Finite Group Databasebeta

← Group #10613607

Character table — Group #10613607

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size111122222222224444448888888888888888881010101016161616161616162020404040404040
order1222445510101010101044202020202444882020202040404040404040402244101020202020202044444488
χ11111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ41111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ611111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ711111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ811111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ911111111111111-1-111111-11-11-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1-111-11-11-1
χ1011111111111111-1-111111-11-11-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-11-1-11-11-11
χ1111111111111111-1-111111-1-11-11-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-111-1-11-11
χ1211111111111111-1-111111-1-11-11-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111-1-111-11-1
χ1311111111111111-1-11111-111-1-11-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-11-111-1-11
χ1411111111111111-1-11111-111-1-11-1-1-1-1-1-1-1-11111-1-111-1-11111-1-11-11-1-111-1
χ1511111111111111-1-11111-11-111-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-11-11-111-1
χ1611111111111111-1-11111-11-111-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1111-11-11-1-11
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+52−1−52−1−520000−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5200000000
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+520000−1+52−1−52−1+52−1−521−521+521−521+5200000000
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+5200001−521+521−521+52−1+52−1−52−1+52−1−5200000000
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+52−1−52−1−5200001−521+521−521+521−521+521−521+5200000000
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+520000−1+52−1−521−521+52−1+52−1−521−521+5200000000
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+52−1−52−1−520000−1+52−1−521−521+521−521+52−1+52−1−5200000000
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+52−1−52−1−5200001−521+52−1+52−1−52−1+52−1−521−521+5200000000
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+5200001−521+52−1+52−1−521−521+52−1+52−1−5200000000
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+520000−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5200000000
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+521−521−520000−1−52−1+52−1−52−1+521+521−521+521−5200000000
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+521−521−5200001+521−521+521−52−1−52−1+52−1−52−1+5200000000
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+5200001+521−521+521−521+521−521+521−5200000000
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+521−521−520000−1−52−1+521+521−52−1−52−1+521+521−5200000000
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+520000−1−52−1+521+521−521+521−52−1−52−1+5200000000
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+5200001+521−52−1−52−1+52−1−52−1+521+521−5200000000
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+521−521−5200001+521−52−1−52−1+521+521−52−1−52−1+5200000000
χ332222-2-2222222222-2-2-2-2-20000002-22-200000000222200000000-2-2000000
χ342222-2-2222222222-2-2-2-2-20000002-22-200000000-2-2-2-20000000022000000
χ352222-2-222222222-22-2-2-2-2000000-22-220000000022-2-2000000002-2000000
χ362222-2-222222222-22-2-2-2-2000000-22-2200000000-2-22200000000-22000000
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+51−5−1−51+50000000000000000000000000000
χ384444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5-441−51−51+51+50000001−5−1+51+5−1−50000000000000000000000000000
χ394444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+54-41+51+51−51−5000000−1−51+5−1+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+5−1−51−5−1+50000000000000000000000000000
χ4144-4-400444-44-4-4-4000000000000000000000000004-40000000000000000
χ4244-4-400444-44-4-4-400000000000000000000000000-440000000000000000
χ434-44-40044-44-44-4-40000000000000000000000004-4000000000000000000
χ444-44-40044-44-44-4-4000000000000000000000000-44000000000000000000
χ454-4-444-444-4-4-4-444004-44-400000000000000000000000000000000000000
χ464-4-444-4−1+5−1−51−51−51+51+5−1+5−1−500−1+51−5−1−51+500000000002ζ−2ζ4−2ζ+2ζ42ζ2−2ζ3−2ζ2+2ζ3000000000000000000000000
χ474-4-444-4−1+5−1−51−51−51+51+5−1+5−1−500−1+51−5−1−51+50000000000−2ζ+2ζ42ζ−2ζ4−2ζ2+2ζ32ζ2−2ζ3000000000000000000000000
χ484-4-444-4−1−5−1+51+51+51−51−5−1−5−1+500−1−51+5−1+51−500000000002ζ2−2ζ3−2ζ2+2ζ3−2ζ+2ζ42ζ−2ζ4000000000000000000000000
χ494-4-444-4−1−5−1+51+51+51−51−5−1−5−1+500−1−51+5−1+51−50000000000−2ζ2+2ζ32ζ2−2ζ32ζ−2ζ4−2ζ+2ζ4000000000000000000000000
χ504-4-44-4444-4-4-4-44400-44-4400000000000000000000000000000000000000
χ514-4-44-44−1+5−1−51−51−51+51+5−1+5−1−5001−5−1+51+5−1−5000000000000002ζ−2ζ4−2ζ+2ζ42ζ2−2ζ3−2ζ2+2ζ300000000000000000000
χ524-4-44-44−1+5−1−51−51−51+51+5−1+5−1−5001−5−1+51+5−1−500000000000000−2ζ+2ζ42ζ−2ζ4−2ζ2+2ζ32ζ2−2ζ300000000000000000000
χ534-4-44-44−1−5−1+51+51+51−51−5−1−5−1+5001+5−1−51−5−1+5000000000000002ζ2−2ζ3−2ζ2+2ζ3−2ζ+2ζ42ζ−2ζ400000000000000000000
χ544-4-44-44−1−5−1+51+51+51−51−5−1−5−1+5001+5−1−51−5−1+500000000000000−2ζ2+2ζ32ζ2−2ζ32ζ−2ζ4−2ζ+2ζ400000000000000000000
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
χ578-88-800−2+25−2−252−25−2+252+25−2−252−252+2500000000000000000000000000000000000000000000
χ588-88-800−2−25−2+252+25−2−252−25−2+252+252−2500000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 5 (ζ5 = 1).