Finite Group Databasebeta

← Group #10612521

Character table — Group #10612521

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size1111222222222244444444448888888888888888101010101010101016161616161616162020202040404040
order1222445510101010101024888820202020244410102020404040404040404044444444101020202020202088882444
χ11111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-111111-11-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-11-1
χ61111111111111111-1-1-1-111111-11-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11
χ71111111111111111-1-1-1-11111-11-111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-11-11
χ81111111111111111-1-1-1-11111-11-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1
χ911111111111111-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-1
χ1011111111111111-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-111-1-1-1-111-1-111
χ1111111111111111-1-111-1-11111-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1-111-1-11111-1-1-1-111
χ1211111111111111-1-111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111-1-11111-1-1
χ1311111111111111-1-1-1-11111111-1-11-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-111-1-1111-1-11
χ1411111111111111-1-1-1-11111111-1-11-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-111-1
χ1511111111111111-1-1-1-1111111-111-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-111-111-1
χ1611111111111111-1-1-1-1111111-111-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-1-111-1-11-1-11
χ17222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52222222−1+52−1−52−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000−1+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+52−1−52−1−52222222−1+52−1−52−1+52−1−52-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000001−521+521−521+521−521+521−521+5200000000
χ19222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222-2-2-2-2−1+52−1−52−1+52−1−522-22-2−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+5200000000−1+52−1−52−1+52−1−521−521+521−521+5200000000
χ20222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222-2-2-2-2−1+52−1−52−1+52−1−52-22-22−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52000000001−521+521−521+52−1+52−1−52−1+52−1−5200000000
χ21222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-222-2-2−1+52−1−52−1+52−1−5222-2-21−521+521−521+52−1+52−1+52−1−52−1−521−521−521+521+5200000000−1+52−1−521−521+52−1+52−1−521−521+5200000000
χ22222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-222-2-2−1+52−1−52−1+52−1−52-2-2221−521+521−521+52−1+52−1+52−1−52−1−521−521−521+521+52000000001−521+52−1+52−1−521−521+52−1+52−1−5200000000
χ23222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-2-2-222−1+52−1−52−1+52−1−522-2-221−521+521−521+521−521−521+521+52−1+52−1+52−1−52−1−5200000000−1+52−1−521−521+521−521+52−1+52−1−5200000000
χ24222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-2-2-222−1+52−1−52−1+52−1−52-222-21−521+521−521+521−521−521+521+52−1+52−1+52−1−52−1−52000000001−521+52−1+52−1−52−1+52−1−521−521+5200000000
χ25222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52222222−1−52−1+52−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000000−1−52−1+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+52222222−1−52−1+52−1−52−1+52-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000001+521−521+521−521+521−521+521−5200000000
χ27222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222-2-2-2-2−1−52−1+52−1−52−1+522-22-2−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−5200000000−1−52−1+52−1−52−1+521+521−521+521−5200000000
χ28222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222-2-2-2-2−1−52−1+52−1−52−1+52-22-22−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52000000001+521−521+521−52−1−52−1+52−1−52−1+5200000000
χ29222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-222-2-2−1−52−1+52−1−52−1+5222-2-21+521−521+521−52−1−52−1−52−1+52−1+521+521+521−521−5200000000−1−52−1+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+52-2-222-2-2−1−52−1+52−1−52−1+52-2-2221+521−521+521−52−1−52−1−52−1+52−1+521+521+521−521−52000000001+521−52−1−52−1+521+521−52−1−52−1+5200000000
χ31222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-2-2-222−1−52−1+52−1−52−1+522-2-221+521−521+521−521+521+521−521−52−1−52−1−52−1+52−1+5200000000−1−52−1+521+521−521+521−52−1−52−1+5200000000
χ32222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-2-2-222−1−52−1+52−1−52−1+52-222-21+521−521+521−521+521+521−521−52−1−52−1−52−1+52−1+52000000001+521−52−1−52−1+52−1−52−1+521+521−5200000000
χ332222-2-2222222222-20000-2-2-2-2000022-2-2000000002222-2-2-2-20000000000000000
χ342222-2-2222222222-20000-2-2-2-2000022-2-200000000-2-2-2-222220000000000000000
χ352222-2-222222222-220000-2-2-2-20000-2-2220000000022-2-2-2-2220000000000000000
χ362222-2-222222222-220000-2-2-2-20000-2-22200000000-2-22222-2-20000000000000000
χ372-22-22-222-2-22-22-2002-200-2-222000000002-22-20000002i−2i002i−2i00000000002i−2i0000
χ382-22-22-222-2-22-22-2002-200-2-222000000002-22-2000000−2i2i00−2i2i0000000000−2i2i0000
χ392-22-22-222-2-22-22-200-2200-2-22200000000-22-220000002i−2i002i−2i0000000000−2i2i0000
χ402-22-22-222-2-22-22-200-2200-2-22200000000-22-22000000−2i2i00−2i2i00000000002i−2i0000
χ412-22-2-2222-2-22-22-200002i−2i22-2-20000000000002i−2i2i−2i002i−2i00−2i2i000000002-2000000
χ422-22-2-2222-2-22-22-200002i−2i22-2-20000000000002i−2i2i−2i00−2i2i002i−2i00000000-22000000
χ432-22-2-2222-2-22-22-20000−2i2i22-2-2000000000000−2i2i−2i2i002i−2i00−2i2i00000000-22000000
χ442-22-2-2222-2-22-22-20000−2i2i22-2-2000000000000−2i2i−2i2i00−2i2i002i−2i000000002-2000000
χ454444-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−54-400001−51+51−51+50000−1+5−1−51−51+500000000000000000000000000000000
χ464444-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5-4400001−51+51−51+500001−51+5−1+5−1−500000000000000000000000000000000
χ474444-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+54-400001+51−51+51−50000−1−5−1+51+51−500000000000000000000000000000000
χ484444-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5-4400001+51−51+51−500001+51−5−1−5−1+500000000000000000000000000000000
χ4944-4-4004444-4-4-4-4000000000000000000000000004-40000000000000000000000
χ5044-4-4004444-4-4-4-400000000000000000000000000-440000000000000000000000
χ514-44-44-4−1+5−1−51−51+5−1+51−5−1−51+5004-4001−51+5−1+5−1−500000000−1+51−5−1−51+50000000000000000000000000000
χ524-44-44-4−1+5−1−51−51+5−1+51−5−1−51+500-44001−51+5−1+5−1−5000000001−5−1+51+5−1−50000000000000000000000000000
χ534-44-44-4−1−5−1+51+51−5−1−51+5−1+51−5004-4001+51−5−1−5−1+500000000−1−51+5−1+51−50000000000000000000000000000
χ544-44-44-4−1−5−1+51+51−5−1−51+5−1+51−500-44001+51−5−1−5−1+5000000001+5−1−51−5−1+50000000000000000000000000000
χ554-44-4-44−1+5−1−51−51+5−1+51−5−1−51+500004i−4i−1+5−1−51−51+5000000000000−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7000000000000000000000000
χ564-44-4-44−1+5−1−51−51+5−1+51−5−1−51+50000−4i4i−1+5−1−51−51+50000000000002ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ7000000000000000000000000
χ574-44-4-44−1−5−1+51+51−5−1−51+5−1+51−500004i−4i−1−5−1+51+51−5000000000000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19000000000000000000000000
χ584-44-4-44−1−5−1+51+51−5−1−51+5−1+51−50000−4i4i−1−5−1+51+51−50000000000002ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ19000000000000000000000000
χ594-4-440044-4-4-44-440000000000000000000000000000004-4000000000000000000
χ604-4-440044-4-4-44-44000000000000000000000000000000-44000000000000000000
χ6188-8-800−2+25−2−25−2+25−2−252−252−252+252+2500000000000000000000000000000000000000000000000000
χ6288-8-800−2−25−2+25−2−25−2+252+252+252−252−2500000000000000000000000000000000000000000000000000
χ638-8-8800−2+25−2−252−252+252−25−2+252+25−2−2500000000000000000000000000000000000000000000000000
χ648-8-8800−2−25−2+252+252−252+25−2−252−25−2+2500000000000000000000000000000000000000000000000000

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