Finite Group Databasebeta

← Group #12252058

Character table — Group #12252058

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11222222222224444444444448888888888888888888888888888888101010101616161616161616161616161616161616161616202020202020404040404040404040404040
order1222255101010101010222244441010101044444448888101010101010101020202020202020202020202022442020202020202020202020204040404040404040222444244444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-111111-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-111111-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111-1-111111-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-111111-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1
χ9111111111111111-1-1-111-111111-1-1ii−i−iii−i−i1111-1-1-1-1-1-111111111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-1-11-1-111-1-1ii−i−iii−i−i
χ10111111111111111-1-1-111-111111-1-1ii−i−iii−i−i1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-111-111-1-111−i−iii−i−iii
χ11111111111111111-1-1-111-111111-1-1−i−iii−i−iii1111-1-1-1-1-1-111111111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-1-11-1-111-1-1−i−iii−i−iii
χ12111111111111111-1-1-111-111111-1-1−i−iii−i−iii1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-111-111-1-111ii−i−iii−i−i
χ13111111111111111-1-1-1-1-1-11111-111ii−i−i−i−iii1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii1-1-11-1-1-1-111ii−i−i−i−iii
χ14111111111111111-1-1-1-1-1-11111-111ii−i−i−i−iii1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-111-11111-1-1−i−iiiii−i−i
χ15111111111111111-1-1-1-1-1-11111-111−i−iiiii−i−i1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i1-1-11-1-1-1-111−i−iiiii−i−i
χ16111111111111111-1-1-1-1-1-11111-111−i−iiiii−i−i1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-111-11111-1-1ii−i−i−i−iii
χ1711-1-1111-1-1-1-1111-11-1111-1-1-111-11-1i−ii−ii−ii−i11-1-111-1-1111111-1-1-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i11-1-11-1-111-1i−ii−ii−ii−i
χ1811-1-1111-1-1-1-1111-11-1111-1-1-111-11-1i−ii−ii−ii−i11-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1ii−i−iii−i−iii−i−iii−i−i-1-111-111-1-11−ii−ii−ii−ii
χ1911-1-1111-1-1-1-1111-11-1111-1-1-111-11-1−ii−ii−ii−ii11-1-111-1-1111111-1-1-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii11-1-11-1-111-1−ii−ii−ii−ii
χ2011-1-1111-1-1-1-1111-11-1111-1-1-111-11-1−ii−ii−ii−ii11-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1−i−iii−i−iii−i−iii−i−iii-1-111-111-1-11i−ii−ii−ii−i
χ2111-1-1111-1-1-1-1111-11-11-1-1-1-1-1111-11i−ii−i−ii−ii11-1-111-1-111-1-1-1-11111-1-111-1-1-1-111ii−i−iii−i−i−i−iii−i−iii11-1-11-11-1-11i−ii−i−ii−ii
χ2211-1-1111-1-1-1-1111-11-11-1-1-1-1-1111-11i−ii−i−ii−ii11-1-111-1-111-1-1-1-11111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii-1-111-11-111-1−ii−iii−ii−i
χ2311-1-1111-1-1-1-1111-11-11-1-1-1-1-1111-11−ii−iii−ii−i11-1-111-1-111-1-1-1-11111-1-111-1-1-1-111−i−iii−i−iiiii−i−iii−i−i11-1-11-11-1-11−ii−iii−ii−i
χ2411-1-1111-1-1-1-1111-11-11-1-1-1-1-1111-11−ii−iii−ii−i11-1-111-1-111-1-1-1-11111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i-1-111-11-111-1i−ii−i−ii−ii
χ2511-1-1111-1-1-1-1111-1-11-1111-1-111-1-111-1-111-1-1111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111-11-1-11-11-111-1-111-1-11
χ2611-1-1111-1-1-1-1111-1-11-1111-1-111-1-111-1-111-1-1111-1-1-1-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-11-111-11-11-1-111-1-111-1
χ2711-1-1111-1-1-1-1111-1-11-1111-1-111-1-11-111-1-111-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-11-11-1-11-11-11-111-1-111-1
χ2811-1-1111-1-1-1-1111-1-11-1111-1-111-1-11-111-1-111-111-1-1-1-111-1-11111-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-11-111-11-11-11-1-111-1-11
χ2911-1-1111-1-1-1-1111-1-11-1-1-11-1-11111-11-1-11-111-111-1-1-1-111-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111-1-11111-1-11-11-1-111-11-11-1-11-111-1
χ3011-1-1111-1-1-1-1111-1-11-1-1-11-1-11111-11-1-11-111-111-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-111-1-1-1-111-1-11111-1-1-11-111-1-11-11-111-11-1-11
χ3111-1-1111-1-1-1-1111-1-11-1-1-11-1-11111-1-111-11-1-1111-1-1-1-111-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-111-1-1-1-1111-11-1-111-11-1-111-11-1-11
χ3211-1-1111-1-1-1-1111-1-11-1-1-11-1-11111-1-111-11-1-1111-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-111-1-1-1-111-11-111-1-11-111-1-11-111-1
χ332222222222222-2-222-200-2222200000000000-2-2-2-22222-2-200000000-2-2222200000000000000000000-2-22-22-2000000000000
χ342222222222222-2-222-200-2222200000000000-2-2-2-22222-2-200000000-2-2-2-2-2-20000000000000000000022-22-22000000000000
χ352222222222222-2-2-2-22002222200000000000-2-2-2-2-2-2-2-2220000000022222200000000000000000000-22-2-2-22000000000000
χ362222222222222-2-2-2-22002222200000000000-2-2-2-2-2-2-2-2220000000022-2-2-2-2000000000000000000002-2222-2000000000000
χ3722222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222222222−1+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+52−1−520000−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52000000000000000000
χ3822222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222222222−1+52−1−52−1+52−1−52222-2-2-2-2-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−520000−1+52−1−52−1+52−1−521−521+521−521+521−521+521−521+521−521+521−521+521−521+521−521+52000000000000000000
χ3922222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222222-2-22−1+52−1−52−1+52−1−52-2-2-22222-2-2-2-2−1+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+52−1+52−1−5200001−521+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
χ4022222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222222-2-22−1+52−1−52−1+52−1−52-2-2-2-2-2-2-22222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1−5200001−521+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
χ4122222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222-2-2-222-2−1+52−1−52−1+52−1−522-2-22i2i−2i−2i2i2i−2i−2i−1+52−1−52−1+52−1−521−521+521−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521+5200001−521+521−521+52−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7000000000000000000
χ4222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222-2-2-222-2−1+52−1−52−1+52−1−522-2-2−2i−2i2i2i−2i−2i2i2i−1+52−1−52−1+52−1−521−521+521−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521+5200001−521+521−521+52ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7000000000000000000
χ4322222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222-2-2-2-2-2-2−1+52−1−52−1+52−1−52-2222i2i−2i−2i−2i−2i2i2i−1+52−1−52−1+52−1−521−521+521−521+521−521+521−521−521+521+521−521−521+521+521−521+520000−1+52−1−52−1+52−1−52−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7000000000000000000
χ4422222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222-2-2-2-2-2-2−1+52−1−52−1+52−1−52-222−2i−2i2i2i2i2i−2i−2i−1+52−1−52−1+52−1−521−521+521−521+521−521+521−521−521+521+521−521−521+521+521−521+520000−1+52−1−52−1+52−1−52ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7000000000000000000
χ4522222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222222222−1−52−1+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+520000−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+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
χ4622222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222222222−1−52−1+52−1−52−1+52222-2-2-2-2-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+520000−1−52−1+52−1−52−1+521+521−521+521−521+521−521+521−521+521−521+521−521+521−521+521−52000000000000000000
χ4722222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222222-2-22−1−52−1+52−1−52−1+52-2-2-22222-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1+5200001+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
χ4822222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222222-2-22−1−52−1+52−1−52−1+52-2-2-2-2-2-2-22222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1+5200001+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
χ4922222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222-2-2-222-2−1−52−1+52−1−52−1+522-2-22i2i−2i−2i2i2i−2i−2i−1−52−1+52−1−52−1+521+521−521+521−521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521−5200001+521−521+521−52−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19000000000000000000
χ5022222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222-2-2-222-2−1−52−1+52−1−52−1+522-2-2−2i−2i2i2i−2i−2i2i2i−1−52−1+52−1−52−1+521+521−521+521−521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521−5200001+521−521+521−52ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19000000000000000000
χ5122222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222-2-2-2-2-2-2−1−52−1+52−1−52−1+52-2222i2i−2i−2i−2i−2i2i2i−1−52−1+52−1−52−1+521+521−521+521−521+521−521+521+521−521−521+521+521−521−521+521−520000−1−52−1+52−1−52−1+52−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19000000000000000000
χ5222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222-2-2-2-2-2-2−1−52−1+52−1−52−1+52-222−2i−2i2i2i2i2i−2i−2i−1−52−1+52−1−52−1+521+521−521+521−521+521−521+521+521−521−521+521+521−521−521+521−520000−1−52−1+52−1−52−1+52ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19000000000000000000
χ5322-2-2222-2-2-2-222-222-2-2002-2-22200000000000-2-22222-2-2-2-2000000002222-2-200000000000000000000-2-2-2222000000000000
χ5422-2-2222-2-2-2-222-222-2-2002-2-22200000000000-2-22222-2-2-2-20000000022-2-22200000000000000000000222-2-2-2000000000000
χ5522-2-2222-2-2-2-222-22-22200-2-2-22200000000000-2-222-2-2222200000000-2-222-2-200000000000000000000-2222-2-2000000000000
χ5622-2-2222-2-2-2-222-22-22200-2-2-22200000000000-2-222-2-2222200000000-2-2-2-222000000000000000000002-2-2-222000000000000
χ5722-2-22−1+52−1−521−521−521+521+52−1+52−1−522-22-2222-21−521+52−1+52−1−52-22-22i−2i2i−2i2i−2i2i−2i−1+52−1−521−521+52−1+52−1−521−521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521+520000−1+52−1−521−521+52−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7000000000000000000
χ5822-2-22−1+52−1−521−521−521+521+52−1+52−1−522-22-2222-21−521+52−1+52−1−52-22-2−2i2i−2i2i−2i2i−2i2i−1+52−1−521−521+52−1+52−1−521−521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521+520000−1+52−1−521−521+52ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7000000000000000000
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Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.