Finite Group Databasebeta

← Group #12080800

Character table — Group #12080800

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111122222222444888888888888888810101010161616161616161616161616161616161616161616161616161620203232404040404040404040408080
order1222551010101010104442444448888202020202020224448101020202020202020202020404040404040404040404040442020224444888848
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-11111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1
χ4111111111111111111111-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111-11-1-1-111-1-111111111111-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-11-111-1-11-1
χ61111111111111111-11-1-1-111-1-1111111-1-1-1-11-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1111-11-1-111-11
χ71111111111111111-11-1-1-1-1-1111111111111-1111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-11-1-1-11-1-1-111-11
χ81111111111111111-11-1-1-1-1-111111111-1-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1111-1111-1-11-1
χ9111111111111111-11-11-1-111-1-11111111111-11-1-111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-11-1-1111-1-1-11
χ10111111111111111-11-11-1-111-1-1111111-1-1-1-1-11-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-111-1-1-1111-1
χ11111111111111111-11-11-1-1-1-11111111111111-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-1-11-1-1111-1
χ12111111111111111-11-11-1-1-1-111111111-1-1-1-11-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-111-111-1-1-11
χ13111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-11-11-1-11111-1-1
χ14111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11-11-111-1-1-1-111
χ15111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-11-11-1-1-1-1-1-111
χ16111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111-11-1111111-1-1
χ172222222222222-2-200002-2000022-2-2-2-222-2-2000000000022-2-20000000000002-200020-200000000
χ182222222222222-2-200002-2000022-2-2-2-2-2-222000000000022-2-2000000000000-22000-20200000000
χ192222222222222-2-20000-22000022-2-2-2-222-2-20000000000-2-2220000000000002-2000-20200000000
χ202222222222222-2-20000-22000022-2-2-2-2-2-2220000000000-2-222000000000000-2200020-200000000
χ21222222222222-22-2020-2000000-2-222-2-2222200002200-2-20000000000000000-2-20000200-2000000
χ22222222222222-22-2020-2000000-2-222-2-2-2-2-2-200002200-2-20000000000000000220000-2002000000
χ23222222222222-22-20-202000000-2-222-2-222220000-2-200220000000000000000-2-20000-2002000000
χ24222222222222-22-20-202000000-2-222-2-2-2-2-2-20000-2-200220000000000000000220000200-2000000
χ25222222222222-2-2220-20000000-2-2-2-22222-2-2002200-2-2000000000000000000-2200-200020000000
χ26222222222222-2-2220-20000000-2-2-2-222-2-222002200-2-20000000000000000002-2002000-20000000
χ27222222222222-2-22-2020000000-2-2-2-22222-2-200-2-20022000000000000000000-22002000-20000000
χ28222222222222-2-22-2020000000-2-2-2-222-2-22200-2-200220000000000000000002-200-200020000000
χ292222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522222222222222−1+52−1−52−1+52−1−52−1+52−1−52000022−1+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+52−1−52−1−5200−1+52−1−52000000000000
χ302222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52222222222-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−520000-2-2−1+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+52001−521+52000000000000
χ312222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522222-22-2-2-222-2-2−1+52−1−52−1+52−1−52−1+52−1−5200002-2−1+52−1−521−521+52−1+52−1−521−521+521−521+521−521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+5200−1+52−1−52000000000000
χ322222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522222-22-2-2-2-2-222−1+52−1−52−1+52−1−52−1+52−1−520000-22−1+52−1−521−521+52−1+52−1−521−521+521−521+521−521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52001−521+52000000000000
χ332222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52222-22-22-2-222-2-2−1+52−1−52−1+52−1−52−1+52−1−520000-221−521+52−1+52−1−521−521+52−1+52−1−521−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+52001−521+52000000000000
χ342222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52222-22-22-2-2-2-222−1+52−1−52−1+52−1−52−1+52−1−5200002-21−521+52−1+52−1−521−521+52−1+52−1−521−521+521−521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−5200−1+52−1−52000000000000
χ352222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52222-2-2-2-2222222−1+52−1−52−1+52−1−52−1+52−1−520000-2-21−521+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+52−1−52−1−52001−521+52000000000000
χ362222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52222-2-2-2-222-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−520000221−521+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+5200−1+52−1−52000000000000
χ372222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522222222222222−1−52−1+52−1−52−1+52−1−52−1+52000022−1−52−1+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+5200−1−52−1+52000000000000
χ382222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52222222222-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+520000-2-2−1−52−1+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+521−521−52001+521−52000000000000
χ392222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522222-22-2-2-222-2-2−1−52−1+52−1−52−1+52−1−52−1+5200002-2−1−52−1+521+521−52−1−52−1+521+521−521+521−521+521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−5200−1−52−1+52000000000000
χ402222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522222-22-2-2-2-2-222−1−52−1+52−1−52−1+52−1−52−1+520000-22−1−52−1+521+521−52−1−52−1+521+521−521+521−521+521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52001+521−52000000000000
χ412222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52222-22-22-2-222-2-2−1−52−1+52−1−52−1+52−1−52−1+520000-221+521−52−1−52−1+521+521−52−1−52−1+521+521−521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−52001+521−52000000000000
χ422222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52222-22-22-2-2-2-222−1−52−1+52−1−52−1+52−1−52−1+5200002-21+521−52−1−52−1+521+521−52−1−52−1+521+521−521+521−521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+5200−1−52−1+52000000000000
χ432222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52222-2-2-2-2222222−1−52−1+52−1−52−1+52−1−52−1+520000-2-21+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+52001+521−52000000000000
χ442222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52222-2-2-2-222-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+520000221+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+521−521−5200−1−52−1+52000000000000
χ454444−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−54-4-400004-40000−1+5−1−51−51+51−51+500000000000000−1+5−1−51−51+50000000000000000000000000000
χ464444−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−54-4-40000-440000−1+5−1−51−51+51−51+5000000000000001−51+5−1+5−1−50000000000000000000000000000
χ474444−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5-44-4040-40000001−51+5−1+5−1−51−51+500000000−1+5−1−5001−51+500000000000000000000000000000000
χ484444−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5-44-40-4040000001−51+5−1+5−1−51−51+5000000001−51+500−1+5−1−500000000000000000000000000000000
χ494444−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5-4-4440-400000001−51+51−51+5−1+5−1−5000000−1+5−1−5001−51+50000000000000000000000000000000000
χ504444−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5-4-44-40400000001−51+51−51+5−1+5−1−50000001−51+500−1+5−1−50000000000000000000000000000000000
χ514444−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+54-4-400004-40000−1−5−1+51+51−51+51−500000000000000−1−5−1+51+51−50000000000000000000000000000
χ524444−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+54-4-40000-440000−1−5−1+51+51−51+51−5000000000000001+51−5−1−5−1+50000000000000000000000000000
χ534444−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5-44-4040-40000001+51−5−1−5−1+51+51−500000000−1−5−1+5001+51−500000000000000000000000000000000
χ544444−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5-44-40-4040000001+51−5−1−5−1+51+51−5000000001+51−500−1−5−1+500000000000000000000000000000000
χ554444−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5-4-4440-400000001+51−51+51−5−1−5−1+5000000−1−5−1+5001+51−50000000000000000000000000000000000
χ564444−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5-4-44-40400000001+51−51+51−5−1−5−1+50000001+51−500−1−5−1+50000000000000000000000000000000000
χ574-44-444-4-44-44-4000000000002i−2i000000004-400000000000000000000002i−2i2i−2i0000000000002i−2i00
χ584-44-444-4-44-44-4000000000002i−2i00000000-4400000000000000000000002i−2i2i−2i000000000000−2i2i00
χ594-44-444-4-44-44-400000000000−2i2i000000004-40000000000000000000000−2i2i−2i2i000000000000−2i2i00
χ604-44-444-4-44-44-400000000000−2i2i00000000-440000000000000000000000−2i2i−2i2i0000000000002i−2i00
χ614-4-4444-4-4-44-440000000002i−2i000000004-400000000000000002i−2i2i−2i0000000000000000002i−2i0000
χ624-4-4444-4-4-44-440000000002i−2i00000000-4400000000000000002i−2i2i−2i000000000000000000−2i2i0000
χ634-4-4444-4-4-44-44000000000−2i2i000000004-40000000000000000−2i2i−2i2i000000000000000000−2i2i0000
χ644-4-4444-4-4-44-44000000000−2i2i00000000-440000000000000000−2i2i−2i2i0000000000000000002i−2i0000
χ6588-8-88888-8-8-8-800000000000000000000000000000000000000000000000000000000000000000
χ6688-8-8−2+25−2−25−2+25−2−252−252−252+252+25000000000000000000000000000000000000000002ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ1800000000000000000000
χ6788-8-8−2+25−2−25−2+25−2−252−252−252+252+2500000000000000000000000000000000000000000−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ1800000000000000000000
χ6888-8-8−2−25−2+25−2−25−2+252+252+252−252−2500000000000000000000000000000000000000000−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ1400000000000000000000
χ6988-8-8−2−25−2+25−2−25−2+252+252+252−252−25000000000000000000000000000000000000000002ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ1400000000000000000000
χ708-88-8−2+25−2−252−252+25−2+252−25−2−252+25000000000004i−4i00000000000000000000000000000000−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ70000000000000000
χ718-88-8−2+25−2−252−252+25−2+252−25−2−252+2500000000000−4i4i000000000000000000000000000000002ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ70000000000000000
χ728-88-8−2−25−2+252+252−25−2−252+25−2+252−25000000000004i−4i00000000000000000000000000000000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ190000000000000000
χ738-88-8−2−25−2+252+252−25−2−252+25−2+252−2500000000000−4i4i000000000000000000000000000000002ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ190000000000000000
χ748-8-88−2+25−2−252−252+252−25−2+252+25−2−250000000004i−4i00000000000000000000000000−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7000000000000000000000000
χ758-8-88−2+25−2−252−252+252−25−2+252+25−2−25000000000−4i4i000000000000000000000000002ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ7000000000000000000000000
χ768-8-88−2−25−2+252+252−252+25−2−252−25−2+250000000004i−4i00000000000000000000000000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19000000000000000000000000
χ778-8-88−2−25−2+252+252−252+25−2−252−25−2+25000000000−4i4i000000000000000000000000002ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ19000000000000000000000000

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