Finite Group Databasebeta

← Group #13017821

Character table — Group #13017821

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111122224444444445555888888888888888810101010161616161616161616202020202020202020202020204040404040404040404040408080
order12224444444445101010222222442020202020202020202020204444101010102020202020444448888888822448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111-1-1-1-11111111111111111-1-1-1-1111111111-1-1-1-1-1iiii−i−i−i−i-1-1-1-1iiii−i−i−i−ii−i
χ411111111111111111-1-1-1-11111111111111111-1-1-1-1111111111-1-1-1-1-1−i−i−i−iiiii-1-1-1-1−i−i−i−iiiii−ii
χ51111111111-1-11111111111-1-1-111111111-1-1-1-1111111-1-11-1-1-1-111-1-11111111111-1-1-111-1-111-1-1-1-1
χ61111111111-1-11111111111-1-1-111111111-1-1-1-1111111-1-11-1-1-1-111-1-11-1-1-1-1-1-1-1-11-1-1-1-1-111-1-11111
χ71111111111-1-111111-1-1-1-11-1-1-111111111-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1-111-1iiii−i−i−i−i-1111ii−i−i−i−iii−ii
χ81111111111-1-111111-1-1-1-11-1-1-111111111-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1-111-1−i−i−i−iiiii-1111−i−iiiii−i−ii−i
χ911111111-1-111111111111-11-1-11111-1-1-1-111111111-1-1111-1-1-1-1-1-111111111111-11-1-1-1-111-1-111-1-1
χ1011111111-1-111111111111-11-1-11111-1-1-1-111111111-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-11-1-111-1-111-1-111
χ1111111111-1-11111111-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-1-1-1111-1-1-1-111-1-1-1iiii−i−i−i−i1-111−i−iiiii−i−i−ii
χ1211111111-1-11111111-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-1-1-1111-1-1-1-111-1-1-1−i−i−i−iiiii1-111ii−i−i−i−iiii−i
χ1311111111-1-1-1-1111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-111
χ1411111111-1-1-1-1111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ1511111111-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1iiii−i−i−i−i11-1-1−i−i−i−iiiiii−i
χ1611111111-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1−i−i−i−iiiii11-1-1iiii−i−i−i−i−ii
χ17222222-2-20022-2222222220-20022-2-2000022222-22-200-2-2-200000022-2000000000-2000000000000
χ18222222-2-20022-22222-2-2-2-20-20022-2-200002222-22-2200-2-2-2000000-2-220000000002000000000000
χ19222222-2-200-2-2-222222222020022-2-20000-2-2-2-22-22-20022-2000000-2-2-20000000002000000000000
χ20222222-2-200-2-2-22222-2-2-2-2020022-2-20000-2-2-2-2-22-220022-2000000222000000000-2000000000000
χ212222-2-2222200-222222222-2000-2-22222220000-22-22-2-200-200002200-200000000-20000000000000
χ222222-2-2222200-22222-2-2-2-2-2000-2-222222200002-22-2-2-200-20000-2-20020000000020000000000000
χ232222-2-222-2-200-2222222222000-2-222-2-2-2-20000-22-222200-20000-2-200-20000000020000000000000
χ242222-2-222-2-200-22222-2-2-2-22000-2-222-2-2-2-200002-22-22200-200002200200000000-20000000000000
χ252222-2-2-2-20000222222222002-2-2-2-2-200000000-2-2-2-20000222-2-20000200000000002-20000000000
χ262222-2-2-2-2000022222222200-22-2-2-2-200000000-2-2-2-200002-2-222000020000000000-220000000000
χ272222-2-2-2-2000022222-2-2-2-2002-2-2-2-2-20000000022220000222-2-20000-20000000000-220000000000
χ282222-2-2-2-2000022222-2-2-2-200-22-2-2-2-200000000222200002-2-2220000-200000000002-20000000000
χ2922-2-2002-22i−2i00022-2-222-2-20000002-22i2i−2i−2i00000-2020000000002i−2i00022−2−222−2−20000i2−i200i2−i20000
χ3022-2-2002-22i−2i00022-2-222-2-20000002-22i2i−2i−2i00000-2020000000002i−2i000−2−222−2−2220000−i2i200−i2i20000
χ3122-2-2002-22i−2i00022-2-2-2-2220000002-22i2i−2i−2i0000020-2000000000−2i2i000i2i2−i2−i2−i2−i2i2i20000−22002−20000
χ3222-2-2002-22i−2i00022-2-2-2-2220000002-22i2i−2i−2i0000020-2000000000−2i2i000−i2−i2i2i2i2i2−i2−i200002−200−220000
χ3322-2-2002-2−2i2i00022-2-222-2-20000002-2−2i−2i2i2i00000-202000000000−2i2i00022−2−222−2−20000−i2i200−i2i20000
χ3422-2-2002-2−2i2i00022-2-222-2-20000002-2−2i−2i2i2i00000-202000000000−2i2i000−2−222−2−2220000i2−i200i2−i20000
χ3522-2-2002-2−2i2i00022-2-2-2-2220000002-2−2i−2i2i2i0000020-20000000002i−2i000i2i2−i2−i2−i2−i2i2i200002−200−220000
χ3622-2-2002-2−2i2i00022-2-2-2-2220000002-2−2i−2i2i2i0000020-20000000002i−2i000−i2−i2i2i2i2i2−i2−i20000−22002−20000
χ372-22-22-200002i−2i02-22-22-22-200002-20000002i2i−2i−2i-2020000000000002i−2i02−22−22−22−2000000i2−i200i2−i200
χ382-22-22-200002i−2i02-22-22-22-200002-20000002i2i−2i−2i-2020000000000002i−2i0−22−22−22−22000000−i2i200−i2i200
χ392-22-22-200002i−2i02-22-2-22-2200002-20000002i2i−2i−2i20-2000000000000−2i2i0i2−i2i2−i2−i2i2−i2i2000000−22002−200
χ402-22-22-200002i−2i02-22-2-22-2200002-20000002i2i−2i−2i20-2000000000000−2i2i0−i2i2−i2i2i2−i2i2−i20000002−200−2200
χ412-22-22-20000−2i2i02-22-22-22-200002-2000000−2i−2i2i2i-202000000000000−2i2i02−22−22−22−2000000−i2i200−i2i200
χ422-22-22-20000−2i2i02-22-22-22-200002-2000000−2i−2i2i2i-202000000000000−2i2i0−22−22−22−22000000i2−i200i2−i200
χ432-22-22-20000−2i2i02-22-2-22-2200002-2000000−2i−2i2i2i20-20000000000002i−2i0i2−i2i2−i2−i2i2−i2i20000002−200−2200
χ442-22-22-20000−2i2i02-22-2-22-2200002-2000000−2i−2i2i2i20-20000000000002i−2i0−i2i2−i2i2i2−i2i2−i2000000−22002−200
χ454444444444444-1-1-1-100004444-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-1000000000000000000000000000
χ464444444444-4-44-1-1-1-100004-4-4-4-1-1-1-1-1-1-1-111110000-1-111-11111000000000000000000000000000
χ4744444444-4-4444-1-1-1-10000-44-4-4-1-1-1-11111-1-1-1-1000011-1-1-11111000000000000000000000000000
χ4844444444-4-4-4-44-1-1-1-10000-4-444-1-1-1-11111111100001111-1-1-1-1-1000000000000000000000000000
χ49444444-4-40044-4-1-1-1-100000-400-1-1115−55−5-1-1-1-100005−51115−55−5000000000000000000000000000
χ50444444-4-40044-4-1-1-1-100000-400-1-111−55−55-1-1-1-10000−55111−55−55000000000000000000000000000
χ51444444-4-400-4-4-4-1-1-1-100000400-1-1115−55−5111100005−5-1-11−55−55000000000000000000000000000
χ52444444-4-400-4-4-4-1-1-1-100000400-1-111−55−5511110000−55-1-115−55−5000000000000000000000000000
χ534444-4-4444400-4-1-1-1-10000-400011-1-1-1-1-1-15−55−50000115−515−5−55000000000000000000000000000
χ544444-4-4444400-4-1-1-1-10000-400011-1-1-1-1-1-1−55−55000011−551−555−5000000000000000000000000000
χ554444-4-444-4-400-4-1-1-1-10000400011-1-111115−55−50000-1-15−51−555−5000000000000000000000000000
χ564444-4-444-4-400-4-1-1-1-10000400011-1-11111−55−550000-1-1−5515−5−55000000000000000000000000000
χ574444-4-4-4-400004-1-1-1-10000004-411115−55−55−55−50000−55−55-1-1-111000000000000000000000000000
χ584444-4-4-4-400004-1-1-1-10000004-41111−55−55−55−5500005−55−5-1-1-111000000000000000000000000000
χ594444-4-4-4-400004-1-1-1-1000000-4411115−55−5−55−550000−555−5-111-1-1000000000000000000000000000
χ604444-4-4-4-400004-1-1-1-1000000-441111−55−555−55−500005−5−55-111-1-1000000000000000000000000000
χ6144-4-400-440000044-4-444-4-4000000-4400000000040-4000000000000000000000000000000000000
χ6244-4-400-440000044-4-4-4-444000000-44000000000-404000000000000000000000000000000000000
χ634-44-4-4400000004-44-44-44-40000-44000000000040-40000000000000000000000000000000000000
χ644-44-4-4400000004-44-4-44-440000-440000000000-4040000000000000000000000000000000000000
χ654-4-440000000004-4-444-4-4400000000000000000000000000000000002-2-222-2-2200000000000000
χ664-4-440000000004-4-444-4-440000000000000000000000000000000000-222-2-222-200000000000000
χ674-4-440000000004-4-44-444-400000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ684-4-440000000004-4-44-444-40000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ6988-8-8008-88i−8i000-2-2220000000000-22−2i−2i2i2i00000000000000000000000000000000000000000000
χ7088-8-8008-8−8i8i000-2-2220000000000-222i2i−2i−2i00000000000000000000000000000000000000000000
χ7188-8-800-8800000-2-22200000000002-22i5−2i5−2i52i500000000000000000000000000000000000000000000
χ7288-8-800-8800000-2-22200000000002-2−2i52i52i5−2i500000000000000000000000000000000000000000000
χ738-88-88-800008i−8i0-22-2200000000-22000000−2i−2i2i2i0000000000000000000000000000000000000000
χ748-88-88-80000−8i8i0-22-2200000000-220000002i2i−2i−2i0000000000000000000000000000000000000000
χ758-88-8-880000000-22-22000000002-20000002i5−2i5−2i52i50000000000000000000000000000000000000000
χ768-88-8-880000000-22-22000000002-2000000−2i52i52i5−2i50000000000000000000000000000000000000000
χ7716-16-1616000000000-444-4000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).