Finite Group Databasebeta

← Group #12080708

Character table — Group #12080708

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222244488888888888888101016161616161616161616161616161616161616161616161616161620202032324040404040404040808080
order1222551010101010104442244448820202020202044488101010102020202020202020404040404040404040404040244202044444488488
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1111111111111111111111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-111111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111111-1-1-1-1-1
χ4111111111111111111111-1-1111111-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ51111111111111111-11-1-1-11111111111-11-111-1-111-1-1-1-1-1-111111111-1-1-1-1111-1-11-1-1-11-111-11-1
χ61111111111111111-11-1-1-111111111-1-1-11-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111-11-1-11-11
χ71111111111111111-11-1-1-1-1-1111111111-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-11-1-1-11-11
χ81111111111111111-11-1-1-1-1-1111111-1-11-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1111-1111-11-1
χ9111111111111111-11-1-11-111111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111-111-1-1-1111-1-1
χ10111111111111111-11-1-11-111111111-1-11-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1-1-111
χ11111111111111111-11-1-11-1-1-111111111-111-1-111-1-111-1-1-1-1-1-1-1-111111111111-1-1-111-1-1-1-1-1-111
χ12111111111111111-11-1-11-1-1-1111111-1-1-111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-1111111-1-1
χ13111111111111111-1-1-11-111111111111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111111-1-1-1-1-11-1111-1-11
χ14111111111111111-1-1-11-1111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1111-11-1-1-111-1
χ15111111111111111-1-1-11-11-1-11111111111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-1-11-11-1-111-1
χ16111111111111111-1-1-11-11-1-1111111-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-111111-11-111-1-11
χ172222222222222-2-200020-20022-2-2-2-2220000000000022-2-20000000000002-2-200000-20200000
χ182222222222222-2-200020-20022-2-2-2-2-2-20000000000022-2-2000000000000-2220000020-200000
χ192222222222222-2-2000-2020022-2-2-2-22200000000000-2-2220000000000002-2-20000020-200000
χ202222222222222-2-2000-2020022-2-2-2-2-2-200000000000-2-222000000000000-22200000-20200000
χ21222222222222-22-220-200000-2-222-2-2220002200-2-2000000000000000000-2-22002000-2000000
χ22222222222222-22-220-200000-2-222-2-2-2-20002200-2-200000000000000000022-200-20002000000
χ23222222222222-22-2-20200000-2-222-2-222000-2-20022000000000000000000-2-2200-20002000000
χ24222222222222-22-2-20200000-2-222-2-2-2-2000-2-2002200000000000000000022-2002000-2000000
χ25222222222222-2-220200-2000-2-2-2-22222000002200-2-20000000000000000-22-20002-200000000
χ26222222222222-2-220200-2000-2-2-2-222-2-2000002200-2-200000000000000002-22000-2200000000
χ27222222222222-2-220-2002000-2-2-2-2222200000-2-200220000000000000000-22-2000-2200000000
χ28222222222222-2-220-2002000-2-2-2-222-2-200000-2-2002200000000000000002-220002-200000000
χ292222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−5222222222222−1+52−1−52−1+52−1−52−1+52−1−5200222−1+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+52−1−52−1−52000−1+52−1−5200000000000
χ302222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52222222222-2-2−1+52−1−52−1+52−1−52−1+52−1−5200-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+521−521−521+521+520001−521+5200000000000
χ312222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−522222-22-2-2-222−1+52−1−52−1+52−1−52−1+52−1−5200-22-2−1+52−1−521−521+52−1+52−1−521−521+521−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+520001−521+5200000000000
χ322222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−522222-22-2-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52002-22−1+52−1−521−521+52−1+52−1−521−521+521−521+521−521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52000−1+52−1−5200000000000
χ332222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52222-22-2-22-222−1+52−1−52−1+52−1−52−1+52−1−52002-2-21−521+52−1+52−1−521−521+52−1+52−1−521−521+521−521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52000−1+52−1−5200000000000
χ342222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52222-22-2-22-2-2-2−1+52−1−52−1+52−1−52−1+52−1−5200-2221−521+52−1+52−1−521−521+52−1+52−1−521−521+521−521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520001−521+5200000000000
χ352222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52222-2-2-22-2222−1+52−1−52−1+52−1−52−1+52−1−5200-2-221−521+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+52−1+52−1+52−1−52−1−520001−521+5200000000000
χ362222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52222-2-2-22-22-2-2−1+52−1−52−1+52−1−52−1+52−1−520022-21−521+521−521+521−521+521−521+52−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52000−1+52−1−5200000000000
χ372222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+5222222222222−1−52−1+52−1−52−1+52−1−52−1+5200222−1−52−1+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+52000−1−52−1+5200000000000
χ382222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52222222222-2-2−1−52−1+52−1−52−1+52−1−52−1+5200-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−521+521+521−521−520001+521−5200000000000
χ392222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+522222-22-2-2-222−1−52−1+52−1−52−1+52−1−52−1+5200-22-2−1−52−1+521+521−52−1−52−1+521+521−521+521−521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−520001+521−5200000000000
χ402222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+522222-22-2-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52002-22−1−52−1+521+521−52−1−52−1+521+521−521+521−521+521−521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52000−1−52−1+5200000000000
χ412222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52222-22-2-22-222−1−52−1+52−1−52−1+52−1−52−1+52002-2-21+521−52−1−52−1+521+521−52−1−52−1+521+521−521+521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52000−1−52−1+5200000000000
χ422222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52222-22-2-22-2-2-2−1−52−1+52−1−52−1+52−1−52−1+5200-2221+521−52−1−52−1+521+521−52−1−52−1+521+521−521+521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520001+521−5200000000000
χ432222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52222-2-2-22-2222−1−52−1+52−1−52−1+52−1−52−1+5200-2-221+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+521−521−52−1−52−1−52−1+52−1+520001+521−5200000000000
χ442222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52222-2-2-22-22-2-2−1−52−1+52−1−52−1+52−1−52−1+520022-21+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+521+521+521−521−52000−1−52−1+5200000000000
χ454444−1+5−1−5−1+5−1+5−1+5−1−5−1−5−1−54-4-400040-400−1+5−1−51−51+51−51+50000000000000−1+5−1−51−51+50000000000000000000000000000
χ464444−1+5−1−5−1+5−1+5−1+5−1−5−1−5−1−54-4-4000-40400−1+5−1−51−51+51−51+500000000000001−51+5−1+5−1−50000000000000000000000000000
χ474444−1+5−1−5−1+5−1+5−1+5−1−5−1−5−1−5-44-440-4000001−51+5−1+5−1−51−51+500000−1+5−1−5001−51+50000000000000000000000000000000000
χ484444−1+5−1−5−1+5−1+5−1+5−1−5−1−5−1−5-44-4-404000001−51+5−1+5−1−51−51+5000001−51+500−1+5−1−50000000000000000000000000000000000
χ494444−1+5−1−5−1+5−1+5−1+5−1−5−1−5−1−5-4-440400-40001−51+51−51+5−1+5−1−50000000−1+5−1−5001−51+500000000000000000000000000000000
χ504444−1+5−1−5−1+5−1+5−1+5−1−5−1−5−1−5-4-440-40040001−51+51−51+5−1+5−1−500000001−51+500−1+5−1−500000000000000000000000000000000
χ514444−1−5−1+5−1−5−1−5−1−5−1+5−1+5−1+54-4-400040-400−1−5−1+51+51−51+51−50000000000000−1−5−1+51+51−50000000000000000000000000000
χ524444−1−5−1+5−1−5−1−5−1−5−1+5−1+5−1+54-4-4000-40400−1−5−1+51+51−51+51−500000000000001+51−5−1−5−1+50000000000000000000000000000
χ534444−1−5−1+5−1−5−1−5−1−5−1+5−1+5−1+5-44-440-4000001+51−5−1−5−1+51+51−500000−1−5−1+5001+51−50000000000000000000000000000000000
χ544444−1−5−1+5−1−5−1−5−1−5−1+5−1+5−1+5-44-4-404000001+51−5−1−5−1+51+51−5000001+51−500−1−5−1+50000000000000000000000000000000000
χ554444−1−5−1+5−1−5−1−5−1−5−1+5−1+5−1+5-4-440400-40001+51−51+51−5−1−5−1+50000000−1−5−1+5001+51−500000000000000000000000000000000
χ564444−1−5−1+5−1−5−1−5−1−5−1+5−1+5−1+5-4-440-40040001+51−51+51−5−1−5−1+500000001+51−500−1−5−1+500000000000000000000000000000000
χ574-4-44444-4-44-4-40000000002i−2i0000004i−4i0000000000000002i−2i2i−2i00000000000000000002-2000
χ584-4-44444-4-44-4-40000000002i−2i000000−4i4i0000000000000002i−2i2i−2i0000000000000000000-22000
χ594-4-44444-4-44-4-4000000000−2i2i0000004i−4i000000000000000−2i2i−2i2i0000000000000000000-22000
χ604-4-44444-4-44-4-4000000000−2i2i000000−4i4i000000000000000−2i2i−2i2i00000000000000000002-2000
χ6188-8-888-88-8-88-800000000000000000000000000000000000000000000000000000000000000
χ6288-8-8−2+25−2−252−25−2+252−252+25−2−252+2500000000000000000000000000000000000000−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ700000000000000000000
χ6388-8-8−2+25−2−252−25−2+252−252+25−2−252+25000000000000000000000000000000000000002ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ700000000000000000000
χ6488-8-8−2−25−2+252+25−2−252+252−25−2+252−25000000000000000000000000000000000000002ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ1900000000000000000000
χ6588-8-8−2−25−2+252+25−2−252+252−25−2+252−2500000000000000000000000000000000000000−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ1900000000000000000000
χ668-88-888-8-88-8-8800000000000000000000000000000000000000000000000000000000000000
χ678-88-8−2+25−2−252−252−25−2+252+252+25−2−25000000000000000000000000000000000000000000−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ70000000000000000
χ688-88-8−2+25−2−252−252−25−2+252+252+25−2−250000000000000000000000000000000000000000002ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ70000000000000000
χ698-88-8−2−25−2+252+252+25−2−252−252−25−2+250000000000000000000000000000000000000000002ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ190000000000000000
χ708-88-8−2−25−2+252+252+25−2−252−252−25−2+25000000000000000000000000000000000000000000−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ190000000000000000
χ718-8-88−2+25−2−25−2+252−252−25−2−252+252+250000000004i−4i00000000000000000000000−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7000000000000000000000000
χ728-8-88−2+25−2−25−2+252−252−25−2−252+252+25000000000−4i4i000000000000000000000002ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ7000000000000000000000000
χ738-8-88−2−25−2+25−2−252+252+25−2+252−252−250000000004i−4i00000000000000000000000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19000000000000000000000000
χ748-8-88−2−25−2+25−2−252+252+25−2+252−252−25000000000−4i4i000000000000000000000002ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ19000000000000000000000000

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