Finite Group Databasebeta

← Group #12253480

Character table — Group #12253480

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11112222222222444444444444448888888888888888888888161616161616161616161616161616161616161616161616202020202020202040404040404040408080
order1244245510102020202022244444441010202024101010101010202020202020202020202020202088881010202040404040404040404040404040404040444444442222444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ511111111111111111-1-1-1-11111111-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-1111-111-1-1
χ611111111111111111-1-1-1-11111111-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-11-1-111
χ711111111111111111-1-1-1-11111111-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-1-11-1-1-111
χ811111111111111111-1-1-1-11111111-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1111-1111-1-1
χ911-1-11-11111-1-1-1-1-1-1-111-1-111111-1-11-1-1-1-1-1-1-1111111-1-1-1-111111-11-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-11-1-111-11-1
χ1011-1-11-11111-1-1-1-1-1-1-111-1-111111-1-11-1-1-1-1-1-1-1111111-1-1-1-111111-11-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-11-111-1-11-11
χ1111-1-11-11111-1-1-1-1-1-1-111-1-111111-1-11-1-1-1-1-1-1-1111111-1-1-1-11111-11-1111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-11-1-11-11-11-11
χ1211-1-11-11111-1-1-1-1-1-1-111-1-111111-1-11-1-1-1-1-1-1-1111111-1-1-1-11111-11-1111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-111-11-11-11-1
χ1311-1-11-11111-1-1-1-1-1-1-1-1-11111111-1-1-11-1-1-1-1-1-111-1-1-1-1111111111-1-11-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111111-1-1-11-1-11
χ1411-1-11-11111-1-1-1-1-1-1-1-1-11111111-1-1-11-1-1-1-1-1-111-1-1-1-1111111111-1-11-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1111-111-1
χ1511-1-11-11111-1-1-1-1-1-1-1-1-11111111-1-1-11-1-1-1-1-1-111-1-1-1-111111111-111-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-11111-11-1-1-111-1
χ1611-1-11-11111-1-1-1-1-1-1-1-1-11111111-1-1-11-1-1-1-1-1-111-1-1-1-111111111-111-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11-1111-1-11
χ17222222222222222-2-200002-2-222220022-2-2-2-2-2-20000000022-2-200000000000000000000000022220000-2000-200000
χ18222222222222222-2-200002-2-222220022-2-2-2-2-2-20000000022-2-2000000000000000000000000-2-2-2-200002000200000
χ1922222222222222-22-20000-22-2222200-2-222-2-2-2-200000000-2-222000000000000000000000000000022220-2000-20000
χ2022222222222222-22-20000-22-2222200-2-222-2-2-2-200000000-2-2220000000000000000000000000000-2-2-2-20200020000
χ2122222222222222-2-222222-2-222222-2-2-2-2-2-2222222222222-2-2-2-20000-2-2-2-20000000000000000000000000000000000
χ2222222222222222-2-22-2-2-2-2-2-22222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2000022220000000000000000000000000000000000
χ23222222−1+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
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+52−1−52−1−52222-2-2-2-2222−1+52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−5222-2-21−521+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+52−1−52−1−52222-2-2-2-2222−1+52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−52-2-2221−521+521−521+521−521−521+521+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+52−1−52−1−52-2-222222-2-22−1+52−1−52−1+52−1−52-2-21−521+521−521+52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521+521−521+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+52−1−52−1−52-2-222222-2-22−1+52−1−52−1+52−1−52-2-21−521+521−521+52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521+521−521+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+52−1−52−1−52-2-22-2-2-2-2-2-22−1+52−1−52−1+52−1−52221−521+521−521+52−1+52−1−52−1+52−1−521−521−521+521+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+52−1−52−1−52-2-22-2-2-2-2-2-22−1+52−1−52−1+52−1−52221−521+521−521+52−1+52−1−52−1+52−1−521−521−521+521+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+52222-2-2-2-2222−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+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+52222-2-2-2-2222−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+52-2-2221+521−521+521−521+521+521−521−521+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+52-2-222222-2-22−1−52−1+52−1−52−1+52-2-21+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+521+521−521+521−5200001+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+52-2-222222-2-22−1−52−1+52−1−52−1+52-2-21+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+521+521−521+521−5200001+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+52-2-22-2-2-2-2-2-22−1−52−1+52−1−52−1+52221+521−521+521−52−1−52−1+52−1−52−1+521+521+521−521−521+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+52-2-22-2-2-2-2-2-22−1−52−1+52−1−52−1+52221+521−521+521−52−1−52−1+52−1−52−1+521+521+521−521−521+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
χ3922-2-22-22222-2-2-2-222-222-2-2-2-2222-2-2-222222-2-2222222-2-2-2-2-2-2-2-20000-2-2220000000000000000000000000000000000
χ4022-2-22-22222-2-2-2-222-2-2-222-2-2222-2-22-22222-2-222-2-2-2-22222-2-2-2-2000022-2-20000000000000000000000000000000000
χ4122-2-22-22222-2-2-2-22-220000-22-222-2-20022-2-222-2-200000000-2-222000000000000000000000000000022-2-202000-20000
χ4222-2-22-22222-2-2-2-22-220000-22-222-2-20022-2-222-2-200000000-2-2220000000000000000000000000000-2-2220-200020000
χ4322-2-22-22222-2-2-2-2-22200002-2-222-2-200-2-22222-2-20000000022-2-200000000000000000000000022-2-20000-2000200000
χ4422-2-22-22222-2-2-2-2-22200002-2-222-2-200-2-22222-2-20000000022-2-2000000000000000000000000-2-22200002000-200000
χ4522-2-22-2−1+52−1−52−1+52−1−521−521−521+521+5222-222-2-2-2-22−1+52−1−521−521+52-22−1+52−1−52−1+52−1−521−521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+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+52−1−52−1+52−1−521−521−521+521+5222-222-2-2-2-22−1+52−1−521−521+52-22−1+52−1−52−1+52−1−521−521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+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+52−1−52−1+52−1−521−521−521+521+5222-2-2-222-2-22−1+52−1−521−521+522-2−1+52−1−52−1+52−1−521−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521+521−521+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+52−1−52−1+52−1−521−521−521+521+5222-2-2-222-2-22−1+52−1−521−521+522-2−1+52−1−52−1+52−1−521−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521+521−521+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+52−1−52−1+52−1−521−521−521+521+52-2-2-222-2-2222−1+52−1−521−521+522-21−521+521−521+521−521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−52−1+52−1−522-22-2−1+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+52−1−52−1+52−1−521−521−521+521+52-2-2-222-2-2222−1+52−1−521−521+522-21−521+521−521+521−521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−52−1+52−1−52-22-22−1+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+52−1−52−1+52−1−521−521−521+521+52-2-2-2-2-222222−1+52−1−521−521+52-221−521+521−521+521−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−522-2-221−521+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+52−1−52−1+52−1−521−521−521+521+52-2-2-2-2-222222−1+52−1−521−521+52-221−521+521−521+521−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52-222-21−521+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+52−1−52−1+521+521+521−521−5222-222-2-2-2-22−1−52−1+521+521−52-22−1−52−1+52−1−52−1+521+521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+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+52−1−52−1+521+521+521−521−5222-222-2-2-2-22−1−52−1+521+521−52-22−1−52−1+52−1−52−1+521+521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+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
χ5522-2-22-2−1−52−1+52−1−52−1+521+521+521−521−5222-2-2-222-2-22−1−52−1+521+521−522-2−1−52−1+52−1−52−1+521+521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521−521+521−520000−1−52−1+521+521−52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19000000000000000000
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χ898-8−8i8i00−2+25−2−252−252+254ζ11+4ζ19−4ζ11−4ζ194ζ3+4ζ7−4ζ3−4ζ70004i−4i-4400000000000000000−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ71−5−1+51+5−1−50000000000000000000000000000000000000000000000
χ908-8−8i8i00−2+25−2−252−252+254ζ11+4ζ19−4ζ11−4ζ194ζ3+4ζ7−4ζ3−4ζ7000−4i4i4-4000000000000000002ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ7−1+51−5−1−51+50000000000000000000000000000000000000000000000
χ918-8−8i8i00−2−25−2+252+252−254ζ3+4ζ7−4ζ3−4ζ74ζ11+4ζ19−4ζ11−4ζ190004i−4i-4400000000000000000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ191+5−1−51−5−1+50000000000000000000000000000000000000000000000
χ928-8−8i8i00−2−25−2+252+252−254ζ3+4ζ7−4ζ3−4ζ74ζ11+4ζ19−4ζ11−4ζ19000−4i4i4-4000000000000000002ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ19−1−51+5−1+51−50000000000000000000000000000000000000000000000

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