Finite Group Databasebeta

← Group #13017595

Character table — Group #13017595

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111222244444444444888888888888888881010101016161616161616162020202020202020404040404040404040404080808080
order12222244444510101010101010444442020202020202020202020204444202020202020202022444444244444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ4111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ51111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111-1-111111111-1-1-1-1
χ61111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111iiii−i−i−i−i−i−iii
χ81111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111−i−i−i−iiiiiii−i−i
χ911111111-1-111111111111-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-111-1-111-1-11-11-1
χ1011111111-1-111111111111-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-111-1-111-11-11
χ1111111111-1-111111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111ii−i−i−i−iiii−i−ii
χ1211111111-1-111111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111−i−iiiii−i−i−iii−i
χ1311111111-1-1111111111-1-111-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-11111-1-111-1-1-11-11
χ1411111111-1-1111111111-1-111-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-111-1-111-1-1111-11-1
χ1511111111-1-1111111111-1-111-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111-1-1ii−i−i−i−iii−iii−i
χ1611111111-1-1111111111-1-111-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111-1-1−i−iiiii−i−ii−i−ii
χ17222222-2-222-2222222220000-2-2-2-2-2-2-2-2-22222222200000000-2-2000022-200000000000000
χ18222222-2-222-2222222220000-2-2-2-2-2-2-2-2-22222-2-2-2-200000000220000-2-2200000000000000
χ19222222-2-2-2-2-22222222200002-2-2-2-22222-2-2-2-2222200000000-2-20000-2-2200000000000000
χ20222222-2-2-2-2-22222222200002-2-2-2-22222-2-2-2-2-2-2-2-20000000022000022-200000000000000
χ212222-2-22200-22-2-2-2-22222-200022-2-20000000022-2-222-2-200002-222-2-200000000000000000
χ222222-2-22200-22-2-2-2-22222-200022-2-200000000-2-22222-2-20000-22-2-22200000000000000000
χ232222-2-22200-22-2-2-2-2222-2200022-2-20000000022-2-2-2-22200002-2-2-22200000000000000000
χ242222-2-22200-22-2-2-2-2222-2200022-2-200000000-2-222-2-2220000-2222-2-200000000000000000
χ252222-2-2-2-20022-2-2-2-2222002-20-2-2220000000022-2-2000022-2-2-2200000002-2000000000000
χ262222-2-2-2-20022-2-2-2-2222002-20-2-22200000000-2-222000022-2-22-20000000-22000000000000
χ272222-2-2-2-20022-2-2-2-222200-220-2-2220000000022-2-20000-2-222-220000000-22000000000000
χ282222-2-2-2-20022-2-2-2-222200-220-2-22200000000-2-2220000-2-2222-200000002-2000000000000
χ2922-2-22-2002-20222-2-2-2-22000000000000022-2-22i−2i2i−2i000000000000002i−2i0001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ3022-2-22-2002-20222-2-2-2-22000000000000022-2-22i−2i2i−2i000000000000002i−2i000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ3122-2-22-2002-20222-2-2-2-22000000000000022-2-2−2i2i−2i2i00000000000000−2i2i0001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ3222-2-22-2002-20222-2-2-2-22000000000000022-2-2−2i2i−2i2i00000000000000−2i2i000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ3322-2-22-200-220222-2-2-2-220000000000000-2-2222i−2i2i−2i00000000000000−2i2i0001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000
χ3422-2-22-200-220222-2-2-2-220000000000000-2-2222i−2i2i−2i00000000000000−2i2i000−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000
χ3522-2-22-200-220222-2-2-2-220000000000000-2-222−2i2i−2i2i000000000000002i−2i0001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000
χ3622-2-22-200-220222-2-2-2-220000000000000-2-222−2i2i−2i2i000000000000002i−2i000−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000
χ3744444444444-1-1-1-1-1-1-1-144444-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-100000000000000000000000
χ3844444444444-1-1-1-1-1-1-1-1-4-4-4-44-1-1-1-1-1-1-1-1-1-1-1-100001111111100000000000000000000000
χ3944444444-4-44-1-1-1-1-1-1-1-144-4-4-4-1-1-1-1111111110000-1-1-1-1111100000000000000000000000
χ4044444444-4-44-1-1-1-1-1-1-1-1-4-444-4-1-1-1-11111111100001111-1-1-1-100000000000000000000000
χ41444444-4-444-4-1-1-1-1-1-1-1-10000-411111111-1-1-1-100005−55−55−55−500000000000000000000000
χ42444444-4-444-4-1-1-1-1-1-1-1-10000-411111111-1-1-1-10000−55−55−55−5500000000000000000000000
χ43444444-4-4-4-4-4-1-1-1-1-1-1-1-1000041111-1-1-1-1111100005−55−5−55−5500000000000000000000000
χ44444444-4-4-4-4-4-1-1-1-1-1-1-1-1000041111-1-1-1-111110000−55−555−55−500000000000000000000000
χ454444-4-44400-4-11111-1-1-14-4000-1-11155−5−55−55−50000-1-1115−5−5500000000000000000000000
χ464444-4-44400-4-11111-1-1-14-4000-1-111−5−555−55−550000-1-111−555−500000000000000000000000
χ474444-4-44400-4-11111-1-1-1-44000-1-11155−5−55−55−5000011-1-1−555−500000000000000000000000
χ484444-4-44400-4-11111-1-1-1-44000-1-111−5−555−55−55000011-1-15−5−5500000000000000000000000
χ494444-4-4-4-4004-11111-1-1-1004-4011-1-155−5−5−55−550000−555−5-1-11100000000000000000000000
χ504444-4-4-4-4004-11111-1-1-1004-4011-1-1−5−5555−55−500005−5−55-1-11100000000000000000000000
χ514444-4-4-4-4004-11111-1-1-100-44011-1-155−5−5−55−5500005−5−5511-1-100000000000000000000000
χ524444-4-4-4-4004-11111-1-1-100-44011-1-1−5−5555−55−50000−555−511-1-100000000000000000000000
χ5344-4-4-44000004-4-444-4-44000000000000000004i−4i−4i4i0000000000000000000000000000000
χ5444-4-4-44000004-4-444-4-4400000000000000000−4i4i4i−4i0000000000000000000000000000000
χ554-4-44004-4000400004-4-4000004-4000000000000000000000000004i−4i00000000000000000
χ564-4-44004-4000400004-4-4000004-400000000000000000000000000−4i4i00000000000000000
χ574-4-4400-44000400004-4-400000-440000000000000000000000004i−4i0000000000000000000
χ584-4-4400-44000400004-4-400000-44000000000000000000000000−4i4i0000000000000000000
χ5988-8-88-8008-80-2-2-22222-20000000000000-2-22200000000000000000000000000000000000
χ6088-8-88-800-880-2-2-22222-2000000000000022-2-200000000000000000000000000000000000
χ6188-8-8-8800000-222-2-222-2000000000000025−25−252500000000000000000000000000000000000
χ6288-8-8-8800000-222-2-222-20000000000000−252525−2500000000000000000000000000000000000
χ638-88-8000000080000-88-80000000000000000000000000000000000000000000000000000
χ648-88-80000000-225−2525−252-22000000000−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ18000000000000000000000000000000000000000
χ658-88-80000000-225−2525−252-220000000002ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ18000000000000000000000000000000000000000
χ668-88-80000000-2−2525−25252-22000000000−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ18000000000000000000000000000000000000000
χ678-88-80000000-2−2525−25252-220000000002ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ18000000000000000000000000000000000000000
χ688-8-88008-8000-225−25−2525-22200000-2225−250000000000000000000000000000000000000000000
χ698-8-88008-8000-2−252525−25-22200000-22−25250000000000000000000000000000000000000000000
χ708-8-8800-88000-225−25−2525-222000002-2−25250000000000000000000000000000000000000000000
χ718-8-8800-88000-2−252525−25-222000002-225−250000000000000000000000000000000000000000000

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