Finite Group Databasebeta

← Group #13020307

Character table — Group #13020307

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111122444444444444448810101010101016161616161616161616161616161620202020202020202020202020202020202020202040408080808080
order12222244444451010101010101044444444210101010202020202020202020204444488888888888888884428888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1ii−i−i
χ41111111111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1−i−iii
χ511111111111111111111-1-1111111-1-1-1-1-111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1
χ611111111111111111111-1-1111111-1-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i111−i−iii
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii111ii−i−i
χ911111111-1-1-1-11111111111111111-1-1-1-1-1-1-1111111-1-11-1-1-1-11111-1-1-1-11111-1-1-1-111-11-11-1
χ1011111111-1-1-1-11111111111111111-1-1-1-1-1-1-1111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11-11
χ1111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11i−i−ii
χ1211111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11−iii−i
χ1311111111-1-1-1-111111111-1-111111111111-1-1-1-1-1-111-1-11-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11-11-11
χ1411111111-1-1-1-111111111-1-111111111111-1-1-1-1-1-111-1-11-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-11-1
χ1511111111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-111-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1−iii−i
χ1611111111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-111-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1i−i−ii
χ17222222-2-222-2-2222222220022-2-22200000-2-20000-2-222-222-2-200000000000000000000000
χ18222222-2-222-2-22222222200-2-222-2-200000-2-20000-2-2222-2-22200000000000000000000000
χ19222222-2-2-2-222222222220022-2-22200000220000-2-2-2-2-2-2-22200000000000000000000000
χ20222222-2-2-2-2222222222200-2-222-2-200000220000-2-2-2-2222-2-200000000000000000000000
χ212222-2-22-2000022-2-22-2-22002-2222-2000000000002-200-20000000022-2-2000022-2-20000000
χ222222-2-22-2000022-2-22-2-22002-2222-2000000000002-200-200000000-2-2220000-2-2220000000
χ232222-2-22-2000022-2-22-2-2200-22-2-2-22000000000002-2002000000002i2i−2i−2i0000−2i−2i2i2i0000000
χ242222-2-22-2000022-2-22-2-2200-22-2-2-22000000000002-200200000000−2i−2i2i2i00002i2i−2i−2i0000000
χ252222-2-2-22000022-2-22-2-22002-2-2-22-200000000000-2200200002i2i−2i−2i00002i2i−2i−2i00000000000
χ262222-2-2-22000022-2-22-2-22002-2-2-22-200000000000-220020000−2i−2i2i2i0000−2i−2i2i2i00000000000
χ272222-2-2-22000022-2-22-2-2200-2222-2200000000000-2200-2000022-2-20000-2-22200000000000
χ282222-2-2-22000022-2-22-2-2200-2222-2200000000000-2200-20000-2-222000022-2-200000000000
χ292-2-222-2002i−2i002-2222-2-2-2002-200-2200000000000002i−2i02i−2i002−22−2i2−i2i2−i22−22−2i2−i2i2−i20000000
χ302-2-222-2002i−2i002-2222-2-2-2002-200-2200000000000002i−2i02i−2i00−22−22−i2i2−i2i2−22−22−i2i2−i2i20000000
χ312-2-222-2002i−2i002-2222-2-2-200-22002-200000000000002i−2i0−2i2i00i2−i2i2−i2−22−22−i2i2−i2i22−22−20000000
χ322-2-222-2002i−2i002-2222-2-2-200-22002-200000000000002i−2i0−2i2i00−i2i2−i2i22−22−2i2−i2i2−i2−22−220000000
χ332-2-222-200−2i2i002-2222-2-2-2002-200-220000000000000−2i2i0−2i2i002−22−2−i2i2−i2i22−22−2−i2i2−i2i20000000
χ342-2-222-200−2i2i002-2222-2-2-2002-200-220000000000000−2i2i0−2i2i00−22−22i2−i2i2−i2−22−22i2−i2i2−i20000000
χ352-2-222-200−2i2i002-2222-2-2-200-22002-20000000000000−2i2i02i−2i00i2−i2i2−i22−22−2−i2i2−i2i2−22−220000000
χ362-2-222-200−2i2i002-2222-2-2-200-22002-20000000000000−2i2i02i−2i00−i2i2−i2i2−22−22i2−i2i2−i22−22−20000000
χ372-2-22-2200002-22-2-2-2222-2002200-2-2000002-2000000000002-2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000
χ382-2-22-2200002-22-2-2-2222-2002200-2-2000002-2000000000002-2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000
χ392-2-22-2200002-22-2-2-2222-200-2-20022000002-200000000000-222−2−222−2−22−222−2−222−20000000
χ402-2-22-2200002-22-2-2-2222-200-2-20022000002-200000000000-22−222−2−222−22−2−222−2−220000000
χ412-2-22-220000-222-2-2-2222-2002200-2-200000-2200000000000-22i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000
χ422-2-22-220000-222-2-2-2222-2002200-2-200000-2200000000000-22−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000
χ432-2-22-220000-222-2-2-2222-200-2-2002200000-22000000000002-22−2−22−222−2−222−22−2−220000000
χ442-2-22-220000-222-2-2-2222-200-2-2002200000-22000000000002-2−222−22−2−222−2−22−222−20000000
χ45444444444444-1-1-1-1-1-1-1-1440000004-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000
χ46444444444444-1-1-1-1-1-1-1-1-4-4000000-41111-1-11111-1-1-1-10000000000000000000000000000
χ4744444444-4-4-4-4-1-1-1-1-1-1-1-144000000-4111111-1-1-1-1-1-1110000000000000000000000000000
χ4844444444-4-4-4-4-1-1-1-1-1-1-1-1-4-40000004-1-1-1-1111111-1-1110000000000000000000000000000
χ49444444-4-444-4-4-1-1-1-1-1-1-1-100000000055−5−51155−5−511-1-10000000000000000000000000000
χ50444444-4-444-4-4-1-1-1-1-1-1-1-1000000000−5−55511−5−55511-1-10000000000000000000000000000
χ51444444-4-4-4-444-1-1-1-1-1-1-1-100000000055−5−5-1-1−5−55511110000000000000000000000000000
χ52444444-4-4-4-444-1-1-1-1-1-1-1-1000000000−5−555-1-155−5−511110000000000000000000000000000
χ5344-4-4000000004400-400-42i−2i004-40000000002i−2i2i−2i00000000000000000000000002i−2i00000
χ5444-4-4000000004400-400-42i−2i00-440000000002i−2i2i−2i0000000000000000000000000−2i2i00000
χ5544-4-4000000004400-400-4−2i2i004-4000000000−2i2i−2i2i0000000000000000000000000−2i2i00000
χ5644-4-4000000004400-400-4−2i2i00-44000000000−2i2i−2i2i00000000000000000000000002i−2i00000
χ578888-8-88-80000-2-222-222-20000000000000000000-22000000000000000000000000000000
χ588888-8-8-880000-2-222-222-200000000000000000002-2000000000000000000000000000000
χ5988-8-800000000-2-225−25225−2524i−4i0000000000000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ3800000000000000000000000000000000
χ6088-8-800000000-2-225−25225−252−4i4i00000000000002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ3800000000000000000000000000000000
χ6188-8-800000000-2-2−25252−252524i−4i0000000000000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ1400000000000000000000000000000000
χ6288-8-800000000-2-2−25252−25252−4i4i00000000000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ1400000000000000000000000000000000
χ638-88-8000000008-800-8008000000000000000000000000000000000000000000000000000
χ648-88-800000000-2225−252−2525-2000000000−2ζ4+2ζ362ζ4−2ζ362ζ12−2ζ28−2ζ12+2ζ2800000000000000000000000000000000000000
χ658-88-800000000-2225−252−2525-20000000002ζ4−2ζ36−2ζ4+2ζ36−2ζ12+2ζ282ζ12−2ζ2800000000000000000000000000000000000000
χ668-88-800000000-22−2525225−25-20000000002ζ12−2ζ28−2ζ12+2ζ282ζ4−2ζ36−2ζ4+2ζ3600000000000000000000000000000000000000
χ678-88-800000000-22−2525225−25-2000000000−2ζ12+2ζ282ζ12−2ζ28−2ζ4+2ζ362ζ4−2ζ3600000000000000000000000000000000000000
χ688-8-888-8008i−8i00-22-2-2-2222000000000000000000000−2i2i0000000000000000000000000000
χ698-8-888-800−8i8i00-22-2-2-22220000000000000000000002i−2i0000000000000000000000000000
χ708-8-88-8800008-8-2222-2-2-220000000000000-22000000000000000000000000000000000000
χ718-8-88-880000-88-2222-2-2-2200000000000002-2000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.