Finite Group Databasebeta

← Group #13024592

Character table — Group #13024592

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11112222444444444448888888888888161616161616161616162020202020204040404040404040404040404080808080
order12222222244510101010101010410101010202020202020202044202020202020202044444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-11-1-111111111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111iiii−i−i−i−i−i−iii
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111−i−i−i−iiiiiii−i−i
χ91111-1-111-1-1-1111111111-1-1-1-11111-1-1-1-11-11111-1-1-1-111-1-1-1-1111-1-1ii−i−iii−i−ii−ii−i
χ101111-1-111-1-1-1111111111-1-1-1-11111-1-1-1-11-11111-1-1-1-111-1-1-1-1111-1-1−i−iii−i−iii−ii−ii
χ111111-1-111-1-1-1111111111-1-1-1-11111-1-1-1-11-11111-1-1-1-1-1-11111-1-1-11111-1-1-1-1111-1-11
χ121111-1-111-1-1-1111111111-1-1-1-11111-1-1-1-11-11111-1-1-1-1-1-11111-1-1-111-1-11111-1-1-111-1
χ131111-1-111-1-1-1111111111-1-1-1-11111-1-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1111ii−i−iii−i−i−ii−ii
χ141111-1-111-1-1-1111111111-1-1-1-11111-1-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1111−i−iii−i−iiii−ii−i
χ151111-1-111-1-1-1111111111-1-1-1-11111-1-1-1-1-11-1-1-1-11111-1-1111111-1-1-111-1-1-1-111-111-1
χ161111-1-111-1-1-1111111111-1-1-1-11111-1-1-1-1-11-1-1-1-11111-1-1111111-1-1-1-1-11111-1-11-1-11
χ17222222222-2-222222222-22222-2-2-2-2-2-2-2-200000000002222-2-200-200000000000000
χ18222222222-2-222222222-22222-2-2-2-2-2-2-2-20000000000-2-2-2-22200200000000000000
χ192222-2-222-22222222222-2-2-2-2-2-2-2-2-22222000000000022-2-22200-200000000000000
χ202222-2-222-22222222222-2-2-2-2-2-2-2-2-222220000000000-2-222-2-200200000000000000
χ212-2-22002-202i−2i22-222-2-2-20000000002i2i−2i−2i00000000002i−2i002-200000i2−i22−22−2i2−i20000
χ222-2-22002-202i−2i22-222-2-2-20000000002i2i−2i−2i00000000002i−2i002-200000−i2i2−22−22−i2i20000
χ232-2-22002-202i−2i22-222-2-2-20000000002i2i−2i−2i0000000000−2i2i00-22000002−2−i2i2i2−i2−220000
χ242-2-22002-202i−2i22-222-2-2-20000000002i2i−2i−2i0000000000−2i2i00-2200000−22i2−i2−i2i22−20000
χ252-2-22002-20−2i2i22-222-2-2-2000000000−2i−2i2i2i00000000002i−2i00-22000002−2i2−i2−i2i2−220000
χ262-2-22002-20−2i2i22-222-2-2-2000000000−2i−2i2i2i00000000002i−2i00-2200000−22−i2i2i2−i22−20000
χ272-2-22002-20−2i2i22-222-2-2-2000000000−2i−2i2i2i0000000000−2i2i002-200000i2−i2−22−22i2−i20000
χ282-2-22002-20−2i2i22-222-2-2-2000000000−2i−2i2i2i0000000000−2i2i002-200000−i2i22−22−2−i2i20000
χ2944444444444-1-1-1-1-1-1-1-14-1-1-1-1-1-1-1-1-1-1-1-144-1-1-1-1-1-1-1-100000000000000000000000
χ3044444444444-1-1-1-1-1-1-1-14-1-1-1-1-1-1-1-1-1-1-1-1-4-41111111100000000000000000000000
χ31444444444-4-4-1-1-1-1-1-1-1-1-4-1-1-1-1111111110055−5−555−5−500000000000000000000000
χ32444444444-4-4-1-1-1-1-1-1-1-1-4-1-1-1-11111111100−5−555−5−55500000000000000000000000
χ33444444-4-4-400444-4-4-4-44044-4-400000000000000000000000000000000000000000
χ34444444-4-4-400-1-1-11111-10-1-11155−5−55−55−500−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−ζ3800000000000000000000000
χ35444444-4-4-400-1-1-11111-10-1-11155−5−55−55−500ζ6−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+ζ3800000000000000000000000
χ36444444-4-4-400-1-1-11111-10-1-111−5−555−55−5500ζ6−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+ζ3800000000000000000000000
χ37444444-4-4-400-1-1-11111-10-1-111−5−555−55−5500−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−ζ3800000000000000000000000
χ384444-4-444-444-1-1-1-1-1-1-1-1-411111111-1-1-1-10055−5−5−5−55500000000000000000000000
χ394444-4-444-444-1-1-1-1-1-1-1-1-411111111-1-1-1-100−5−55555−5−500000000000000000000000
χ404444-4-444-4-4-4-1-1-1-1-1-1-1-141111-1-1-1-111114-4-1-1-1-1111100000000000000000000000
χ414444-4-444-4-4-4-1-1-1-1-1-1-1-141111-1-1-1-11111-441111-1-1-1-100000000000000000000000
χ424444-4-4-4-4400444-4-4-4-440-4-44400000000000000000000000000000000000000000
χ434444-4-4-4-4400-1-1-11111-1011-1-155−5−5−55−5500−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+ζ3800000000000000000000000
χ444444-4-4-4-4400-1-1-11111-1011-1-155−5−5−55−5500ζ6−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−ζ3800000000000000000000000
χ454444-4-4-4-4400-1-1-11111-1011-1-1−5−5555−55−500ζ6−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−ζ3800000000000000000000000
χ464444-4-4-4-4400-1-1-11111-1011-1-1−5−5555−55−500−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+ζ3800000000000000000000000
χ474-44-44-4000004-4-40000404-4000000000000000000000000002i−2i02i−2i000000000000
χ484-44-44-4000004-4-40000404-400000000000000000000000000−2i2i0−2i2i000000000000
χ494-44-4-44000004-4-4000040-44000000000000000000000000002i−2i0−2i2i000000000000
χ504-44-4-44000004-4-4000040-4400000000000000000000000000−2i2i02i−2i000000000000
χ514-4-4400-4400044-4-4-444-400000000000000000000000004i−4i0000000000000000000
χ524-4-4400-4400044-4-4-444-40000000000000000000000000−4i4i0000000000000000000
χ5388-8-800000008-880000-80000000000000000000000000000000000000000000000
χ5488-8-80000000-22-225−2525−25200000−2ζ6+2ζ14−2ζ22+2ζ382ζ6−2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ380000000000000000000000000000000000000
χ5588-8-80000000-22-225−2525−252000002ζ6−2ζ14+2ζ22−2ζ38−2ζ6+2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ380000000000000000000000000000000000000
χ5688-8-80000000-22-2−2525−25252000002ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14+2ζ22−2ζ38−2ζ6+2ζ14−2ζ22+2ζ380000000000000000000000000000000000000
χ5788-8-80000000-22-2−2525−2525200000−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14−2ζ22+2ζ382ζ6−2ζ14+2ζ22−2ζ380000000000000000000000000000000000000
χ588-88-88-800000-22225−25−2525-20-2225−2500000000000000000000000000000000000000000
χ598-88-88-800000-222−252525−25-20-22−252500000000000000000000000000000000000000000
χ608-88-8-8800000-22225−25−2525-202-2−252500000000000000000000000000000000000000000
χ618-88-8-8800000-222−252525−25-202-225−2500000000000000000000000000000000000000000
χ628-8-88008-808i−8i-2-22-2-2222000000000−2i−2i2i2i000000000000000000000000000000000
χ638-8-88008-80−8i8i-2-22-2-22220000000002i2i−2i−2i000000000000000000000000000000000
χ648-8-8800-88000-2-2222-2-220000000002i5−2i5−2i52i5000000000000000000000000000000000
χ658-8-8800-88000-2-2222-2-22000000000−2i52i52i5−2i5000000000000000000000000000000000

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