Finite Group Databasebeta

← Group #13107643

Character table — Group #13107643

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112
size112444455101010101022488881010202020202022488881010202020202055102020202025255050505050112444455101010101022488881010202020202022488881010202020202055102020202025255050505050
order12251010104448888510105101010202020404040405101051010102020204040404022210101010444888822210101010444888810101010101010202020404040401010101010101020202040404040222101010104448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-1
χ31111111-1-1-1ii−i−i1111111-1-1-1ii−i−i1111111-1-1-1ii−i−i1111111-1-1-1ii−i−i1111111-1-1-1ii−i−i1111111-1-1-1ii−i−i1111111-1-1-1ii−i−i1111111-1-1-1ii−i−i
χ41111111-1-1-1−i−iii1111111-1-1-1−i−iii1111111-1-1-1−i−iii1111111-1-1-1−i−iii1111111-1-1-1−i−iii1111111-1-1-1−i−iii1111111-1-1-1−i−iii1111111-1-1-1−i−iii
χ511-111-1-111-11-11-111-111-1-111-11-11-111-111-1-111-11-11-111-111-1-111-11-11-111-111-1-111-11-11-111-111-1-111-11-11-111-111-1-111-11-11-111-111-1-111-11-11-1
χ611-111-1-111-1-11-1111-111-1-111-1-11-1111-111-1-111-1-11-1111-111-1-111-1-11-1111-111-1-111-1-11-1111-111-1-111-1-11-1111-111-1-111-1-11-1111-111-1-111-1-11-11
χ711-111-1-1-1-11i−i−ii11-111-1-1-1-11i−i−ii11-111-1-1-1-11i−i−ii11-111-1-1-1-11i−i−ii11-111-1-1-1-11i−i−ii11-111-1-1-1-11i−i−ii11-111-1-1-1-11i−i−ii11-111-1-1-1-11i−i−ii
χ811-111-1-1-1-11−iii−i11-111-1-1-1-11−iii−i11-111-1-1-1-11−iii−i11-111-1-1-1-11−iii−i11-111-1-1-1-11−iii−i11-111-1-1-1-11−iii−i11-111-1-1-1-11−iii−i11-111-1-1-1-11−iii−i
χ92-202-2002i−2i000002-202-2002i−2i000002-202-2002i−2i000002-202-2002i−2i000002-202-2002i−2i000002-202-2002i−2i000002-202-2002i−2i000002-202-2002i−2i00000
χ102-202-200−2i2i000002-202-200−2i2i000002-202-200−2i2i000002-202-200−2i2i000002-202-200−2i2i000002-202-200−2i2i000002-202-200−2i2i000002-202-200−2i2i00000
χ11444-1-1-1-10000000444-1-1-1-10000000444-1-1-1-10000000444-1-1-1-10000000444-1-1-1-10000000444-1-1-1-10000000444-1-1-1-10000000444-1-1-1-10000000
χ1244-4-1-111000000044-4-1-111000000044-4-1-111000000044-4-1-111000000044-4-1-111000000044-4-1-111000000044-4-1-111000000044-4-1-1110000000
χ134-40-115−500000004-40-115−500000004-40-115−500000004-40-115−500000004-40-115−500000004-40-115−500000004-40-115−500000004-40-115−50000000
χ144-40-11−5500000004-40-11−5500000004-40-11−5500000004-40-11−5500000004-40-11−5500000004-40-11−5500000004-40-11−5500000004-40-11−550000000
χ15111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ161111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ171111111-1-1-1ii−i−i1111111-1-1-1ii−i−i1111111-1-1-1ii−i−i-1-1-1-1-1-1-1111−i−iii1111111-1-1-1ii−i−i1111111-1-1-1ii−i−i1111111-1-1-1ii−i−i-1-1-1-1-1-1-1111−i−iii
χ181111111-1-1-1−i−iii1111111-1-1-1−i−iii1111111-1-1-1−i−iii-1-1-1-1-1-1-1111ii−i−i1111111-1-1-1−i−iii1111111-1-1-1−i−iii1111111-1-1-1−i−iii-1-1-1-1-1-1-1111ii−i−i
χ1911-111-1-111-11-11-111-111-1-111-11-11-111-111-1-111-11-11-1-1-11-1-111-1-11-11-1111-111-1-111-11-11-111-111-1-111-11-11-111-111-1-111-11-11-1-1-11-1-111-1-11-11-11
χ2011-111-1-111-1-11-1111-111-1-111-1-11-1111-111-1-111-1-11-11-1-11-1-111-1-111-11-111-111-1-111-1-11-1111-111-1-111-1-11-1111-111-1-111-1-11-11-1-11-1-111-1-111-11-1
χ2111-111-1-1-1-11i−i−ii11-111-1-1-1-11i−i−ii11-111-1-1-1-11i−i−ii-1-11-1-11111-1−iii−i11-111-1-1-1-11i−i−ii11-111-1-1-1-11i−i−ii11-111-1-1-1-11i−i−ii-1-11-1-11111-1−iii−i
χ2211-111-1-1-1-11−iii−i11-111-1-1-1-11−iii−i11-111-1-1-1-11−iii−i-1-11-1-11111-1i−i−ii11-111-1-1-1-11−iii−i11-111-1-1-1-11−iii−i11-111-1-1-1-11−iii−i-1-11-1-11111-1i−i−ii
χ232-202-2002i−2i000002-202-2002i−2i000002-202-2002i−2i00000-220-2200−2i2i000002-202-2002i−2i000002-202-2002i−2i000002-202-2002i−2i00000-220-2200−2i2i00000
χ242-202-200−2i2i000002-202-200−2i2i000002-202-200−2i2i00000-220-22002i−2i000002-202-200−2i2i000002-202-200−2i2i000002-202-200−2i2i00000-220-22002i−2i00000
χ25444-1-1-1-10000000444-1-1-1-10000000444-1-1-1-10000000-4-4-411110000000444-1-1-1-10000000444-1-1-1-10000000444-1-1-1-10000000-4-4-411110000000
χ2644-4-1-111000000044-4-1-111000000044-4-1-1110000000-4-4411-1-1000000044-4-1-111000000044-4-1-111000000044-4-1-1110000000-4-4411-1-10000000
χ274-40-115−500000004-40-115−500000004-40-115−50000000-4401-1−5500000004-40-115−500000004-40-115−500000004-40-115−50000000-4401-1−550000000
χ284-40-11−5500000004-40-11−5500000004-40-11−550000000-4401-15−500000004-40-11−5500000004-40-11−5500000004-40-11−550000000-4401-15−50000000
χ2922222222222222−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−520000000000000022222222222222−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−5200000000000000
χ302222222222-2-2-2-2−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+52000000000000002222222222-2-2-2-2−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+5200000000000000
χ312222222-2-2-22i2i−2i−2i−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−52−ζ11−ζ19−ζ11−ζ19ζ11+ζ19ζ11+ζ19−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+52−ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ3+ζ7000000000000002222222-2-2-22i2i−2i−2i−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−52−ζ11−ζ19−ζ11−ζ19ζ11+ζ19ζ11+ζ19−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+52−ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ3+ζ700000000000000
χ322222222-2-2-2−2i−2i2i2i−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−52ζ11+ζ19ζ11+ζ19−ζ11−ζ19−ζ11−ζ19−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+52ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ3−ζ7000000000000002222222-2-2-2−2i−2i2i2i−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−52ζ11+ζ19ζ11+ζ19−ζ11−ζ19−ζ11−ζ19−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+52ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ3−ζ700000000000000
χ3322-222-2-222-22-22-2−1+52−1+521−52−1+52−1+521−521−52−1+52−1+521−52−1+521−52−1+521−52−1−52−1−521+52−1−52−1−521+521+52−1−52−1−521+52−1−521+52−1−521+520000000000000022-222-2-222-22-22-2−1+52−1+521−52−1+52−1+521−521−52−1+52−1+521−52−1+521−52−1+521−52−1−52−1−521+52−1−52−1−521+521+52−1−52−1−521+52−1−521+52−1−521+5200000000000000
χ3422-222-2-222-2-22-22−1+52−1+521−52−1+52−1+521−521−52−1+52−1+521−521−52−1+521−52−1+52−1−52−1−521+52−1−52−1−521+521+52−1−52−1−521+521+52−1−521+52−1−520000000000000022-222-2-222-2-22-22−1+52−1+521−52−1+52−1+521−521−52−1+52−1+521−521−52−1+521−52−1+52−1−52−1−521+52−1−52−1−521+521+52−1−52−1−521+521+52−1−521+52−1−5200000000000000
χ3522-222-2-2-2-222i−2i−2i2i−1+52−1+521−52−1+52−1+521−521−521−521−52−1+52−ζ11−ζ19ζ11+ζ19ζ11+ζ19−ζ11−ζ19−1−52−1−521+52−1−52−1−521+521+521+521+52−1−52−ζ3−ζ7ζ3+ζ7ζ3+ζ7−ζ3−ζ70000000000000022-222-2-2-2-222i−2i−2i2i−1+52−1+521−52−1+52−1+521−521−521−521−52−1+52−ζ11−ζ19ζ11+ζ19ζ11+ζ19−ζ11−ζ19−1−52−1−521+52−1−52−1−521+521+521+521+52−1−52−ζ3−ζ7ζ3+ζ7ζ3+ζ7−ζ3−ζ700000000000000
χ3622-222-2-2-2-22−2i2i2i−2i−1+52−1+521−52−1+52−1+521−521−521−521−52−1+52ζ11+ζ19−ζ11−ζ19−ζ11−ζ19ζ11+ζ19−1−52−1−521+52−1−52−1−521+521+521+521+52−1−52ζ3+ζ7−ζ3−ζ7−ζ3−ζ7ζ3+ζ70000000000000022-222-2-2-2-22−2i2i2i−2i−1+52−1+521−52−1+52−1+521−521−521−521−52−1+52ζ11+ζ19−ζ11−ζ19−ζ11−ζ19ζ11+ζ19−1−52−1−521+52−1−52−1−521+521+521+521+52−1−52ζ3+ζ7−ζ3−ζ7−ζ3−ζ7ζ3+ζ700000000000000
χ374-404-4004i−4i00000−1+51−50−1+51−500−2ζ11−2ζ192ζ11+2ζ1900000−1−51+50−1−51+500−2ζ3−2ζ72ζ3+2ζ700000000000000000004-404-4004i−4i00000−1+51−50−1+51−500−2ζ11−2ζ192ζ11+2ζ1900000−1−51+50−1−51+500−2ζ3−2ζ72ζ3+2ζ70000000000000000000
χ384-404-400−4i4i00000−1+51−50−1+51−5002ζ11+2ζ19−2ζ11−2ζ1900000−1−51+50−1−51+5002ζ3+2ζ7−2ζ3−2ζ700000000000000000004-404-400−4i4i00000−1+51−50−1+51−5002ζ11+2ζ19−2ζ11−2ζ1900000−1−51+50−1−51+5002ζ3+2ζ7−2ζ3−2ζ70000000000000000000
χ39888-2-2-2-20000000−2+25−2+25−2+251−521−521−521−520000000−2−25−2−25−2−251+521+521+521+52000000000000000000000888-2-2-2-20000000−2+25−2+25−2+251−521−521−521−520000000−2−25−2−25−2−251+521+521+521+52000000000000000000000
χ4088-8-2-2220000000−2+25−2+252−251−521−52−1+52−1+520000000−2−25−2−252+251+521+52−1−52−1−5200000000000000000000088-8-2-2220000000−2+25−2+252−251−521−52−1+52−1+520000000−2−25−2−252+251+521+52−1−52−1−52000000000000000000000
χ418-80-2225−250000000−2+252−2501−52−1+525−52−5+520000000−2−252+2501+52−1−52−5−525+520000000000000000000008-80-2225−250000000−2+252−2501−52−1+525−52−5+520000000−2−252+2501+52−1−52−5−525+52000000000000000000000
χ428-80-22−25250000000−2+252−2501−52−1+52−5+525−520000000−2−252+2501+52−1−525+52−5−520000000000000000000008-80-22−25250000000−2+252−2501−52−1+52−5+525−520000000−2−252+2501+52−1−525+52−5−52000000000000000000000
χ4322222222222222−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+520000000000000022222222222222−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1+52−1+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
χ442222222222-2-2-2-2−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−52000000000000002222222222-2-2-2-2−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−5200000000000000
χ452222222-2-2-22i2i−2i−2i−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+52−ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ3+ζ7−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−52−ζ11−ζ19−ζ11−ζ19ζ11+ζ19ζ11+ζ19000000000000002222222-2-2-22i2i−2i−2i−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+52−ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ3+ζ7−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−52−ζ11−ζ19−ζ11−ζ19ζ11+ζ19ζ11+ζ1900000000000000
χ462222222-2-2-2−2i−2i2i2i−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+52ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ3−ζ7−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−52ζ11+ζ19ζ11+ζ19−ζ11−ζ19−ζ11−ζ19000000000000002222222-2-2-2−2i−2i2i2i−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+52ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ3−ζ7−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−52ζ11+ζ19ζ11+ζ19−ζ11−ζ19−ζ11−ζ1900000000000000
χ4722-222-2-222-22-22-2−1−52−1−521+52−1−52−1−521+521+52−1−52−1−521+52−1−521+52−1−521+52−1+52−1+521−52−1+52−1+521−521−52−1+52−1+521−52−1+521−52−1+521−520000000000000022-222-2-222-22-22-2−1−52−1−521+52−1−52−1−521+521+52−1−52−1−521+52−1−521+52−1−521+52−1+52−1+521−52−1+52−1+521−521−52−1+52−1+521−52−1+521−52−1+521−5200000000000000
χ4822-222-2-222-2-22-22−1−52−1−521+52−1−52−1−521+521+52−1−52−1−521+521+52−1−521+52−1−52−1+52−1+521−52−1+52−1+521−521−52−1+52−1+521−521−52−1+521−52−1+520000000000000022-222-2-222-2-22-22−1−52−1−521+52−1−52−1−521+521+52−1−52−1−521+521+52−1−521+52−1−52−1+52−1+521−52−1+52−1+521−521−52−1+52−1+521−521−52−1+521−52−1+5200000000000000
χ4922-222-2-2-2-222i−2i−2i2i−1−52−1−521+52−1−52−1−521+521+521+521+52−1−52−ζ3−ζ7ζ3+ζ7ζ3+ζ7−ζ3−ζ7−1+52−1+521−52−1+52−1+521−521−521−521−52−1+52−ζ11−ζ19ζ11+ζ19ζ11+ζ19−ζ11−ζ190000000000000022-222-2-2-2-222i−2i−2i2i−1−52−1−521+52−1−52−1−521+521+521+521+52−1−52−ζ3−ζ7ζ3+ζ7ζ3+ζ7−ζ3−ζ7−1+52−1+521−52−1+52−1+521−521−521−521−52−1+52−ζ11−ζ19ζ11+ζ19ζ11+ζ19−ζ11−ζ1900000000000000
χ5022-222-2-2-2-22−2i2i2i−2i−1−52−1−521+52−1−52−1−521+521+521+521+52−1−52ζ3+ζ7−ζ3−ζ7−ζ3−ζ7ζ3+ζ7−1+52−1+521−52−1+52−1+521−521−521−521−52−1+52ζ11+ζ19−ζ11−ζ19−ζ11−ζ19ζ11+ζ190000000000000022-222-2-2-2-22−2i2i2i−2i−1−52−1−521+52−1−52−1−521+521+521+521+52−1−52ζ3+ζ7−ζ3−ζ7−ζ3−ζ7ζ3+ζ7−1+52−1+521−52−1+52−1+521−521−521−521−52−1+52ζ11+ζ19−ζ11−ζ19−ζ11−ζ19ζ11+ζ1900000000000000
χ514-404-4004i−4i00000−1−51+50−1−51+500−2ζ3−2ζ72ζ3+2ζ700000−1+51−50−1+51−500−2ζ11−2ζ192ζ11+2ζ1900000000000000000004-404-4004i−4i00000−1−51+50−1−51+500−2ζ3−2ζ72ζ3+2ζ700000−1+51−50−1+51−500−2ζ11−2ζ192ζ11+2ζ190000000000000000000
χ524-404-400−4i4i00000−1−51+50−1−51+5002ζ3+2ζ7−2ζ3−2ζ700000−1+51−50−1+51−5002ζ11+2ζ19−2ζ11−2ζ1900000000000000000004-404-400−4i4i00000−1−51+50−1−51+5002ζ3+2ζ7−2ζ3−2ζ700000−1+51−50−1+51−5002ζ11+2ζ19−2ζ11−2ζ190000000000000000000
χ53888-2-2-2-20000000−2−25−2−25−2−251+521+521+521+520000000−2+25−2+25−2+251−521−521−521−52000000000000000000000888-2-2-2-20000000−2−25−2−25−2−251+521+521+521+520000000−2+25−2+25−2+251−521−521−521−52000000000000000000000
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χ558-80-2225−250000000−2−252+2501+52−1−52−5−525+520000000−2+252−2501−52−1+525−52−5+520000000000000000000008-80-2225−250000000−2−252+2501+52−1−52−5−525+520000000−2+252−2501−52−1+525−52−5+52000000000000000000000
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χ109888-2-2-2-20000000−2−25−2−25−2−251+521+521+521+520000000−2+25−2+25−2+251−521−521−521−52000000000000000000000-8-8-8222200000002+252+252+25−1−52−1−52−1−52−1−5200000002−252−252−25−1+52−1+52−1+52−1+52000000000000000000000
χ11088-8-2-2220000000−2−25−2−252+251+521+52−1−52−1−520000000−2+25−2+252−251−521−52−1+52−1+52000000000000000000000-8-8822-2-200000002+252+25−2−25−1−52−1−521+521+5200000002−252−25−2+25−1+52−1+521−521−52000000000000000000000
χ1118-80-2225−250000000−2−252+2501+52−1−52−5−525+520000000−2+252−2501−52−1+525−52−5+52000000000000000000000-8802-2−252500000002+25−2−250−1−521+525+52−5−5200000002−25−2+250−1+521−52−5+525−52000000000000000000000
χ1128-80-22−25250000000−2−252+2501+52−1−525+52−5−520000000−2+252−2501−52−1+52−5+525−52000000000000000000000-8802-225−2500000002+25−2−250−1−521+52−5−525+5200000002−25−2+250−1+521−525−52−5+52000000000000000000000

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