Finite Group Databasebeta

← Group #13103695

Character table — Group #13103695

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size112222244444448888888888888888888810101010202020202020202020202525404040404040404040404040404050100100100100100
order12255101045101010101055101010101010202020202020202020202020444444888820202020222020202020204040404040404040248888
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111-1-11-1ii−i−i-1-1-1-1-1-1-1-11111iiii−i−i−i−i-1-1ii−i−i
χ4111111111111111111111111111111111111-1-11-1−i−iii-1-1-1-1-1-1-1-11111−i−i−i−iiiii-1-1−i−iii
χ51111111111111111111111111111111111-1-111-1111111111-1-111-1-1-1-111111111-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-111-11-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111111-1-1-1-1-1-1ii−i−i-1-1-1-111-1-1-1-1-1-1iiii−i−i−i−i11−i−iii
χ81111111111111111111111111111111111-1-1-1-1-1-1−i−iii-1-1-1-111-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i
χ91111111-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-11-1111111-1-111-1-111-1-111-1-11-11-11-1
χ101111111-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11-11111111-1-111-1-1-1-111-1-1111-1-11-11
χ111111111-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11i−i−ii-1-1-1-1-1-11111-1-1ii−i−i−i−iii-11i−i−ii
χ121111111-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11−iii−i-1-1-1-1-1-11111-1-1−i−iiiii−i−i-11−iii−i
χ131111111-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-11-11111-1-1-1-1-1-11111-1-111-1-1-11-11-11
χ141111111-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-111111-1-1-1-1-1-111-1-111-1-111-111-11-1
χ151111111-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111i−i−ii-1-1-1-11111-1-111ii−i−i−i−iii1-1−iii−i
χ161111111-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−iii−i-1-1-1-11111-1-111−i−iiiii−i−i1-1i−i−ii
χ17222−1+52−1−52−1+52−1−5222−1+52−1−52222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−5222−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−520022022222−1+52−1+52−1−52−1−5200−1+52−1−520000−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52000000
χ18222−1+52−1−52−1+52−1−5222−1+52−1−52222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−5222−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52002202-2-2-2-2−1+52−1+52−1−52−1−5200−1+52−1−5200001−521+521−521+521−521+521−521+52000000
χ19222−1+52−1−52−1+52−1−5222−1+52−1−52222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−5222−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200-2-20-22i2i−2i−2i1−521−521+521+52001−521+520000−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7000000
χ20222−1+52−1−52−1+52−1−5222−1+52−1−52222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−5222−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200-2-20-2−2i−2i2i2i1−521−521+521+52001−521+520000ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7000000
χ21222−1+52−1−52−1+52−1−52-22−1+52−1−52222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521+52-2-21−521−521−521−521+521+521+521+5200220-22-22-2−1+52−1+52−1−52−1−52001−521+520000−1+52−1−521−521+52−1+52−1−521−521+52000000
χ22222−1+52−1−52−1+52−1−52-22−1+52−1−52222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521+52-2-21−521−521−521−521+521+521+521+5200220-2-22-22−1+52−1+52−1−52−1−52001−521+5200001−521+52−1+52−1−521−521+52−1+52−1−52000000
χ23222−1+52−1−52−1+52−1−52-22−1+52−1−52222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521+52-2-21−521−521−521−521+521+521+521+5200-2-2022i−2i−2i2i1−521−521+521+5200−1+52−1−520000−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7000000
χ24222−1+52−1−52−1+52−1−52-22−1+52−1−52222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521+52-2-21−521−521−521−521+521+521+521+5200-2-202−2i2i2i−2i1−521−521+521+5200−1+52−1−520000ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7000000
χ25222−1−52−1+52−1−52−1+5222−1−52−1+52222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+5222−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+520022022222−1−52−1−52−1+52−1+5200−1−52−1+520000−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52000000
χ26222−1−52−1+52−1−52−1+5222−1−52−1+52222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+5222−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52002202-2-2-2-2−1−52−1−52−1+52−1+5200−1−52−1+5200001+521−521+521−521+521−521+521−52000000
χ27222−1−52−1+52−1−52−1+5222−1−52−1+52222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+5222−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200-2-20-22i2i−2i−2i1+521+521−521−52001+521−520000−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19000000
χ28222−1−52−1+52−1−52−1+5222−1−52−1+52222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+5222−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200-2-20-2−2i−2i2i2i1+521+521−521−52001+521−520000ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19000000
χ29222−1−52−1+52−1−52−1+52-22−1−52−1+52222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521−52-2-21+521+521+521+521−521−521−521−5200220-22-22-2−1−52−1−52−1+52−1+52001+521−520000−1−52−1+521+521−52−1−52−1+521+521−52000000
χ30222−1−52−1+52−1−52−1+52-22−1−52−1+52222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521−52-2-21+521+521+521+521−521−521−521−5200220-2-22-22−1−52−1−52−1+52−1+52001+521−5200001+521−52−1−52−1+521+521−52−1−52−1+52000000
χ31222−1−52−1+52−1−52−1+52-22−1−52−1+52222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521−52-2-21+521+521+521+521−521−521−521−5200-2-2022i−2i−2i2i1+521+521−521−5200−1−52−1+520000−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19000000
χ32222−1−52−1+52−1−52−1+52-22−1−52−1+52222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521−52-2-21+521+521+521+521−521−521−521−5200-2-202−2i2i2i−2i1+521+521−521−5200−1−52−1+520000ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19000000
χ3322-2222202-2-2-2-2222-2-2-2-2220000000000002-22-20000002-22-222002-20000000000-200000
χ3422-2222202-2-2-2-2222-2-2-2-2220000000000002-2-22000000-22-22-2-2002-20000000000200000
χ3522-2222202-2-2-2-2222-2-2-2-222000000000000-222-20000002-22-2-2-200-220000000000200000
χ3622-2222202-2-2-2-2222-2-2-2-222000000000000-22-22000000-22-222200-220000000000-200000
χ3744444444-144-1-1-1-1-1-1-1-1-1-1-144-1-1-1-1-1-1-1-1-1-1440040000000000000-1-1-1-100000000000000
χ3844444444-144-1-1-1-1-1-1-1-1-1-1-144-1-1-1-1-1-1-1-1-1-1-4-400-40000000000000111100000000000000
χ394444444-4-144-1-1-1-1-1-1-1-1-1-1-1-4-411111111114400-40000000000000-1-11100000000000000
χ404444444-4-144-1-1-1-1-1-1-1-1-1-1-1-4-41111111111-4-4004000000000000011-1-100000000000000
χ4144-444440-1-4-411-1-1-11111-1-1005−555−5−555−5−54-40000000000000000-115−500000000000000
χ4244-444440-1-4-411-1-1-11111-1-1005−555−5−555−5−5-4400000000000000001-1−5500000000000000
χ4344-444440-1-4-411-1-1-11111-1-100−55−5−555−5−5554-40000000000000000-11−5500000000000000
χ4444-444440-1-4-411-1-1-11111-1-100−55−5−555−5−555-4400000000000000001-15−500000000000000
χ4544-4−1+5−1−5−1+5−1−5041−51+5-4-44−1+5−1−51−51−51+51+5−1+5−1−5000000000000004-4000000−1+51−5−1−51+50000000000000000000000
χ4644-4−1+5−1−5−1+5−1−5041−51+5-4-44−1+5−1−51−51−51+51+5−1+5−1−500000000000000-440000001−5−1+51+5−1−50000000000000000000000
χ4744-4−1−5−1+5−1−5−1+5041+51−5-4-44−1−5−1+51+51+51−51−5−1−5−1+5000000000000004-4000000−1−51+5−1+51−50000000000000000000000
χ4844-4−1−5−1+5−1−5−1+5041+51−5-4-44−1−5−1+51+51+51−51−5−1−5−1+500000000000000-440000001+5−1−51−5−1+50000000000000000000000
χ494-4044-4-4040000-4440000-4-4000000000000000000000000004-400000000000000000000
χ504-4044-4-4040000-4440000-4-400000000000000000000000000-4400000000000000000000
χ51888−2+25−2−25−2+25−2−258-2−2+25−2−25-2-2-21−521+521−521−521+521+521−521+52−2+25−2−25-2-21−521−521−521−521+521+521+521+52000000000000000000000000000000000000
χ52888−2+25−2−25−2+25−2−25-8-2−2+25−2−25-2-2-21−521+521−521−521+521+521−521+522−252+2522−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52000000000000000000000000000000000000
χ53888−2−25−2+25−2−25−2+258-2−2−25−2+25-2-2-21+521−521+521+521−521−521+521−52−2−25−2+25-2-21+521+521+521+521−521−521−521−52000000000000000000000000000000000000
χ54888−2−25−2+25−2−25−2+25-8-2−2−25−2+25-2-2-21+521−521+521+521−521−521+521−522+252−2522−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52000000000000000000000000000000000000
χ5588-8−2+25−2−25−2+25−2−250-22−252+2522-21−521+52−1+52−1+52−1−52−1−521−521+520025−255−525−52−5+52−5+52−5−52−5−525+525+52000000000000000000000000000000000000
χ5688-8−2+25−2−25−2+25−2−250-22−252+2522-21−521+52−1+52−1+52−1−52−1−521−521+5200−2525−5+52−5+525−525−525+525+52−5−52−5−52000000000000000000000000000000000000
χ5788-8−2−25−2+25−2−25−2+250-22+252−2522-21+521−52−1−52−1−52−1+52−1+521+521−520025−25−5−52−5−525+525+525−525−52−5+52−5+52000000000000000000000000000000000000
χ5888-8−2−25−2+25−2−25−2+250-22+252−2522-21+521−52−1−52−1−52−1+52−1+521+521−5200−25255+525+52−5−52−5−52−5+52−5+525−525−52000000000000000000000000000000000000
χ598-8088-8-80-20025−252-2-225−2525−2522000000000000000000000000000000000000000000000000
χ608-8088-8-80-200−25252-2-2−2525−252522000000000000000000000000000000000000000000000000
χ618-80−2+25−2−252−252+25080000-8−2+25−2−2500002−252+25000000000000000000000000000000000000000000000000
χ628-80−2+25−2−252−252+250-20025−2521−521+525−52−5+52−5−525+52−1+52−1−520000−2ζ3−2ζ7−3ζ11−3ζ192ζ3+2ζ7+3ζ11+3ζ194ζ3+4ζ7+ζ11+ζ19−4ζ3−4ζ7−ζ11−ζ19−ζ3−ζ7−4ζ11−4ζ19ζ3+ζ7+4ζ11+4ζ193ζ3+3ζ7+2ζ11+2ζ19−3ζ3−3ζ7−2ζ11−2ζ19000000000000000000000000000000000000
χ638-80−2+25−2−252−252+250-20025−2521−521+525−52−5+52−5−525+52−1+52−1−5200002ζ3+2ζ7+3ζ11+3ζ19−2ζ3−2ζ7−3ζ11−3ζ19−4ζ3−4ζ7−ζ11−ζ194ζ3+4ζ7+ζ11+ζ19ζ3+ζ7+4ζ11+4ζ19−ζ3−ζ7−4ζ11−4ζ19−3ζ3−3ζ7−2ζ11−2ζ193ζ3+3ζ7+2ζ11+2ζ19000000000000000000000000000000000000
χ648-80−2+25−2−252−252+250-200−252521−521+52−5+525−525+52−5−52−1+52−1−5200004ζ3+4ζ7+ζ11+ζ19−4ζ3−4ζ7−ζ11−ζ192ζ3+2ζ7+3ζ11+3ζ19−2ζ3−2ζ7−3ζ11−3ζ19−3ζ3−3ζ7−2ζ11−2ζ193ζ3+3ζ7+2ζ11+2ζ19−ζ3−ζ7−4ζ11−4ζ19ζ3+ζ7+4ζ11+4ζ19000000000000000000000000000000000000
χ658-80−2+25−2−252−252+250-200−252521−521+52−5+525−525+52−5−52−1+52−1−520000−4ζ3−4ζ7−ζ11−ζ194ζ3+4ζ7+ζ11+ζ19−2ζ3−2ζ7−3ζ11−3ζ192ζ3+2ζ7+3ζ11+3ζ193ζ3+3ζ7+2ζ11+2ζ19−3ζ3−3ζ7−2ζ11−2ζ19ζ3+ζ7+4ζ11+4ζ19−ζ3−ζ7−4ζ11−4ζ19000000000000000000000000000000000000
χ668-80−2−25−2+252+252−25080000-8−2−25−2+2500002+252−25000000000000000000000000000000000000000000000000
χ678-80−2−25−2+252+252−250-20025−2521+521−52−5−525+525−52−5+52−1−52−1+520000−ζ3−ζ7−4ζ11−4ζ19ζ3+ζ7+4ζ11+4ζ19−3ζ3−3ζ7−2ζ11−2ζ193ζ3+3ζ7+2ζ11+2ζ192ζ3+2ζ7+3ζ11+3ζ19−2ζ3−2ζ7−3ζ11−3ζ194ζ3+4ζ7+ζ11+ζ19−4ζ3−4ζ7−ζ11−ζ19000000000000000000000000000000000000
χ688-80−2−25−2+252+252−250-20025−2521+521−52−5−525+525−52−5+52−1−52−1+520000ζ3+ζ7+4ζ11+4ζ19−ζ3−ζ7−4ζ11−4ζ193ζ3+3ζ7+2ζ11+2ζ19−3ζ3−3ζ7−2ζ11−2ζ19−2ζ3−2ζ7−3ζ11−3ζ192ζ3+2ζ7+3ζ11+3ζ19−4ζ3−4ζ7−ζ11−ζ194ζ3+4ζ7+ζ11+ζ19000000000000000000000000000000000000
χ698-80−2−25−2+252+252−250-200−252521+521−525+52−5−52−5+525−52−1−52−1+5200003ζ3+3ζ7+2ζ11+2ζ19−3ζ3−3ζ7−2ζ11−2ζ19−ζ3−ζ7−4ζ11−4ζ19ζ3+ζ7+4ζ11+4ζ194ζ3+4ζ7+ζ11+ζ19−4ζ3−4ζ7−ζ11−ζ19−2ζ3−2ζ7−3ζ11−3ζ192ζ3+2ζ7+3ζ11+3ζ19000000000000000000000000000000000000
χ708-80−2−25−2+252+252−250-200−252521+521−525+52−5−52−5+525−52−1−52−1+520000−3ζ3−3ζ7−2ζ11−2ζ193ζ3+3ζ7+2ζ11+2ζ19ζ3+ζ7+4ζ11+4ζ19−ζ3−ζ7−4ζ11−4ζ19−4ζ3−4ζ7−ζ11−ζ194ζ3+4ζ7+ζ11+ζ192ζ3+2ζ7+3ζ11+3ζ19−2ζ3−2ζ7−3ζ11−3ζ19000000000000000000000000000000000000

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