Finite Group Databasebeta

← Group #13024671

Character table — Group #13024671

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11112222444444444448888888888888161616161616161616162020202020204040404040404040404040404080808080
order12222244224510101010101010410101010202020202020202044202020202020202022444422224888888884444
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
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1iiii−i−i−i−i−i−iii
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1−i−i−i−iiiiiii−i−i
χ9111111-1-1-1-1-1111111111-1-1-1-11111-1-1-1-11-11111-1-1-1-111-1-11111-1-1-111-1-111-1-11-11-1
χ10111111-1-1-1-1-1111111111-1-1-1-11111-1-1-1-11-11111-1-1-1-111-1-11111-1-1-1-1-111-1-111-11-11
χ11111111-1-1-1-1-1111111111-1-1-1-11111-1-1-1-11-11111-1-1-1-1-1-111-1-1-1-1111ii−i−i−i−iiii−i−ii
χ12111111-1-1-1-1-1111111111-1-1-1-11111-1-1-1-11-11111-1-1-1-1-1-111-1-1-1-1111−i−iiiii−i−i−iii−i
χ13111111-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-11-1-1-1-1111111-1-111-1-111-111-1-111-1-1-11-11
χ14111111-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-11-1-1-1-1111111-1-111-1-111-1-1-111-1-1111-11-1
χ15111111-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-11-1-1-1-11111-1-111-1-111-1-11ii−i−i−i−iii−iii−i
χ16111111-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-11-1-1-1-11111-1-111-1-111-1-11−i−iiiii−i−ii−i−ii
χ1722222222-2-2222222222-2-2-2-2-2-2-2-2-22222000000000022-2-2-2-200002000000000000
χ1822222222-2-2222222222-2-2-2-2-2-2-2-2-222220000000000-2-222220000-2000000000000
χ19222222-2-222-222222222-22222-2-2-2-2-2-2-2-200000000002222-2-20000-2000000000000
χ20222222-2-222-222222222-22222-2-2-2-2-2-2-2-20000000000-2-2-2-22200002000000000000
χ2122-2-2-22002-2022-2-2-222-2022-2-20000000000000000002-22-20000000i2−i2i2−i2i2−i2i2−i20000
χ2222-2-2-22002-2022-2-2-222-2022-2-20000000000000000002-22-20000000−i2i2−i2i2−i2i2−i2i20000
χ2322-2-2-22002-2022-2-2-222-2022-2-2000000000000000000-22-2200000002−22−2−22−220000
χ2422-2-2-22002-2022-2-2-222-2022-2-2000000000000000000-22-220000000−22−222−22−20000
χ2522-2-2-2200-22022-2-2-222-20-2-2220000000000000000002-2-220000000i2−i2−i2i2i2−i2−i2i20000
χ2622-2-2-2200-22022-2-2-222-20-2-2220000000000000000002-2-220000000−i2i2i2−i2−i2i2i2−i20000
χ2722-2-2-2200-22022-2-2-222-20-2-222000000000000000000-222-200000002−2−22−222−20000
χ2822-2-2-2200-22022-2-2-222-20-2-222000000000000000000-222-20000000−222−22−2−220000
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
χ3144444444-4-44-1-1-1-1-1-1-1-1-411111111-1-1-1-10055−5−555−5−500000000000000000000000
χ3244444444-4-44-1-1-1-1-1-1-1-1-411111111-1-1-1-100−5−555−5−55500000000000000000000000
χ33444444-4-444-4-1-1-1-1-1-1-1-1-4-1-1-1-1111111110055−5−5−5−55500000000000000000000000
χ34444444-4-444-4-1-1-1-1-1-1-1-1-4-1-1-1-11111111100−5−55555−5−500000000000000000000000
χ35444444-4-4-4-4-4-1-1-1-1-1-1-1-141111-1-1-1-111114-4-1-1-1-1111100000000000000000000000
χ36444444-4-4-4-4-4-1-1-1-1-1-1-1-141111-1-1-1-11111-441111-1-1-1-100000000000000000000000
χ374444-4-44400-4444-4-4-4-4400000000044-4-4000000000000000000000000000000000
χ384444-4-44400-4-1-1-11111-105−55−555−5−5-1-11100−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
χ394444-4-44400-4-1-1-11111-105−55−555−5−5-1-11100ζ6−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
χ404444-4-44400-4-1-1-11111-10−55−55−5−555-1-11100ζ6−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
χ414444-4-44400-4-1-1-11111-10−55−55−5−555-1-11100−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
χ424444-4-4-4-4004444-4-4-4-44000000000-4-444000000000000000000000000000000000
χ434444-4-4-4-4004-1-1-11111-105−55−5−5−55511-1-100ζ6−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
χ444444-4-4-4-4004-1-1-11111-105−55−5−5−55511-1-100−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
χ454444-4-4-4-4004-1-1-11111-10−55−5555−5−511-1-100−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
χ464444-4-4-4-4004-1-1-11111-10−55−5555−5−511-1-100ζ6−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
χ4744-4-44-40000044-444-4-4-40000000000000000000000000004i−4i00000000000000000
χ4844-4-44-40000044-444-4-4-4000000000000000000000000000−4i4i00000000000000000
χ494-4-44004-40004-4-4000040000000004-40000000000000000002-22-20000000000000
χ504-4-44004-40004-4-4000040000000004-4000000000000000000-22-220000000000000
χ514-4-4400-440004-4-400004000000000-440000000000000000002-2-220000000000000
χ524-4-4400-440004-4-400004000000000-44000000000000000000-222-20000000000000
χ5388-8-88-800000-2-22-2-2222025−25−252500000000000000000000000000000000000000000
χ5488-8-88-800000-2-22-2-22220−252525−2500000000000000000000000000000000000000000
χ5588-8-8-88008-80-2-2222-2-220-2-22200000000000000000000000000000000000000000
χ5688-8-8-8800-880-2-2222-2-22022-2-200000000000000000000000000000000000000000
χ578-88-800000008-880000-80000000000000000000000000000000000000000000000
χ588-88-80000000-22-225−2525−25200000−2ζ6+2ζ14−2ζ22+2ζ382ζ6−2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ380000000000000000000000000000000000000
χ598-88-80000000-22-225−2525−252000002ζ6−2ζ14+2ζ22−2ζ38−2ζ6+2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ380000000000000000000000000000000000000
χ608-88-80000000-22-2−2525−25252000002ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14+2ζ22−2ζ38−2ζ6+2ζ14−2ζ22+2ζ380000000000000000000000000000000000000
χ618-88-80000000-22-2−2525−2525200000−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14−2ζ22+2ζ382ζ6−2ζ14+2ζ22−2ζ380000000000000000000000000000000000000
χ628-8-88008-8000-22225−25−2525-2000000000-2225−25000000000000000000000000000000000
χ638-8-88008-8000-222−252525−25-2000000000-22−2525000000000000000000000000000000000
χ648-8-8800-88000-22225−25−2525-20000000002-2−2525000000000000000000000000000000000
χ658-8-8800-88000-222−252525−25-20000000002-225−25000000000000000000000000000000000

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