Finite Group Databasebeta

← Group #13013905

Character table — Group #13013905

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111122222244444444444488888888888810101010101010101616161616161616161620202020404040404040404040404040404040408080
order124422244444445101010202020201010202020202020202020208888888888404040404040404088881616161616161616161616161616161688
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
χ911-1-1-1-1111-111-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1i−iiiii−i−i−i−i11-1-111-1-111-1-1ii−i−iii−i−ii−i
χ1011-1-1-1-1111-111-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1i−iiiii−i−i−i−i11-1-1-1-111-1-111−i−iii−i−iiii−i
χ1111-1-1-1-1111-111-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1−ii−i−i−i−iiiii11-1-111-1-111-1-1−i−iii−i−iii−ii
χ1211-1-1-1-1111-111-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1−ii−i−i−i−iiiii11-1-1-1-111-1-111ii−i−iii−i−i−ii
χ1311-1-1-1-1111-111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111i−iiiii−i−i−i−i-1-111ii−i−i−i−iii-1-11111-1-1−ii
χ1411-1-1-1-1111-111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111i−iiiii−i−i−i−i-1-111−i−iiiii−i−i11-1-1-1-111−ii
χ1511-1-1-1-1111-111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111−ii−i−i−i−iiiii-1-111ii−i−i−i−iii11-1-1-1-111i−i
χ1611-1-1-1-1111-111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111−ii−i−i−i−iiiii-1-111−i−iiiii−i−i-1-11111-1-1i−i
χ172222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-222-2-2-2-22200000000002-22-2000000000000000000
χ182222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-22222-2-20000000000-22-22000000000000000000
χ1922222-2-22-2-2000022-2-222-2-22-22-2000000000022220000000000000-20-200000000i2−i2i2−i2i2−i2i2−i200
χ2022222-2-22-2-2000022-2-222-2-22-22-2000000000022220000000000000-20-200000000−i2i2−i2i2−i2i2−i2i200
χ2122222-2-22-2-2000022-2-222-2-22-22-20000000000-2-2-2-20000000000000202000000002−22−2−22−2200
χ2222222-2-22-2-2000022-2-222-2-22-22-20000000000-2-2-2-2000000000000020200000000−22−222−22−200
χ232222-22-2-22-2000022-2-222-2-2-22-2200000000220000220000000000-20-20i2−i2i2−i2i2−i2i2−i20000000000
χ242222-22-2-22-2000022-2-222-2-2-22-2200000000220000220000000000-20-20−i2i2−i2i2−i2i2−i2i20000000000
χ252222-22-2-22-2000022-2-222-2-2-22-2200000000-2-20000-2-2000000000020202−22−2−22−220000000000
χ262222-22-2-22-2000022-2-222-2-2-22-2200000000-2-20000-2-200000000002020−22−222−22−20000000000
χ2722-2-22-2-2-222000022-2-2-2-2222-2-2200000000220000-2-20000000000-2020i2−i2−i2i2i2−i2−i2i20000000000
χ2822-2-22-2-2-222000022-2-2-2-2222-2-2200000000220000-2-20000000000-2020−i2i2i2−i2−i2i2i2−i20000000000
χ2922-2-22-2-2-222000022-2-2-2-2222-2-2200000000-2-2000022000000000020-202−2−22−222−20000000000
χ3022-2-22-2-2-222000022-2-2-2-2222-2-2200000000-2-2000022000000000020-20−222−22−2−220000000000
χ3122-2-2-22-22-22000022-2-2-2-222-222-2000000000022-2-2000000000000020-200000000i2−i2−i2i2−i2i2i2−i200
χ3222-2-2-22-22-22000022-2-2-2-222-222-2000000000022-2-2000000000000020-200000000−i2i2i2−i2i2−i2−i2i200
χ3322-2-2-22-22-22000022-2-2-2-222-222-20000000000-2-2220000000000000-202000000002−2−222−2−2200
χ3422-2-2-22-22-22000022-2-2-2-222-222-20000000000-2-2220000000000000-20200000000−222−2−222−200
χ3522-2-2-2-2222-2-2-2222222-2-2-2-2-2-222-2-2-2-222222222-2-2-2-200000000002-2-22000000000000000000
χ3622-2-2-2-2222-2-2-2222222-2-2-2-2-2-222-2-2-2-22222-2-2-2-222220000000000-222-2000000000000000000
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
χ414444-4-44-4-44000044444444-4-4-4-4000000000000000000000000000000000000000000000000
χ424444-4-44-4-440000-1-1-1-1-1-1-1-1111155−5−555−5−50000000000−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ360000000000000000000000
χ434444-4-44-4-440000-1-1-1-1-1-1-1-1111155−5−555−5−50000000000ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ360000000000000000000000
χ444444-4-44-4-440000-1-1-1-1-1-1-1-11111−5−555−5−5550000000000−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ360000000000000000000000
χ454444-4-44-4-440000-1-1-1-1-1-1-1-11111−5−555−5−5550000000000ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ360000000000000000000000
χ4644-4-4444-4-4-400004444-4-4-4-444-4-4000000000000000000000000000000000000000000000000
χ4744-4-4444-4-4-40000-1-1-1-11111-1-11155−5−5−5−5550000000000−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
χ4844-4-4444-4-4-40000-1-1-1-11111-1-11155−5−5−5−5550000000000ζ6−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
χ4944-4-4444-4-4-40000-1-1-1-11111-1-111−5−55555−5−50000000000ζ6−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
χ5044-4-4444-4-4-40000-1-1-1-11111-1-111−5−55555−5−50000000000−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
χ5144-4-4-4-4444-444-4-4-1-1-1-1111111-1-1-1-1-1-11111000000004i−4i−i−i−i−iiiii0000000000000000000000
χ5244-4-4-4-4444-444-4-4-1-1-1-1111111-1-1-1-1-1-1111100000000−4i4iiiii−i−i−i−i0000000000000000000000
χ5344-4-4-4-4444-4-4-444-1-1-1-1111111-1-11111-1-1-1-10000000000i5i5−i5−i5−i5−i5i5i50000000000000000000000
χ5444-4-4-4-4444-4-4-444-1-1-1-1111111-1-11111-1-1-1-10000000000−i5−i5i5i5i5i5−i5−i50000000000000000000000
χ554-44i−4i0000002i−2i2-24-4004i−4i0000002i−2i2i−2i2-22-22i2−2i22i2−2i222−2222−2200000000000000000000000000000000
χ564-44i−4i0000002i−2i2-24-4004i−4i0000002i−2i2i−2i2-22-2−2i22i2−2i22i2−2222−222200000000000000000000000000000000
χ574-44i−4i000000−2i2i-224-4004i−4i000000−2i2i−2i2i-22-222i2−2i2−2i22i2−222222−2200000000000000000000000000000000
χ584-44i−4i000000−2i2i-224-4004i−4i000000−2i2i−2i2i-22-22−2i22i22i2−2i222−22−222200000000000000000000000000000000
χ594-4−4i4i0000002i−2i-224-400−4i4i0000002i−2i2i−2i-22-222i2−2i2−2i22i222−22−222200000000000000000000000000000000
χ604-4−4i4i0000002i−2i-224-400−4i4i0000002i−2i2i−2i-22-22−2i22i22i2−2i2−222222−2200000000000000000000000000000000
χ614-4−4i4i000000−2i2i2-24-400−4i4i000000−2i2i−2i2i2-22-22i2−2i22i2−2i2−2222−222200000000000000000000000000000000
χ624-4−4i4i000000−2i2i2-24-400−4i4i000000−2i2i−2i2i2-22-2−2i22i2−2i22i222−2222−2200000000000000000000000000000000
χ6388888-8-88-8-80000-2-222-2-222-22-22000000000000000000000000000000000000000000000000
χ648888-88-8-88-80000-2-222-2-2222-22-2000000000000000000000000000000000000000000000000
χ6588-8-88-8-8-8880000-2-22222-2-2-222-2000000000000000000000000000000000000000000000000
χ6688-8-8-88-88-880000-2-22222-2-22-2-22000000000000000000000000000000000000000000000000
χ678-88i−8i0000004i−4i4-4-2225−25−2i2i2i5−2i50000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ38−1−51+5−1+51−50000000000000000000000000000000000000000
χ688-88i−8i0000004i−4i4-4-22−2525−2i2i−2i52i50000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ14−1+51−5−1−51+50000000000000000000000000000000000000000
χ698-88i−8i000000−4i4i-44-2225−25−2i2i2i5−2i500002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ381+5−1−51−5−1+50000000000000000000000000000000000000000
χ708-88i−8i000000−4i4i-44-22−2525−2i2i−2i52i500002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ141−5−1+51+5−1−50000000000000000000000000000000000000000
χ718-8−8i8i0000004i−4i-44-2225−252i−2i−2i52i50000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ381+5−1−51−5−1+50000000000000000000000000000000000000000
χ728-8−8i8i0000004i−4i-44-22−25252i−2i2i5−2i50000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ141−5−1+51+5−1−50000000000000000000000000000000000000000
χ738-8−8i8i000000−4i4i4-4-2225−252i−2i−2i52i500002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ38−1−51+5−1+51−50000000000000000000000000000000000000000
χ748-8−8i8i000000−4i4i4-4-22−25252i−2i2i5−2i500002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ14−1+51−5−1−51+50000000000000000000000000000000000000000

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