888888888888161616161616161616161616161616161616161616161616202020202020202040404040404040408080
order1222225510101010101022224444441010101022101010101010101020202020202020202020202044441010101020202020202020202020202020202020444444444444444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111-1-1-1-111111-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ61111111111111111111-1-1-1-111111-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ71111111111111111111-1-1-1-111111-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111
χ81111111111111111111-1-1-1-111111-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-111-1-1
χ911-1-11-111-1-1-1-111-1-111111-1-1-1-1-1111-1-1-1-1-1111111-1-11111-1-1-1-11-11-111-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−ii−ii−ii−ii−ii−i
χ1011-1-11-111-1-1-1-111-1-111111-1-1-1-1-1111-1-1-1-1-1111111-1-11111-1-1-1-11-11-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−ii−ii−ii−ii−ii
χ1111-1-11-111-1-1-1-111-1-111111-1-1-1-1-1111-1-1-1-1-1111111-1-11111-1-1-1-1-11-1111-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−ii−iii−ii−i−ii
χ1211-1-11-111-1-1-1-111-1-111111-1-1-1-1-1111-1-1-1-1-1111111-1-11111-1-1-1-1-11-1111-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiii−ii−i−ii−iii−i
χ1311-1-11-111-1-1-1-111-1-1111-1-111-1-1-111-11-1-1-1-1111111-1-1-1-1-1-111111-1-11-1-1111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiii−ii−ii−i−ii−ii
χ1411-1-11-111-1-1-1-111-1-1111-1-111-1-1-111-11-1-1-1-1111111-1-1-1-1-1-111111-1-11-1-1111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−ii−ii−iii−ii−i
χ1511-1-11-111-1-1-1-111-1-1111-1-111-1-1-111-11-1-1-1-1111111-1-1-1-1-1-11111-111-1-1-111-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−ii−iii−i−iii−i
χ1611-1-11-111-1-1-1-111-1-1111-1-111-1-1-111-11-1-1-1-1111111-1-1-1-1-1-11111-111-1-1-111-1-1-1-111111111-1-1-1-1−i−iiiii−i−ii−ii−i−iii−i−ii
χ17222222222222222-22-2-20000-222220022-2-222-2-2-2-2-2-200000000000000000000000000000000222200000000-2-20000
χ18222222222222222-22-2-20000-222220022-2-222-2-2-2-2-2-200000000000000000000000000000000-2-2-2-200000000220000
χ1922222222222222-22-22-20000-2222200-2-222-2-222-2-2-2-20000000000000000000000000000000000002222000000-2-200
χ2022222222222222-22-22-20000-2222200-2-222-2-222-2-2-2-2000000000000000000000000000000000000-2-2-2-20000002200
χ2122222222222222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-22222222222220000-2-2-2-20000000000000000000000000000000000
χ2222222222222222-2-2-2-22-2-2-2-22222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000022220000000000000000000000000000000000
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χ24222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222222222−1+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+52−1−52−1−52-2-2-2-2−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+52000000000000000000
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+52−1−52-2-2−1+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+5222-2-21−521+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+52000000000000000000
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+52−1−52-2-2−1+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+52-2-2221−521+521−521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000000000
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+52−1−52-2-21−521+521−521+521−521+521−521+52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200001−521+521−521+52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7000000000000000000
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+52−1−52-2-21−521+521−521+521−521+521−521+52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200001−521+521−521+52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7000000000000000000
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+52−1−52221−521+521−521+521−521+521−521+52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+520000−1+52−1−52−1+52−1−52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7000000000000000000
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+52−1−52221−521+521−521+521−521+521−521+52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+520000−1+52−1−52−1+52−1−52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7000000000000000000
χ31222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222222222−1−52−1+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+52−1−52−1−52−1+52−1+52000000000000000000
χ32222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222222222−1−52−1+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+52-2-2-2-2−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−52000000000000000000
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+52-2-2−1−52−1+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+521−521−5222-2-21+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+521−521−52000000000000000000
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+52-2-2−1−52−1+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+521−521−52-2-2221+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+52000000000000000000
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+52-2-21+521−521+521−521+521−521+521−52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200001+521−521+521−52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19000000000000000000
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+52-2-21+521−521+521−521+521−521+521−52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200001+521−521+521−52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19000000000000000000
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+52221+521−521+521−521+521−521+521−52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−520000−1−52−1+52−1−52−1+52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19000000000000000000
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+52221+521−521+521−521+521−521+521−52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−520000−1−52−1+52−1−52−1+52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19000000000000000000
χ3922-2-22-222-2-2-2-22222-2-2222-2-2-2-2-222-222222-2-2-2-222-2-22222-2-2-2-20000-2-2220000000000000000000000000000000000
χ4022-2-22-222-2-2-2-22222-2-22-2-222-2-2-2222-22222-2-2-2-222-2-2-2-2-2-22222000022-2-20000000000000000000000000000000000
χ4122-2-22-222-2-2-2-2222-2-22-200002-2-2220022-2-2-2-222-2-2220000000000000000000000000000000000002i2i−2i−2i000000−2i2i00
χ4222-2-22-222-2-2-2-2222-2-22-200002-2-2220022-2-2-2-222-2-222000000000000000000000000000000000000−2i−2i2i2i0000002i−2i00
χ4322-2-22-222-2-2-2-222-222-2-200002-2-22200-2-22222-2-2-2-222000000000000000000000000000000002i2i−2i−2i00000000−2i2i0000
χ4422-2-22-222-2-2-2-222-222-2-200002-2-22200-2-22222-2-2-2-22200000000000000000000000000000000−2i−2i2i2i000000002i−2i0000
χ4522-2-22-2−1+52−1−521−521−521+521+52−1+52−1−5222-2-2222-2-2-21−521+52−1+52−1−52-22−1+52−1−52−1+52−1−521−521+521−521+52−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+5200001−521+52−1+52−1−52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7000000000000000000
χ4622-2-22-2−1+52−1−521−521−521+521+52−1+52−1−5222-2-2222-2-2-21−521+52−1+52−1−52-22−1+52−1−52−1+52−1−521−521+521−521+52−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+5200001−521+52−1+52−1−52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7000000000000000000
χ4722-2-22-2−1+52−1−521−521−521+521+52−1+52−1−5222-2-22-2-222-21−521+52−1+52−1−522-2−1+52−1−52−1+52−1−521−521+521−521+52−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−520000−1+52−1−521−521+52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7000000000000000000
χ4822-2-22-2−1+52−1−521−521−521+521+52−1+52−1−5222-2-22-2-222-21−521+52−1+52−1−522-2−1+52−1−52−1+52−1−521−521+521−521+52−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−520000−1+52−1−521−521+52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7000000000000000000
χ4922-2-22-2−1+52−1−521−521−521+521+52−1+52−1−52-2-222222-2-2-21−521+52−1+52−1−522-21−521+521−521+52−1+52−1−52−1+52−1−52−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+522-22-2−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52000000000000000000
χ5022-2-22-2−1+52−1−521−521−521+521+52−1+52−1−52-2-222222-2-2-21−521+52−1+52−1−522-21−521+521−521+52−1+52−1−52−1+52−1−52−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+52-22-22−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−52000000000000000000
χ5122-2-22-2−1+52−1−521−521−521+521+52−1+52−1−52-2-2222-2-222-21−521+52−1+52−1−52-221−521+521−521+52−1+52−1−52−1+52−1−52−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−522-2-221−521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52000000000000000000
χ5222-2-22-2−1+52−1−521−521−521+521+52−1+52−1−52-2-2222-2-222-21−521+52−1+52−1−52-221−521+521−521+52−1+52−1−52−1+52−1−52−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−52-222-21−521+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+52000000000000000000
χ5322-2-22-2−1−52−1+521+521+521−521−52−1−52−1+5222-2-2222-2-2-21+521−52−1−52−1+52-22−1−52−1+52−1−52−1+521+521−521+521−52−1−52−1+521+521−52−1−52−1−52−1+52−1+521+521+521−521−5200001+521−52−1−52−1+52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19000000000000000000
χ5422-2-22-2−1−52−1+521+521+521−521−52−1−52−1+5222-2-2222-2-2-21+521−52−1−52−1+52-22−1−52−1+52−1−52−1+521+521−521+521−52−1−52−1+521+521−52−1−52−1−52−1+52−1+521+521+521−521−5200001+521−52−1−52−1+52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19000000000000000000
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χ7144-4-4-4444-4-4-4-444000000000044-4-40000000000000000000000000000000000000000000000000000002i−2i−2i2i000000
χ7244-4-4-4444-4-4-4-444000000000044-4-4000000000000000000000000000000000000000000000000000000−2i2i2i−2i000000
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χ908-8-8800−2+25−2−252−25−2+252+25−2−252−252+2500000-444-400000000000000000001−5−1+51+5−1−5−1+51−5−1−51+5000000000000000000000000000000000000000000
χ918-8-8800−2−25−2+252+25−2−252−25−2+252+252−25000004-4-440000000000000000000−1−51+5−1+51−51+5−1−51−5−1+5000000000000000000000000000000000000000000
χ928-8-8800−2−25−2+252+25−2−252−25−2+252+252−2500000-444-400000000000000000001+5−1−51−5−1+5−1−51+5−1+51−5000000000000000000000000000000000000000000

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