Finite Group Databasebeta

← Group #13019687

Character table — Group #13019687

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111111114444444444444488888888888810101010101010101616161616161616161620202020404040404040404040404040404040408080
order12222222224444510101010101010101010102020202020202020444444444420202020202020204444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11
χ911111111-1-111-1-111111111-1-1-1-11111-1-1-1-1111111111-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-11-1
χ1011111111-1-111-1-111111111-1-1-1-11111-1-1-1-1111111111-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1111-1
χ1111111111-1-111-1-111111111-1-1-1-11111-1-1-1-111111111-11-1-1-1-11111-1-1-1-111-1-111-1-1-1-111-1-111-11
χ1211111111-1-111-1-111111111-1-1-1-11111-1-1-1-111111111-11-1-1-1-11111-1-1-1-1-1-111-1-11111-1-111-1-1-11
χ1311111111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii-11
χ1411111111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i-11
χ1511111111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111ii−i−i−i−iii−i−iiiii−i−i1-1
χ1611111111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111−i−iiiii−i−iii−i−i−i−iii1-1
χ172222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-222-2-222-2-2000000000022-2-2000000000000000000
χ182222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-222-2-2220000000000-2-222000000000000000000
χ1922222222-2-2-2-22222222222-2-2-2-2-2-2-2-2222222-2-222-2-20000000000-2-222000000000000000000
χ2022222222-2-2-2-22222222222-2-2-2-2-2-2-2-22222-2-222-2-222000000000022-2-2000000000000000000
χ21222-2-2-2-2200002i−2i222-2-22-2-2000000002i2i−2i−2i002-2002-200000000002i−2i00i2−i22−2i2−i22−20000000000
χ22222-2-2-2-2200002i−2i222-2-22-2-2000000002i2i−2i−2i002-2002-200000000002i−2i00−i2i2−22−i2i2−220000000000
χ23222-2-2-2-2200002i−2i222-2-22-2-2000000002i2i−2i−2i00-2200-220000000000−2i2i002−2−i2i2−22i2−i20000000000
χ24222-2-2-2-2200002i−2i222-2-22-2-2000000002i2i−2i−2i00-2200-220000000000−2i2i00−22i2−i22−2−i2i20000000000
χ25222-2-2-2-220000−2i2i222-2-22-2-200000000−2i−2i2i2i002-2002-20000000000−2i2i00i2−i2−22i2−i2−220000000000
χ26222-2-2-2-220000−2i2i222-2-22-2-200000000−2i−2i2i2i002-2002-20000000000−2i2i00−i2i22−2−i2i22−20000000000
χ27222-2-2-2-220000−2i2i222-2-22-2-200000000−2i−2i2i2i00-2200-2200000000002i−2i002−2i2−i2−22−i2i20000000000
χ28222-2-2-2-220000−2i2i222-2-22-2-200000000−2i−2i2i2i00-2200-2200000000002i−2i00−22−i2i22−2i2−i20000000000
χ292-2-2-222-22002-2002-2-22-222-2000022-2-200002-2222-2-2-200000000000000000000002i−2i002i−2i0000
χ302-2-2-222-22002-2002-2-22-222-2000022-2-200002-2222-2-2-20000000000000000000000−2i2i00−2i2i0000
χ312-2-2-222-22002-2002-2-22-222-2000022-2-20000-22-2-2-222200000000000000000000002-200-220000
χ322-2-2-222-22002-2002-2-22-222-2000022-2-20000-22-2-2-22220000000000000000000000-22002-20000
χ332-2-2-222-2200-22002-2-22-222-20000-2-22200002-2-2-22-2220000000000000000000000002-2002-200
χ342-2-2-222-2200-22002-2-22-222-20000-2-22200002-2-2-22-222000000000000000000000000-2200-2200
χ352-2-2-222-2200-22002-2-22-222-20000-2-2220000-2222-22-2-20000000000000000000000002i−2i00−2i2i00
χ362-2-2-222-2200-22002-2-22-222-20000-2-2220000-2222-22-2-2000000000000000000000000−2i2i002i−2i00
χ3744444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000044-1-1-1-1-1-1-1-10000000000000000000000
χ3844444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-4-4111111110000000000000000000000
χ394444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-111111111000000000055−5−555−5−50000000000000000000000
χ404444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1111111110000000000−5−555−5−5550000000000000000000000
χ4144444444-4-444-4-4-1-1-1-1-1-1-1-11111-1-1-1-11111000000004-4-1-1-1-111110000000000000000000000
χ4244444444-4-444-4-4-1-1-1-1-1-1-1-11111-1-1-1-1111100000000-441111-1-1-1-10000000000000000000000
χ4344444444-4-4-4-444-1-1-1-1-1-1-1-111111111-1-1-1-1000000000055−5−5−5−5550000000000000000000000
χ4444444444-4-4-4-444-1-1-1-1-1-1-1-111111111-1-1-1-10000000000−5−55555−5−50000000000000000000000
χ4544-444-4-4-44-4000044-4-44-44-444-4-4000000000000000000000000000000000000000000000000
χ4644-444-4-4-44-40000-1-111-11-11-1-1115−55−55−55−50000000000−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ380000000000000000000000
χ4744-444-4-4-44-40000-1-111-11-11-1-1115−55−55−55−50000000000ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ380000000000000000000000
χ4844-444-4-4-44-40000-1-111-11-11-1-111−55−55−55−550000000000ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ380000000000000000000000
χ4944-444-4-4-44-40000-1-111-11-11-1-111−55−55−55−550000000000−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ380000000000000000000000
χ5044-444-4-4-4-44000044-4-44-44-4-4-444000000000000000000000000000000000000000000000000
χ5144-444-4-4-4-440000-1-111-11-1111-1-15−55−5−55−550000000000−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ380000000000000000000000
χ5244-444-4-4-4-440000-1-111-11-1111-1-15−55−5−55−550000000000ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ380000000000000000000000
χ5344-444-4-4-4-440000-1-111-11-1111-1-1−55−555−55−50000000000ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ380000000000000000000000
χ5444-444-4-4-4-440000-1-111-11-1111-1-1−55−555−55−50000000000−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ380000000000000000000000
χ5544-4-4-444-400000044-44-4-4-440000000000004400-4-40000000000000000000000000000000000
χ5644-4-4-444-400000044-44-4-4-44000000000000-4-400440000000000000000000000000000000000
χ574-444-44-4-40000004-4444-4-4-40000000000004-400-440000000000000000000000000000000000
χ584-444-44-4-40000004-4444-4-4-4000000000000-44004-40000000000000000000000000000000000
χ594-44-44-44-40000004-44-4-4-444000000000000000000000000000000004i−4i000000000000000000
χ604-44-44-44-40000004-44-4-4-44400000000000000000000000000000000−4i4i000000000000000000
χ614-4-44-4-4440000004-4-4-444-44000000000000004-400-4400000000000000000000000000000000
χ624-4-44-4-4440000004-4-4-444-4400000000000000-44004-400000000000000000000000000000000
χ63888-8-8-8-8800008i−8i-2-2-222-22200000000−2i−2i2i2i0000000000000000000000000000000000000000
χ64888-8-8-8-880000−8i8i-2-2-222-222000000002i2i−2i−2i0000000000000000000000000000000000000000
χ6588-8-8-888-8000000-2-22-2222-2000000002i5−2i5−2i52i50000000000000000000000000000000000000000
χ6688-8-8-888-8000000-2-22-2222-200000000−2i52i52i5−2i50000000000000000000000000000000000000000
χ678-888-88-8-8000000-22-2-2-222225−2525−25000000000000000000000000000000000000000000000000
χ688-888-88-8-8000000-22-2-2-2222−2525−2525000000000000000000000000000000000000000000000000
χ698-88-88-88-8000000-22-2222-2-2000025−25−252500000000000000000000000000000000000000000000
χ708-88-88-88-8000000-22-2222-2-20000−252525−2500000000000000000000000000000000000000000000
χ718-8-88-8-888000000-2222-2-22-225−25−2525000000000000000000000000000000000000000000000000
χ728-8-88-8-888000000-2222-2-22-2−252525−25000000000000000000000000000000000000000000000000
χ738-8-8-888-88008-800-222-22-2-220000-2-22200000000000000000000000000000000000000000000
χ748-8-8-888-8800-8800-222-22-2-22000022-2-200000000000000000000000000000000000000000000

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