Finite Group Databasebeta

← Group #10612628

Character table — Group #10612628

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size111122222222224444448888888888888888881616161616161616202020202020202040404040
order1222445510101010101024202020204444881010202040404040404040402020202020202020444488882444
χ11111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-111-1
χ41111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111111-1-11
χ511111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11-1-11
χ611111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-111-1
χ711111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ811111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ911111111111111-1-111111-11-11-1-1-1-1-11111-1-1-1-111-1-1-1-1111-11-111-1-111-1-1
χ1011111111111111-1-111111-11-11-1-1-1-1-11111-1-1-1-111-1-1-1-111-11-11-1-111-1-111
χ1111111111111111-1-111111-1-11-11-1-1-1-1-1-1-1-111111111-1-1-1-11-11-1-1-111-11-11
χ1211111111111111-1-111111-1-11-11-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1111-1-11-11-1
χ1311111111111111-1-11111-111-1-11-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1-1-1111-11-1
χ1411111111111111-1-11111-111-1-11-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1111-1-1-11-11
χ1511111111111111-1-11111-11-111-1-1-1-1-11111-1-1-1-1-1-11111-1-11-11-111-1-1-1-111
χ1611111111111111-1-11111-11-111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-11-11-1-11111-1-1
χ17222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222−1+52−1−52−1+52−1−52222222−1+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+52−1−52000000000000
χ18222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222−1+52−1−52−1+52−1−5222-2-2-2-2−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1−521−521+52−1+52−1−521−521+52000000000000
χ19222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222−1+52−1−52−1+52−1−52-2-222-2-2−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+521−521+52−1+52−1−521−521+52−1+52−1−52000000000000
χ20222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222−1+52−1−52−1+52−1−52-2-2-2-222−1+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+521−521+521−521+52000000000000
χ21222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−522-22-22-21−521+521−521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−521−521+521−521+52−1+52−1−52000000000000
χ22222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−522-2-22-221−521+521−521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−521−521+521−521+52000000000000
χ23222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−52-222-2-221−521+521−521+521−521−521+521+52−1+52−1+52−1−52−1−521−521+521−521+52−1+52−1−52−1+52−1−52000000000000
χ24222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−52-22-222-21−521+521−521+52−1+52−1+52−1−52−1−521−521−521+521+521−521+52−1+52−1−52−1+52−1−521−521+52000000000000
χ25222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222−1−52−1+52−1−52−1+52222222−1−52−1+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+52000000000000
χ26222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222−1−52−1+52−1−52−1+5222-2-2-2-2−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1+521+521−52−1−52−1+521+521−52000000000000
χ27222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222−1−52−1+52−1−52−1+52-2-222-2-2−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−521+521−52−1−52−1+521+521−52−1−52−1+52000000000000
χ28222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222−1−52−1+52−1−52−1+52-2-2-2-222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521−521+521−521+521−521+521−52000000000000
χ29222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+522-22-22-21+521−521+521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+521+521−521+521−52−1−52−1+52000000000000
χ30222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+522-2-22-221+521−521+521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+521+521−521+521−52000000000000
χ31222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+52-222-2-221+521−521+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+52000000000000
χ32222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+52-22-222-21+521−521+521−52−1−52−1−52−1+52−1+521+521+521−521−521+521−52−1−52−1+52−1−52−1+521+521−52000000000000
χ332222-2-2222222222-2-2-2-2-200000022-2-200000000000000002-2-2200000000
χ342222-2-2222222222-2-2-2-2-200000022-2-20000000000000000-222-200000000
χ352222-2-222222222-22-2-2-2-2000000-2-222000000000000000022-2-200000000
χ362222-2-222222222-22-2-2-2-2000000-2-2220000000000000000-2-22200000000
χ374444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−54-41−51+51−51+5000000−1+5−1−51−51+50000000000000000000000000000
χ384444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5-441−51+51−51+50000001−51+5−1+5−1−50000000000000000000000000000
χ394444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+54-41+51−51+51−5000000−1−5−1+51+51−50000000000000000000000000000
χ404444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5-441+51−51+51−50000001+51−5−1−5−1+50000000000000000000000000000
χ4144-4-400444-44-4-4-400000000000000000000000000000000000022−22000000
χ4244-4-400444-44-4-4-4000000000000000000000000000000000000−2222000000
χ434-44-44-444-4-4-4-4440044-4-400000000000000000000000000000000000000
χ444-44-44-4−1+5−1−51−51−51+51+5−1+5−1−500−1+5−1−51−51+50000000000−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ14000000000000000000000000
χ454-44-44-4−1+5−1−51−51−51+51+5−1+5−1−500−1+5−1−51−51+500000000002ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ14000000000000000000000000
χ464-44-44-4−1−5−1+51+51+51−51−5−1−5−1+500−1−5−1+51+51−500000000002ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ38000000000000000000000000
χ474-44-44-4−1−5−1+51+51+51−51−5−1−5−1+500−1−5−1+51+51−50000000000−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ38000000000000000000000000
χ484-44-4-4444-4-4-4-44400-4-44400000000000000000000000000000000000000
χ494-44-4-44−1+5−1−51−51−51+51+5−1+5−1−5001−51+5−1+5−1−5000000000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ3600000000000000000000
χ504-44-4-44−1+5−1−51−51−51+51+5−1+5−1−5001−51+5−1+5−1−500000000000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ3600000000000000000000
χ514-44-4-44−1−5−1+51+51+51−51−5−1−5−1+5001+51−5−1−5−1+500000000000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ2800000000000000000000
χ524-44-4-44−1−5−1+51+51+51−51−5−1−5−1+5001+51−5−1−5−1+5000000000000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ2800000000000000000000
χ534-4-440044-44-44-4-4000000000000000000000000000000000000002i2−2i20000
χ544-4-440044-44-44-4-400000000000000000000000000000000000000−2i22i20000
χ5588-8-800−2+25−2−25−2+252−25−2−252+252−252+2500000000000000000000000000000000000000000000
χ5688-8-800−2−25−2+25−2−252+25−2+252−252+252−2500000000000000000000000000000000000000000000
χ578-8-8800−2+25−2−252−25−2+252+25−2−252−252+2500000000000000000000000000000000000000000000
χ588-8-8800−2−25−2+252+25−2−252−25−2+252+252−2500000000000000000000000000000000000000000000

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