Finite Group Databasebeta

← Group #72338658

Character table — Group #72338658

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1124448888161616161616161616161616161616323232323232323232323232323232646464646464646464646464128128128128
order12222222222222444444444442244444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ31111111111111111-1-1-1-111111-1-111111111111-1-1-11-11-11-1-1-1-1-1-111-1-1
χ41111111111111111-1-1-1-111111-1-1111-1-1-1-1-1-1-1-1-1-1-11-11-11-1-11111-1-111
χ5111111111111-1-11111-1-1111111-1-11111111111111-1-1-1-1-11-11111-1-1-1-1
χ6111111111111-1-11111-1-1111111-1-111-1-1-1-1-1-1-1-1111-1-1-1-1-11-1-1-1-1-11111
χ7111111111111-1-111-1-11111111-11-11111111111-1-1-1-11-11-1-11-1-1-1-1-1-111
χ8111111111111-1-111-1-11111111-11-111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11111111-1-1
χ91111111-1-111-1111-11111-1-1-1-1-111111iiii−i−i−i−i-1-1-1-1-111-11-1ii−i−ii−ii−i
χ101111111-1-111-1111-11111-1-1-1-1-111111−i−i−i−iiiii-1-1-1-1-111-11-1−i−iii−ii−ii
χ111111111-1-111-1111-1-1-1-1-1-1-1-1-1-1-1-1111iiii−i−i−i−i111-111-1-1-11−i−iiii−i−ii
χ121111111-1-111-1111-1-1-1-1-1-1-1-1-1-1-1-1111−i−i−i−iiiii111-111-1-1-11ii−i−i−iii−i
χ131111111-1-111-1-1-11-111-1-1-1-1-1-1-11-1-111iiii−i−i−i−i-1-1-111-1-1111ii−i−i−ii−ii
χ141111111-1-111-1-1-11-111-1-1-1-1-1-1-11-1-111−i−i−i−iiiii-1-1-111-1-1111−i−iiii−ii−i
χ151111111-1-111-1-1-11-1-1-111-1-1-1-1-1-11-111iiii−i−i−i−i1111-1-111-1-1−i−iii−iii−i
χ161111111-1-111-1-1-11-1-1-111-1-1-1-1-1-11-111−i−i−i−iiiii1111-1-111-1-1ii−i−ii−i−ii
χ1722222222222200222200-2-2-2-22200-2-200000000-2-2200000-2000000000
χ182222222222220022-2-200-2-2-2-22-200-2-20000000022-2000002000000000
χ192222222222-2-200-22002222-2-2-20202-200000000000020-200-200000000
χ202222222222-2-200-2200-2-222-2-2-20-202-2000000000000-20200200000000
χ212222222222-2-222-220000-2-222-2002-220000000000020-20-20000000000
χ222222222222-2-2-2-2-220000-2-222-200-2-2200000000000-202020000000000
χ232222222-2-222-2002-222002222-2200-2-20000000022-200000-2000000000
χ242222222-2-222-2002-2-2-2002222-2-200-2-200000000-2-22000002000000000
χ252222222-2-22-2200-2-20022-2-22220202-2000000000000-20-200200000000
χ262222222-2-22-2200-2-200-2-2-2-22220-202-200000000000020200-200000000
χ272222222-2-22-2222-2-2000022-2-22002-2200000000000-20-2020000000000
χ282222222-2-22-22-2-2-2-2000022-2-2200-2-22000000000002020-20000000000
χ292222-2-2200-2-20002022002i−2i2i−2i0-200001+i1+i−1−i−1−i1−i1−i−1+i−1+i2i−2i000000001+i−1−i1−i−1+i0000
χ302222-2-2200-2-20002022002i−2i2i−2i0-20000−1−i−1−i1+i1+i−1+i−1+i1−i1−i2i−2i00000000−1−i1+i−1+i1−i0000
χ312222-2-2200-2-2000202200−2i2i−2i2i0-200001−i1−i−1+i−1+i1+i1+i−1−i−1−i−2i2i000000001−i−1+i1+i−1−i0000
χ322222-2-2200-2-2000202200−2i2i−2i2i0-20000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−2i2i00000000−1+i1−i−1−i1+i0000
χ332222-2-2200-2-200020-2-2002i−2i2i−2i0200001+i1+i−1−i−1−i1−i1−i−1+i−1+i−2i2i00000000−1−i1+i−1+i1−i0000
χ342222-2-2200-2-200020-2-2002i−2i2i−2i020000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−2i2i000000001+i−1−i1−i−1+i0000
χ352222-2-2200-2-200020-2-200−2i2i−2i2i0200001−i1−i−1+i−1+i1+i1+i−1−i−1−i2i−2i00000000−1+i1−i−1−i1+i0000
χ362222-2-2200-2-200020-2-200−2i2i−2i2i020000−1+i−1+i1−i1−i−1−i−1−i1+i1+i2i−2i000000001−i−1+i1+i−1−i0000
χ37444444-444-400000-4000000000000002-22-22-22-2000000000000000000
χ38444444-444-400000-400000000000000-22-22-22-22000000000000000000
χ39444444-4-4-4-4000004000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000
χ40444444-4-4-4-400000400000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000
χ414444-4-4400-44000-4000004i−4i−4i4i00000000000000000000000000000000
χ424444-4-4400-44000-400000−4i4i4i−4i00000000000000000000000000000000
χ434444-4-4-400404000000000000-4000002i−2i−2i2i−2i2i2i−2i000000000000000000
χ444444-4-4-400404000000000000-400000−2i2i2i−2i2i−2i−2i2i000000000000000000
χ454444-4-4-40040-40000000000004000002-2-222-2-22000000000000000000
χ464444-4-4-40040-4000000000000400000-222-2-222-2000000000000000000
χ47888-88-800000000000044000000-400000000000000000000000000000
χ48888-88-8000000000000-4-4000000400000000000000000000000000000
χ49888-8-88000000440000000000000-40000000000000000000000000000
χ50888-8-88000000-4-4000000000000040000000000000000000000000000
χ511616-1600008-800000000000000000000000000000000000000000000000
χ521616-160000-8800000000000000000000000000000000000000000000000
χ5316-1600000000004-4004-44-4000000000000000000000000000000000000
χ5416-1600000000004-400-44-44000000000000000000000000000000000000
χ5516-160000000000-44004-4-44000000000000000000000000000000000000
χ5616-160000000000-4400-444-4000000000000000000000000000000000000

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