Finite Group Databasebeta

← Group #10599941

Character table — Group #10599941

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46
size1122222444444488888888888161616161616161616161616202020204040404080
order1225510102244410102101010102020202020204410102020202020202020444424448
χ11111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-111-1
χ41111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11
χ5111111111-1-1111-1111111-1-1-1-11-1-1-11111-1-1-1-111-1-1111-1-1
χ6111111111-1-1111-1111111-1-1-1-11-1-1-11111-1-1-1-1-1-111-1-1-111
χ7111111111-1-1111-1111111-1-1-1-1-11-1-1-1-1-1-1111111-1-1-1-11-11
χ8111111111-1-1111-1111111-1-1-1-1-11-1-1-1-1-1-11111-1-11111-11-1
χ922222222-200-222022-2-2-2-20000000000000000220000-200
χ1022222222-200-222022-2-2-2-20000000000000000-2-20000200
χ112222222-2200-2220-2-222-2-200000000000000000022000-20
χ122222222-2200-2220-2-222-2-2000000000000000000-2-200020
χ132222222-2-222222-2-2-2-2-222222200-2-200000000000000000
χ142222222-2-2-2-22222-2-2-2-222-2-2-2-2002200000000000000000
χ15222−1+52−1−52−1+52−1−5222222−1+52−1−522−1+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+52−1−52−1−52000000000
χ16222−1+52−1−52−1+52−1−5222222−1+52−1−522−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-2−1+52−1−521−521−521+521+521−521−521+521+52000000000
χ17222−1+52−1−52−1+52−1−5222-2-22−1+52−1−52-2−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+522-21−521+52−1+52−1+52−1−52−1−521−521−521+521+52000000000
χ18222−1+52−1−52−1+52−1−5222-2-22−1+52−1−52-2−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+52-221−521+521−521−521+521+52−1+52−1+52−1−52−1−52000000000
χ19222−1+52−1−52−1+52−1−52-2-2222−1+52−1−52-21−521+521−521+52−1+52−1−52−1+52−1+52−1−52−1−52001−521+52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7000000000
χ20222−1+52−1−52−1+52−1−52-2-2222−1+52−1−52-21−521+521−521+52−1+52−1−52−1+52−1+52−1−52−1−52001−521+52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7000000000
χ21222−1+52−1−52−1+52−1−52-2-2-2-22−1+52−1−5221−521+521−521+52−1+52−1−521−521−521+521+5200−1+52−1−52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7000000000
χ22222−1+52−1−52−1+52−1−52-2-2-2-22−1+52−1−5221−521+521−521+52−1+52−1−521−521−521+521+5200−1+52−1−52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7000000000
χ23222−1−52−1+52−1−52−1+5222222−1−52−1+522−1−52−1+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+52−1−52−1−52−1+52−1+52000000000
χ24222−1−52−1+52−1−52−1+5222222−1−52−1+522−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-2−1−52−1+521+521+521−521−521+521+521−521−52000000000
χ25222−1−52−1+52−1−52−1+5222-2-22−1−52−1+52-2−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−522-21+521−52−1−52−1−52−1+52−1+521+521+521−521−52000000000
χ26222−1−52−1+52−1−52−1+5222-2-22−1−52−1+52-2−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−52-221+521−521+521+521−521−52−1−52−1−52−1+52−1+52000000000
χ27222−1−52−1+52−1−52−1+52-2-2222−1−52−1+52-21+521−521+521−52−1−52−1+52−1−52−1−52−1+52−1+52001+521−52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19000000000
χ28222−1−52−1+52−1−52−1+52-2-2222−1−52−1+52-21+521−521+521−52−1−52−1+52−1−52−1−52−1+52−1+52001+521−52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19000000000
χ29222−1−52−1+52−1−52−1+52-2-2-2-22−1−52−1+5221+521−521+521−52−1−52−1+521+521+521−521−5200−1−52−1+52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19000000000
χ30222−1−52−1+52−1−52−1+52-2-2-2-22−1−52−1+5221+521−521+521−52−1−52−1+521+521+521−521−5200−1−52−1+52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19000000000
χ31444−1+5−1−5−1+5−1−54-400-4−1+5−1−50−1+5−1−51−51+51−51+50000000000000000000000000
χ32444−1+5−1−5−1+5−1−5-4400-4−1+5−1−501−51+5−1+5−1−51−51+50000000000000000000000000
χ33444−1−5−1+5−1−5−1+54-400-4−1−5−1+50−1−5−1+51+51−51+51−50000000000000000000000000
χ34444−1−5−1+5−1−5−1+5-4400-4−1−5−1+501+51−5−1−5−1+51+51−50000000000000000000000000
χ3544-4444400000-4-40000000000000000000000000002-2000
χ3644-4444400000-4-4000000000000000000000000000-22000
χ374-4044-4-4002-200000000002-22-20000000000002i−2i2i−2i00000
χ384-4044-4-4002-200000000002-22-2000000000000−2i2i−2i2i00000
χ394-4044-4-400-220000000000-22-220000000000002i−2i−2i2i00000
χ404-4044-4-400-220000000000-22-22000000000000−2i2i2i−2i00000
χ4188-8−2+25−2−25−2+25−2−25000002−252+2500000000000000000000000000000000
χ4288-8−2−25−2+25−2−25−2+25000002+252−2500000000000000000000000000000000
χ438-80−2+25−2−252−252+25004-40000000000−1+51−5−1−51+5000000000000000000000
χ448-80−2+25−2−252−252+2500-4400000000001−5−1+51+5−1−5000000000000000000000
χ458-80−2−25−2+252+252−25004-40000000000−1−51+5−1+51−5000000000000000000000
χ468-80−2−25−2+252+252−2500-4400000000001+5−1−51−5−1+5000000000000000000000

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