Finite Group Databasebeta

← Group #12019606

Character table — Group #12019606

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size112444444488161616161622488888881616323232323222488888881616323232323255102020202020202040408080808080
order1224448888224444451010202020404040401010202020202051010202020404040401010202020202022244488882244444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111-1-1-1-11111111111111-1-1-1-11111111111111-1-1-1-11111111111111-1-1-1-1
χ31111111111-1-1-1ii−i−i1111111111-1-1-1ii−i−i1111111111-1-1-1ii−i−i1111111111-1-1-1ii−i−i
χ41111111111-1-1-1−i−iii1111111111-1-1-1−i−iii1111111111-1-1-1−i−iii1111111111-1-1-1−i−iii
χ5111111-1-1-1-111-11-11-1111111-1-1-1-111-11-11-1111111-1-1-1-111-11-11-1111111-1-1-1-111-11-11-1
χ6111111-1-1-1-111-1-11-11111111-1-1-1-111-1-11-11111111-1-1-1-111-1-11-11111111-1-1-1-111-1-11-11
χ7111111-1-1-1-1-1-11i−i−ii111111-1-1-1-1-1-11i−i−ii111111-1-1-1-1-1-11i−i−ii111111-1-1-1-1-1-11i−i−ii
χ8111111-1-1-1-1-1-11−iii−i111111-1-1-1-1-1-11−iii−i111111-1-1-1-1-1-11−iii−i111111-1-1-1-1-1-11−iii−i
χ9222-2-2200002-200000222-2-2200002-200000222-2-2200002-200000222-2-2200002-200000
χ10222-2-220000-2200000222-2-220000-2200000222-2-220000-2200000222-2-220000-2200000
χ1144400-40000000000044400-40000000000044400-40000000000044400-400000000000
χ1244-400022-2-2000000044-400022-2-2000000044-400022-2-2000000044-400022-2-20000000
χ1344-4000-2-222000000044-4000-2-222000000044-4000-2-222000000044-4000-2-2220000000
χ144-402-20002i2−2i200000004-402-20002i2−2i200000004-402-20002i2−2i200000004-402-20002i2−2i20000000
χ154-402-2000−2i22i200000004-402-2000−2i22i200000004-402-2000−2i22i200000004-402-2000−2i22i20000000
χ164-40-2202i2−2i20000000004-40-2202i2−2i20000000004-40-2202i2−2i20000000004-40-2202i2−2i2000000000
χ174-40-220−2i22i20000000004-40-220−2i22i20000000004-40-220−2i22i20000000004-40-220−2i22i2000000000
χ18111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ191111111111111-1-1-1-11111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ201111111111-1-1-1ii−i−i1111111111-1-1-1ii−i−i1111111111-1-1-1ii−i−i-1-1-1-1-1-1-1-1-1-1111−i−iii
χ211111111111-1-1-1−i−iii1111111111-1-1-1−i−iii1111111111-1-1-1−i−iii-1-1-1-1-1-1-1-1-1-1111ii−i−i
χ22111111-1-1-1-111-11-11-1111111-1-1-1-111-11-11-1111111-1-1-1-111-11-11-1-1-1-1-1-1-11111-1-11-11-11
χ23111111-1-1-1-111-1-11-11111111-1-1-1-111-1-11-11111111-1-1-1-111-1-11-11-1-1-1-1-1-11111-1-111-11-1
χ24111111-1-1-1-1-1-11i−i−ii111111-1-1-1-1-1-11i−i−ii111111-1-1-1-1-1-11i−i−ii-1-1-1-1-1-1111111-1−iii−i
χ25111111-1-1-1-1-1-11−iii−i111111-1-1-1-1-1-11−iii−i111111-1-1-1-1-1-11−iii−i-1-1-1-1-1-1111111-1i−i−ii
χ26222-2-2200002-200000222-2-2200002-200000222-2-2200002-200000-2-2-222-20000-2200000
χ27222-2-220000-2200000222-2-220000-2200000222-2-220000-2200000-2-2-222-200002-200000
χ2844400-40000000000044400-40000000000044400-400000000000-4-4-400400000000000
χ2944-400022-2-2000000044-400022-2-2000000044-400022-2-20000000-4-44000-2-2220000000
χ3044-4000-2-222000000044-4000-2-222000000044-4000-2-2220000000-4-4400022-2-20000000
χ314-402-20002i2−2i200000004-402-20002i2−2i200000004-402-20002i2−2i20000000-440-22000−2i22i20000000
χ324-402-2000−2i22i200000004-402-2000−2i22i200000004-402-2000−2i22i20000000-440-220002i2−2i20000000
χ334-40-2202i2−2i20000000004-40-2202i2−2i20000000004-40-2202i2−2i2000000000-4402-20−2i22i2000000000
χ344-40-220−2i22i20000000004-40-220−2i22i20000000004-40-220−2i22i2000000000-4402-202i2−2i2000000000
χ3522222222222222222−1+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+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−5200000000000000000
χ362222222222222-2-2-2-2−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+5200000000000000000
χ372222222222-2-2-22i2i−2i−2i−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−52−ζ22−ζ38−ζ22−ζ38ζ22+ζ38ζ22+ζ38−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+52−ζ6−ζ14−ζ6−ζ14ζ6+ζ14ζ6+ζ1400000000000000000
χ382222222222-2-2-2−2i−2i2i2i−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−52ζ22+ζ38ζ22+ζ38−ζ22−ζ38−ζ22−ζ38−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+52ζ6+ζ14ζ6+ζ14−ζ6−ζ14−ζ6−ζ1400000000000000000
χ39222222-2-2-2-222-22-22-2−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−52−1+52−1+521−52−1+521−52−1+521−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+52−1−52−1−521+52−1−521+52−1−521+5200000000000000000
χ40222222-2-2-2-222-2-22-22−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−52−1+52−1+521−521−52−1+521−52−1+52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+52−1−52−1−521+521+52−1−521+52−1−5200000000000000000
χ41222222-2-2-2-2-2-222i−2i−2i2i−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−521−521−52−1+52−ζ22−ζ38ζ22+ζ38ζ22+ζ38−ζ22−ζ38−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+521+521+52−1−52−ζ6−ζ14ζ6+ζ14ζ6+ζ14−ζ6−ζ1400000000000000000
χ42222222-2-2-2-2-2-22−2i2i2i−2i−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−521−521−52−1+52ζ22+ζ38−ζ22−ζ38−ζ22−ζ38ζ22+ζ38−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+521+521+52−1−52ζ6+ζ14−ζ6−ζ14−ζ6−ζ14ζ6+ζ1400000000000000000
χ43444-4-4400004-400000−1+5−1+5−1+51−51−5−1+50000−1+51−500000−1−5−1−5−1−51+51+5−1−50000−1−51+50000000000000000000000
χ44444-4-440000-4400000−1+5−1+5−1+51−51−5−1+500001−5−1+500000−1−5−1−5−1−51+51+5−1−500001+5−1−50000000000000000000000
χ4588800-800000000000−2+25−2+25−2+25002−2500000000000−2−25−2−25−2−25002+250000000000000000000000000000
χ4688-800044-4-40000000−2+25−2+252−25000−1+5−1+51−51−50000000−2−25−2−252+25000−1−5−1−51+51+5000000000000000000000000
χ4788-8000-4-4440000000−2+25−2+252−250001−51−5−1+5−1+50000000−2−25−2−252+250001+51+5−1−5−1−5000000000000000000000000
χ488-804-40004i2−4i20000000−2+252−250−1+51−50002ζ7+2ζ13+2ζ23+2ζ37−2ζ7−2ζ13−2ζ23−2ζ370000000−2−252+250−1−51+50002ζ21+2ζ29+2ζ31+2ζ39−2ζ21−2ζ29−2ζ31−2ζ39000000000000000000000000
χ498-804-4000−4i24i20000000−2+252−250−1+51−5000−2ζ7−2ζ13−2ζ23−2ζ372ζ7+2ζ13+2ζ23+2ζ370000000−2−252+250−1−51+5000−2ζ21−2ζ29−2ζ31−2ζ392ζ21+2ζ29+2ζ31+2ζ39000000000000000000000000
χ508-80-4404i2−4i2000000000−2+252−2501−5−1+502ζ7+2ζ13+2ζ23+2ζ37−2ζ7−2ζ13−2ζ23−2ζ37000000000−2−252+2501+5−1−502ζ21+2ζ29+2ζ31+2ζ39−2ζ21−2ζ29−2ζ31−2ζ3900000000000000000000000000
χ518-80-440−4i24i2000000000−2+252−2501−5−1+50−2ζ7−2ζ13−2ζ23−2ζ372ζ7+2ζ13+2ζ23+2ζ37000000000−2−252+2501+5−1−50−2ζ21−2ζ29−2ζ31−2ζ392ζ21+2ζ29+2ζ31+2ζ3900000000000000000000000000
χ5222222222222222222−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+5200000000000000000
χ532222222222222-2-2-2-2−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+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+52−1+521−521−521−521−5200000000000000000
χ542222222222-2-2-22i2i−2i−2i−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+52−ζ6−ζ14−ζ6−ζ14ζ6+ζ14ζ6+ζ14−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−52−ζ22−ζ38−ζ22−ζ38ζ22+ζ38ζ22+ζ3800000000000000000
χ552222222222-2-2-2−2i−2i2i2i−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+52ζ6+ζ14ζ6+ζ14−ζ6−ζ14−ζ6−ζ14−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−52ζ22+ζ38ζ22+ζ38−ζ22−ζ38−ζ22−ζ3800000000000000000
χ56222222-2-2-2-222-22-22-2−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+52−1−52−1−521+52−1−521+52−1−521+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−52−1+52−1+521−52−1+521−52−1+521−5200000000000000000
χ57222222-2-2-2-222-2-22-22−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+52−1−52−1−521+521+52−1−521+52−1−52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−52−1+52−1+521−521−52−1+521−52−1+5200000000000000000
χ58222222-2-2-2-2-2-222i−2i−2i2i−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+521+521+52−1−52−ζ6−ζ14ζ6+ζ14ζ6+ζ14−ζ6−ζ14−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−521−521−52−1+52−ζ22−ζ38ζ22+ζ38ζ22+ζ38−ζ22−ζ3800000000000000000
χ59222222-2-2-2-2-2-22−2i2i2i−2i−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+521+521+52−1−52ζ6+ζ14−ζ6−ζ14−ζ6−ζ14ζ6+ζ14−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−521−521−52−1+52ζ22+ζ38−ζ22−ζ38−ζ22−ζ38ζ22+ζ3800000000000000000
χ60444-4-4400004-400000−1−5−1−5−1−51+51+5−1−50000−1−51+500000−1+5−1+5−1+51−51−5−1+50000−1+51−50000000000000000000000
χ61444-4-440000-4400000−1−5−1−5−1−51+51+5−1−500001+5−1−500000−1+5−1+5−1+51−51−5−1+500001−5−1+50000000000000000000000
χ6288800-800000000000−2−25−2−25−2−25002+2500000000000−2+25−2+25−2+25002−250000000000000000000000000000
χ6388-800044-4-40000000−2−25−2−252+25000−1−5−1−51+51+50000000−2+25−2+252−25000−1+5−1+51−51−5000000000000000000000000
χ6488-8000-4-4440000000−2−25−2−252+250001+51+5−1−5−1−50000000−2+25−2+252−250001−51−5−1+5−1+5000000000000000000000000
χ658-804-40004i2−4i20000000−2−252+250−1−51+50002ζ21+2ζ29+2ζ31+2ζ39−2ζ21−2ζ29−2ζ31−2ζ390000000−2+252−250−1+51−50002ζ7+2ζ13+2ζ23+2ζ37−2ζ7−2ζ13−2ζ23−2ζ37000000000000000000000000
χ668-804-4000−4i24i20000000−2−252+250−1−51+5000−2ζ21−2ζ29−2ζ31−2ζ392ζ21+2ζ29+2ζ31+2ζ390000000−2+252−250−1+51−5000−2ζ7−2ζ13−2ζ23−2ζ372ζ7+2ζ13+2ζ23+2ζ37000000000000000000000000
χ678-80-4404i2−4i2000000000−2−252+2501+5−1−502ζ21+2ζ29+2ζ31+2ζ39−2ζ21−2ζ29−2ζ31−2ζ39000000000−2+252−2501−5−1+502ζ7+2ζ13+2ζ23+2ζ37−2ζ7−2ζ13−2ζ23−2ζ3700000000000000000000000000
χ688-80-440−4i24i2000000000−2−252+2501+5−1−50−2ζ21−2ζ29−2ζ31−2ζ392ζ21+2ζ29+2ζ31+2ζ39000000000−2+252−2501−5−1+50−2ζ7−2ζ13−2ζ23−2ζ372ζ7+2ζ13+2ζ23+2ζ3700000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.