Finite Group Databasebeta

← Group #13014308

Character table — Group #13014308

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111224444444444888888888888881616161616161616161640404040404040408080808080808080
order12222244510101010101010442020202020202020202020204420202020202020202244888844448888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1−i−iii−i−iii
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ92222222222222222-2-22222-2-2-2-2-2-2-2-2000000000022-2-2000000000000
χ102222222222222222-2-22222-2-2-2-2-2-2-2-20000000000-2-222000000000000
χ112-22-22-22-2222-22-2-2-20022-2-20000000000000000002-200000000002−22−2
χ122-22-22-22-2222-22-2-2-20022-2-20000000000000000002-20000000000−22−22
χ132-22-22-22-2222-22-2-2-20022-2-2000000000000000000-220000000000i2−i2−i2i2
χ142-22-22-22-2222-22-2-2-20022-2-2000000000000000000-220000000000−i2i2i2−i2
χ152-22-22-2-22222-22-2-2-200-2-222000000000000000000002i−2i00001+i−1−i1−i−1+i0000
χ162-22-22-2-22222-22-2-2-200-2-222000000000000000000002i−2i0000−1−i1+i−1+i1−i0000
χ172-22-22-2-22222-22-2-2-200-2-22200000000000000000000−2i2i00001−i−1+i1+i−1−i0000
χ182-22-22-2-22222-22-2-2-200-2-22200000000000000000000−2i2i0000−1+i1−i−1−i1+i0000
χ1944444444-1-1-1-1-1-1-1-144-1-1-1-1-1-1-1-1-1-1-1-144-1-1-1-1-1-1-1-10000000000000000
χ2044444444-1-1-1-1-1-1-1-144-1-1-1-1-1-1-1-1-1-1-1-1-4-4111111110000000000000000
χ2144444444-1-1-1-1-1-1-1-1-4-4-1-1-1-111111111005555−5−5−5−50000000000000000
χ2244444444-1-1-1-1-1-1-1-1-4-4-1-1-1-11111111100−5−5−5−555550000000000000000
χ23444444-4-44444444400-4-4-4-40000000000000000000000000000000000
χ24444444-4-4-1-1-1-1-1-1-1-10011115555−5−5−5−500−ζ4+ζ12−ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4+ζ12−ζ28−ζ360000000000000000
χ25444444-4-4-1-1-1-1-1-1-1-10011115555−5−5−5−500ζ4−ζ12+ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4−ζ12+ζ28+ζ360000000000000000
χ26444444-4-4-1-1-1-1-1-1-1-1001111−5−5−5−5555500−ζ4−ζ12+ζ28+ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ4+ζ12−ζ28+ζ360000000000000000
χ27444444-4-4-1-1-1-1-1-1-1-1001111−5−5−5−5555500ζ4+ζ12−ζ28−ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ4−ζ12+ζ28−ζ360000000000000000
χ284444-4-4004-4-444-4-44000000000000000000000000000022-2-200000000
χ294444-4-4004-4-444-4-440000000000000000000000000000-2-22200000000
χ304-44-4-44004-4-4-4444-4000000000000002i−2i2i−2i2i−2i2i−2i2i−2i0000000000000000
χ314-44-4-44004-4-4-4444-400000000000000−2i2i−2i2i−2i2i−2i2i−2i2i0000000000000000
χ324-44-4-4400-1111-1-1-11005−55−5−ζ4+ζ12−ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4+ζ12−ζ28−ζ362i−2iζ6−ζ14−ζ22−ζ38−ζ6+ζ14+ζ22+ζ38−ζ6+ζ14−ζ22−ζ38ζ6−ζ14+ζ22+ζ38−ζ6−ζ14−ζ22+ζ38ζ6+ζ14+ζ22−ζ38−ζ6−ζ14+ζ22−ζ38ζ6+ζ14−ζ22+ζ380000000000000000
χ334-44-4-4400-1111-1-1-11005−55−5−ζ4+ζ12−ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4+ζ12−ζ28−ζ36−2i2i−ζ6+ζ14+ζ22+ζ38ζ6−ζ14−ζ22−ζ38ζ6−ζ14+ζ22+ζ38−ζ6+ζ14−ζ22−ζ38ζ6+ζ14+ζ22−ζ38−ζ6−ζ14−ζ22+ζ38ζ6+ζ14−ζ22+ζ38−ζ6−ζ14+ζ22−ζ380000000000000000
χ344-44-4-4400-1111-1-1-11005−55−5ζ4−ζ12+ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4−ζ12+ζ28+ζ362i−2i−ζ6+ζ14−ζ22−ζ38ζ6−ζ14+ζ22+ζ38ζ6−ζ14−ζ22−ζ38−ζ6+ζ14+ζ22+ζ38−ζ6−ζ14+ζ22−ζ38ζ6+ζ14−ζ22+ζ38−ζ6−ζ14−ζ22+ζ38ζ6+ζ14+ζ22−ζ380000000000000000
χ354-44-4-4400-1111-1-1-11005−55−5ζ4−ζ12+ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4−ζ12+ζ28+ζ36−2i2iζ6−ζ14+ζ22+ζ38−ζ6+ζ14−ζ22−ζ38−ζ6+ζ14+ζ22+ζ38ζ6−ζ14−ζ22−ζ38ζ6+ζ14−ζ22+ζ38−ζ6−ζ14+ζ22−ζ38ζ6+ζ14+ζ22−ζ38−ζ6−ζ14−ζ22+ζ380000000000000000
χ364-44-4-4400-1111-1-1-1100−55−55−ζ4−ζ12+ζ28+ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ4+ζ12−ζ28+ζ362i−2i−ζ6−ζ14−ζ22+ζ38ζ6+ζ14+ζ22−ζ38−ζ6−ζ14+ζ22−ζ38ζ6+ζ14−ζ22+ζ38−ζ6+ζ14−ζ22−ζ38ζ6−ζ14+ζ22+ζ38ζ6−ζ14−ζ22−ζ38−ζ6+ζ14+ζ22+ζ380000000000000000
χ374-44-4-4400-1111-1-1-1100−55−55−ζ4−ζ12+ζ28+ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ4+ζ12−ζ28+ζ36−2i2iζ6+ζ14+ζ22−ζ38−ζ6−ζ14−ζ22+ζ38ζ6+ζ14−ζ22+ζ38−ζ6−ζ14+ζ22−ζ38ζ6−ζ14+ζ22+ζ38−ζ6+ζ14−ζ22−ζ38−ζ6+ζ14+ζ22+ζ38ζ6−ζ14−ζ22−ζ380000000000000000
χ384-44-4-4400-1111-1-1-1100−55−55ζ4+ζ12−ζ28−ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ4−ζ12+ζ28−ζ362i−2i−ζ6−ζ14+ζ22−ζ38ζ6+ζ14−ζ22+ζ38−ζ6−ζ14−ζ22+ζ38ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22−ζ38−ζ6+ζ14+ζ22+ζ38−ζ6+ζ14−ζ22−ζ38ζ6−ζ14+ζ22+ζ380000000000000000
χ394-44-4-4400-1111-1-1-1100−55−55ζ4+ζ12−ζ28−ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ4−ζ12+ζ28−ζ36−2i2iζ6+ζ14−ζ22+ζ38−ζ6−ζ14+ζ22−ζ38ζ6+ζ14+ζ22−ζ38−ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22+ζ38ζ6−ζ14−ζ22−ζ38ζ6−ζ14+ζ22+ζ38−ζ6+ζ14−ζ22−ζ380000000000000000
χ404-4-440000400-4-40042-200002-22-22-22-2000000000000000022−2200000000
χ414-4-440000400-4-40042-200002-22-22-22-20000000000000000−222200000000
χ424-4-440000400-4-4004-220000-22-22-22-220000000000000022−220000000000
χ434-4-440000400-4-4004-220000-22-22-22-2200000000000000−22220000000000
χ448888-8-800-222-2-222-20025−25−25250000000000000000000000000000000000
χ458888-8-800-222-2-222-200−252525−250000000000000000000000000000000000
χ4688-8-800008008-800-80000000000000000000000000000000000000000
χ4788-8-80000-225−25-2225−2520000002ζ12−2ζ28−2ζ12+2ζ28−2ζ12+2ζ282ζ12−2ζ28−2ζ4+2ζ362ζ4−2ζ362ζ4−2ζ36−2ζ4+2ζ3600000000000000000000000000
χ4888-8-80000-225−25-2225−252000000−2ζ12+2ζ282ζ12−2ζ282ζ12−2ζ28−2ζ12+2ζ282ζ4−2ζ36−2ζ4+2ζ36−2ζ4+2ζ362ζ4−2ζ3600000000000000000000000000
χ4988-8-80000-2−2525-22−25252000000−2ζ4+2ζ362ζ4−2ζ362ζ4−2ζ36−2ζ4+2ζ36−2ζ12+2ζ282ζ12−2ζ282ζ12−2ζ28−2ζ12+2ζ2800000000000000000000000000
χ5088-8-80000-2−2525-22−252520000002ζ4−2ζ36−2ζ4+2ζ36−2ζ4+2ζ362ζ4−2ζ362ζ12−2ζ28−2ζ12+2ζ28−2ζ12+2ζ282ζ12−2ζ2800000000000000000000000000
χ518-88-88-88-8-2-2-22-222200-2-2220000000000000000000000000000000000
χ528-88-88-8-88-2-2-22-22220022-2-20000000000000000000000000000000000
χ538-8-880000-225−2522−2525-24-40000−1−51+5−1−51+5−1+51−5−1+51−500000000000000000000000000
χ548-8-880000-225−2522−2525-2-4400001+5−1−51+5−1−51−5−1+51−5−1+500000000000000000000000000
χ558-8-880000-2−25252225−25-24-40000−1+51−5−1+51−5−1−51+5−1−51+500000000000000000000000000
χ568-8-880000-2−25252225−25-2-4400001−5−1+51−5−1+51+5−1−51+5−1−500000000000000000000000000

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