Finite Group Databasebeta

← Group #13017817

Character table — Group #13017817

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111122224444444445555888888888888888810101010161616161616161616202020202020202020202020204040404040404040404040408080
order12224444444445101010222244442020202020202020202020204444202020202020202020444448888888844448888888844
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
χ511111111111-1-1111111111-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-111-1-11111111111-1-1-111-1-111-1-1-1-1
χ611111111111-1-1111111111-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-111-1-11-1-1-1-1-1-1-1-11-1-1-1-1-111-1-11111
χ711111111111-1-11111-1-1-1-11-1-1-1111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-1-111-1iiii−i−i−i−i-1111ii−i−i−i−iii−ii
χ811111111111-1-11111-1-1-1-11-1-1-1111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-1-111-1−i−i−i−iiiii-1111−i−iiiii−i−ii−i
χ911111111-1-111111111111-11-1-111-1-1-1-111111111111-1-111-1-1-1-1-1-111111111111-11-1-1-1-111-1-111-1-1
χ1011111111-1-111111111111-11-1-111-1-1-1-111111111111-1-111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-11-1-111-1-111-1-111
χ1111111111-1-11111111-1-1-1-1-11-1-111-1-1-1-1111111-1-1-1-11-1-111-1-1-1-111-1-1-1iiii−i−i−i−i1-111−i−iiiii−i−i−ii
χ1211111111-1-11111111-1-1-1-1-11-1-111-1-1-1-1111111-1-1-1-11-1-111-1-1-1-111-1-1-1−i−i−i−iiiii1-111ii−i−i−i−iiii−i
χ1311111111-1-11-1-111111111-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-111
χ1411111111-1-11-1-111111111-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ1511111111-1-11-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-111111111-1iiii−i−i−i−i11-1-1−i−i−i−iiiiii−i
χ1611111111-1-11-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-111111111-1−i−i−i−iiiii11-1-1iiii−i−i−i−i−ii
χ17222222-2-222-20022222222-20002222220000-2-22-22-2-2-2-20000002200-200000000-20000000000000
χ18222222-2-222-2002222-2-2-2-2-20002222220000-2-2-22-22-2-2-2000000-2-20020000000020000000000000
χ19222222-2-2-2-2-20022222222200022-2-2-2-20000-2-22-22-2-222000000-2-200-20000000020000000000000
χ20222222-2-2-2-2-2002222-2-2-2-2200022-2-2-2-20000-2-2-22-22-2220000002200200000000-20000000000000
χ212222-2-22200-222222222220-200-2-20000222222-22-22-200-2-200000022-2000000000-2000000000000
χ222222-2-22200-2222222-2-2-2-20-200-2-200002222222-22-2-200-2-2000000-2-220000000002000000000000
χ232222-2-22200-2-2-2222222220200-2-20000-2-2-2-222-22-22-20022000000-2-2-20000000002000000000000
χ242222-2-22200-2-2-22222-2-2-2-20200-2-20000-2-2-2-2222-22-2-20022000000222000000000-2000000000000
χ252222-2-2-2-20020022222222002-2-2-200000000-2-2-2-2-2-22000022-2-20000200000000002-20000000000
χ262222-2-2-2-2002002222222200-22-2-200000000-2-2-2-2-2-220000-2-222000020000000000-220000000000
χ272222-2-2-2-2002002222-2-2-2-2002-2-2-200000000-2-222222000022-2-20000-20000000000-220000000000
χ282222-2-2-2-2002002222-2-2-2-200-22-2-200000000-2-2222220000-2-2220000-200000000002-20000000000
χ2922-2-22-2002-200022-2-222-2-200002-222-2-200000020-200000000002-200022−2−222−2−200002−2002−20000
χ3022-2-22-2002-200022-2-222-2-200002-222-2-200000020-200000000002-2000−2−222−2−2220000−2200−220000
χ3122-2-22-2002-200022-2-2-2-22200002-222-2-2000000-2020000000000-22000i2i2−i2−i2−i2−i2i2i20000i2−i200−i2i20000
χ3222-2-22-2002-200022-2-2-2-22200002-222-2-2000000-2020000000000-22000−i2−i2i2i2i2i2−i2−i20000−i2i200i2−i20000
χ3322-2-22-200-2200022-2-222-2-200002-2-2-22200000020-20000000000-2200022−2−222−2−20000−2200−220000
χ3422-2-22-200-2200022-2-222-2-200002-2-2-22200000020-20000000000-22000−2−222−2−22200002−2002−20000
χ3522-2-22-200-2200022-2-2-2-22200002-2-2-222000000-20200000000002-2000i2i2−i2−i2−i2−i2i2i20000−i2i200i2−i20000
χ3622-2-22-200-2200022-2-2-2-22200002-2-2-222000000-20200000000002-2000−i2−i2i2i2i2i2−i2−i20000i2−i200−i2i20000
χ372-2-22002-20002i−2i2-2-222-22-200000000002i2i−2i−2i2-20-202000000000002i−2i0i2−i2i2−i2i2−i2i2−i20000002−2002−200
χ382-2-22002-20002i−2i2-2-222-22-200000000002i2i−2i−2i2-20-202000000000002i−2i0−i2i2−i2i2−i2i2−i2i2000000−2200−2200
χ392-2-22002-20002i−2i2-2-22-22-2200000000002i2i−2i−2i2-2020-200000000000−2i2i02−22−2−22−22000000−i2i200i2−i200
χ402-2-22002-20002i−2i2-2-22-22-2200000000002i2i−2i−2i2-2020-200000000000−2i2i0−22−222−22−2000000i2−i200−i2i200
χ412-2-22002-2000−2i2i2-2-222-22-20000000000−2i−2i2i2i2-20-20200000000000−2i2i0i2−i2i2−i2i2−i2i2−i2000000−2200−2200
χ422-2-22002-2000−2i2i2-2-222-22-20000000000−2i−2i2i2i2-20-20200000000000−2i2i0−i2i2−i2i2−i2i2−i2i20000002−2002−200
χ432-2-22002-2000−2i2i2-2-22-22-220000000000−2i−2i2i2i2-2020-2000000000002i−2i02−22−2−22−22000000i2−i200−i2i200
χ442-2-22002-2000−2i2i2-2-22-22-220000000000−2i−2i2i2i2-2020-2000000000002i−2i0−22−222−22−2000000−i2i200i2−i200
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
χ4644444444444-4-4-1-1-1-100004-4-4-4-1-1-1-1-1-11111-1-10000-1-1-1111111000000000000000000000000000
χ4744444444-4-4444-1-1-1-10000-44-4-4-1-11111-1-1-1-1-1-10000-111-1-11111000000000000000000000000000
χ4844444444-4-44-4-4-1-1-1-10000-4-444-1-111111111-1-10000-11111-1-1-1-1000000000000000000000000000
χ49444444-4-444-400-1-1-1-10000-4000-1-1-1-1-1-15−55−51100001115−55−55−5000000000000000000000000000
χ50444444-4-444-400-1-1-1-10000-4000-1-1-1-1-1-1−55−55110000111−55−55−55000000000000000000000000000
χ51444444-4-4-4-4-400-1-1-1-100004000-1-111115−55−51100001-1-15−5−55−55000000000000000000000000000
χ52444444-4-4-4-4-400-1-1-1-100004000-1-11111−55−551100001-1-1−555−55−5000000000000000000000000000
χ534444-4-44400-444-1-1-1-100000-400115−55−5-1-1-1-1-1-1000015−5115−5−55000000000000000000000000000
χ544444-4-44400-444-1-1-1-100000-40011−55−55-1-1-1-1-1-100001−5511−555−5000000000000000000000000000
χ554444-4-44400-4-4-4-1-1-1-100000400115−55−51111-1-1000015−5-1-1−555−5000000000000000000000000000
χ564444-4-44400-4-4-4-1-1-1-10000040011−55−551111-1-100001−55-1-15−5−55000000000000000000000000000
χ574444-4-4-4-400400-1-1-1-10000004-4115−55−55−55−5110000-1−55−55-1-111000000000000000000000000000
χ584444-4-4-4-400400-1-1-1-10000004-411−55−55−55−55110000-15−55−5-1-111000000000000000000000000000
χ594444-4-4-4-400400-1-1-1-1000000-44115−55−5−55−55110000-1−555−511-1-1000000000000000000000000000
χ604444-4-4-4-400400-1-1-1-1000000-4411−55−555−55−5110000-15−5−5511-1-1000000000000000000000000000
χ6144-4-4-44000000044-4-444-4-40000-440000000000-4040000000000000000000000000000000000000
χ6244-4-4-44000000044-4-4-4-4440000-44000000000040-40000000000000000000000000000000000000
χ634-44-40000000004-44-44-4-4400000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ644-44-40000000004-44-44-4-440000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ654-44-40000000004-44-4-444-400000000000000000000000000000000002-2-22-222-200000000000000
χ664-44-40000000004-44-4-444-40000000000000000000000000000000000-222-22-2-2200000000000000
χ674-4-4400-44000004-4-444-44-400000000000000-44040-4000000000000000000000000000000000000
χ684-4-4400-44000004-4-44-44-4400000000000000-440-404000000000000000000000000000000000000
χ6988-8-88-8008-8000-2-22200000000-22-2-2220000000000000000000000000000000000000000000000
χ7088-8-88-800-88000-2-22200000000-2222-2-20000000000000000000000000000000000000000000000
χ7188-8-8-880000000-2-222000000002-225−25−25250000000000000000000000000000000000000000000000
χ7288-8-8-880000000-2-222000000002-2−252525−250000000000000000000000000000000000000000000000
χ738-8-88008-80008i−8i-222-200000000000000−2i−2i2i2i-220000000000000000000000000000000000000000
χ748-8-88008-8000−8i8i-222-2000000000000002i2i−2i−2i-220000000000000000000000000000000000000000
χ758-8-8800-8800000-222-2000000000000002i5−2i5−2i52i52-20000000000000000000000000000000000000000
χ768-8-8800-8800000-222-200000000000000−2i52i52i5−2i52-20000000000000000000000000000000000000000
χ7716-1616-16000000000-44-44000000000000000000000000000000000000000000000000000000000000

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