Finite Group Databasebeta

← Group #72284035

Character table — Group #72284035

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size112444888888881616161616161616161616161616163232323232323232323232323232646464646464646464646464128128128128
order12222222222244244444444444444224444444444444444444444448888
χ111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-11-1-1111111-1-1-11-11-1-1-1-1-11-1-111-1-1
χ311111111111111111111111111111-11-1-11-1111111-1-1-1-11-11-1-1-1-1-11-1-1-111
χ411111111111111111111111111111-1-11-1-11111111111-1-1-1-11111-1-11-1-1-1-1
χ511111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111111-1-1-1-1111-1-1-1-1
χ611111111111111111-1-1-1-1-1-1-1-111111-1-11-1-111-1-1-1-1-1-1-11-11-111111-1-1-1-111
χ711111111111111111-1-1-1-1-1-1-1-11111-11-1-11-111-1-1-1-1-1-1-1-11-111111-11-111-1-1
χ811111111111111111-1-1-1-1-1-1-1-11111-1-11-1-1111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111
χ9111111-11-1-11-1111-1-1iiii−i−i−i−i-1-1-1-111111111ii−i−i-1-1-1-1-111ii−i−i-1-11i−ii−i
χ10111111-11-1-11-1111-1-1iiii−i−i−i−i-1-1-1-11-1-11-1-111ii−i−i111-111-1−i−iii-11-1i−i−ii
χ11111111-11-1-11-1111-1-1iiii−i−i−i−i-1-1-1-1-11-1-11-111ii−i−i1111-1-11−i−iii1-1-1−iii−i
χ12111111-11-1-11-1111-1-1iiii−i−i−i−i-1-1-1-1-1-11-1-1111ii−i−i-1-1-111-1-1ii−i−i111−ii−ii
χ13111111-11-1-11-1111-1-1−i−i−i−iiiii-1-1-1-111111111−i−iii-1-1-1-1-111−i−iii-1-11−ii−ii
χ14111111-11-1-11-1111-1-1−i−i−i−iiiii-1-1-1-11-1-11-1-111−i−iii111-111-1ii−i−i-11-1−iii−i
χ15111111-11-1-11-1111-1-1−i−i−i−iiiii-1-1-1-1-11-1-11-111−i−iii1111-1-11ii−i−i1-1-1i−i−ii
χ16111111-11-1-11-1111-1-1−i−i−i−iiiii-1-1-1-1-1-11-1-1111−i−iii-1-1-111-1-1−i−iii111i−ii−i
χ172222222222222222200000000-2-2-2-2002002-2-20000-2-220000000000-20000
χ182222222222222222200000000-2-2-2-200-200-2-2-2000022-2000000000020000
χ1922222222-2-222-2-2-22-20000000022-2-20200202-20000000020-200000-200000
χ2022222222-2-222-2-2-22-20000000022-2-20-200-202-200000000-20200000200000
χ2122222222-2-222-2-2-22-200000000-2-222200200-22000000020-200000-2000000
χ2222222222-2-222-2-2-22-200000000-2-222-200-200-220000000-202000002000000
χ23222222-22222-2-2-2-2-220000000022-2-2200200-220000000-20-2000002000000
χ24222222-22222-2-2-2-2-220000000022-2-2-200-200-22000000020200000-2000000
χ25222222-22222-2-2-2-2-2200000000-2-2220200202-200000000-20-200000200000
χ26222222-22222-2-2-2-2-2200000000-2-2220-200-202-20000000020200000-200000
χ27222222-22-2-22-2222-2-2000000002222002002-2-2000022-20000000000-20000
χ28222222-22-2-22-2222-2-200000000222200-200-2-2-20000-2-22000000000020000
χ292222-2-20200-2022-2001+i1+i−1−i−1−i1−i1−i−1+i−1+i2i−2i2i−2i00200-2001+i−1−i1−i−1+i2i−2i000001+i−1−i1−i−1+i0000000
χ302222-2-20200-2022-2001+i1+i−1−i−1−i1−i1−i−1+i−1+i2i−2i2i−2i00-2002001+i−1−i1−i−1+i−2i2i00000−1−i1+i−1+i1−i0000000
χ312222-2-20200-2022-2001−i1−i−1+i−1+i1+i1+i−1−i−1−i−2i2i−2i2i00200-2001−i−1+i1+i−1−i−2i2i000001−i−1+i1+i−1−i0000000
χ322222-2-20200-2022-2001−i1−i−1+i−1+i1+i1+i−1−i−1−i−2i2i−2i2i00-2002001−i−1+i1+i−1−i2i−2i00000−1+i1−i−1−i1+i0000000
χ332222-2-20200-2022-200−1+i−1+i1−i1−i−1−i−1−i1+i1+i−2i2i−2i2i00200-200−1+i1−i−1−i1+i−2i2i00000−1+i1−i−1−i1+i0000000
χ342222-2-20200-2022-200−1+i−1+i1−i1−i−1−i−1−i1+i1+i−2i2i−2i2i00-200200−1+i1−i−1−i1+i2i−2i000001−i−1+i1+i−1−i0000000
χ352222-2-20200-2022-200−1−i−1−i1+i1+i−1+i−1+i1−i1−i2i−2i2i−2i00200-200−1−i1+i−1+i1−i2i−2i00000−1−i1+i−1+i1−i0000000
χ362222-2-20200-2022-200−1−i−1−i1+i1+i−1+i−1+i1−i1−i2i−2i2i−2i00-200200−1−i1+i−1+i1−i−2i2i000001+i−1−i1−i−1+i0000000
χ374444444-400-44000-4022222222000000000000-2-2-2-2000000000000000000
χ384444444-400-44000-40-2-2-2-2-2-2-2-20000000000002222000000000000000000
χ39444444-4-400-4-4000402i2i2i2i−2i−2i−2i−2i000000000000−2i−2i2i2i000000000000000000
χ40444444-4-400-4-400040−2i−2i−2i−2i2i2i2i2i0000000000002i2i−2i−2i000000000000000000
χ414444-4-40400-40-4-4400000000004i−4i−4i4i000000000000000000000000000000
χ424444-4-40400-40-4-440000000000−4i4i4i−4i000000000000000000000000000000
χ434444-4-40-444400000-422-2-222-2-2000000000000-22-22000000000000000000
χ444444-4-40-444400000-4-2-222-2-2220000000000002-22-2000000000000000000
χ454444-4-40-4-4-440000042i2i−2i−2i−2i−2i2i2i000000000000−2i2i2i−2i000000000000000000
χ464444-4-40-4-4-44000004−2i−2i2i2i2i2i−2i−2i0000000000002i−2i−2i2i000000000000000000
χ47888-88-8000000000000000000000000400-40000000000000000000000000
χ48888-88-8000000000000000000000000-40040000000000000000000000000
χ49888-8-8800000000000000000000000400-400000000000000000000000000
χ50888-8-8800000000000000000000000-400400000000000000000000000000
χ5188-8000404-40-44-4000004i−4i004i−4i0000000000000000000000000000000000
χ5288-8000404-40-44-400000−4i4i00−4i4i0000000000000000000000000000000000
χ5388-800040-440-4-440004i−4i004i−4i000000000000000000000000000000000000
χ5488-800040-440-4-44000−4i4i00−4i4i000000000000000000000000000000000000
χ5588-8000-404-404-440004-400-44000000000000000000000000000000000000
χ5688-8000-404-404-44000-44004-4000000000000000000000000000000000000
χ5788-8000-40-44044-4000004-400-440000000000000000000000000000000000
χ5888-8000-40-44044-400000-44004-40000000000000000000000000000000000
χ5932-32000000000000000000000000000000000000000000000000000000000

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