Finite Group Databasebeta

← Group #72283944

Character table — Group #72283944

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size112444888888881616161616161616161616161616163232323232323232323232323232646464646464646464646464128128128128
order12222222222244244444488888888224444444488884444444444448888
χ111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-11-1-111-1-11111-11-11-1-1-1-1-11-1-111-1-1
χ311111111111111111111111111111-11-1-11-111-1-11111-1-11-11-1-1-1-1-11-1-1-111
χ411111111111111111111111111111-1-11-1-11111111111-1-1-1-11111-1-11-1-1-1-1
χ5111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111-1-1-1-1111-1-1-1-1
χ6111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-111-1-1-1-1-1-1-11-11-111111-1-1-1-111
χ7111111111111111111111-1-1-1-1-1-1-1-1-11-1-11-111-1-1-1-1-1-1-1-11-111111-11-111-1-1
χ8111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111111
χ9111111111-1-11-1-1-11-1-1-1-1-1iiii−i−i−i−i11111111-1-1ii−i−i-1-1-111ii−i−i-1-11i−ii−i
χ10111111111-1-11-1-1-11-1-1-1-1-1iiii−i−i−i−i1-1-11-1-11111ii−i−i1-111-1−i−iii-11-1i−i−ii
χ11111111111-1-11-1-1-11-1-1-1-1-1iiii−i−i−i−i-11-1-11-11111ii−i−i11-1-11−i−iii1-1-1−iii−i
χ12111111111-1-11-1-1-11-1-1-1-1-1iiii−i−i−i−i-1-11-1-1111-1-1ii−i−i-111-1-1ii−i−i111−ii−ii
χ13111111111-1-11-1-1-11-1-1-1-1-1−i−i−i−iiiii11111111-1-1−i−iii-1-1-111−i−iii-1-11−ii−ii
χ14111111111-1-11-1-1-11-1-1-1-1-1−i−i−i−iiiii1-1-11-1-11111−i−iii1-111-1ii−i−i-11-1−iii−i
χ15111111111-1-11-1-1-11-1-1-1-1-1−i−i−i−iiiii-11-1-11-11111−i−iii11-1-11ii−i−i1-1-1i−i−ii
χ16111111111-1-11-1-1-11-1-1-1-1-1−i−i−i−iiiii-1-11-1-1111-1-1−i−iii-111-1-1−i−iii111i−ii−i
χ1722222222222222222-2-2-2-200000000002002-2-2-2-2000020000000000-20000
χ1822222222222222222-2-2-2-20000000000-200-2-2-2220000-2000000000020000
χ19222222222-2-22-2-2-22-2222200000000002002-2-2220000-20000000000-20000
χ20222222222-2-22-2-2-22-222220000000000-200-2-2-2-2-200002000000000020000
χ21222222-2-22222-2-2-2-2222-2-2000000000200202-200000000-20-200000200000
χ22222222-2-22222-2-2-2-2222-2-2000000000-200-202-20000000020200000-200000
χ23222222-2-22222-2-2-2-22-2-22200000000200200-220000000-20-2000002000000
χ24222222-2-22222-2-2-2-22-2-22200000000-200-200-22000000020200000-2000000
χ25222222-2-22-2-22222-2-222-2-200000000200200-22000000020-200000-2000000
χ26222222-2-22-2-22222-2-222-2-200000000-200-200-220000000-202000002000000
χ27222222-2-22-2-22222-2-2-2-222000000000200202-20000000020-200000-200000
χ28222222-2-22-2-22222-2-2-2-222000000000-200-202-200000000-20200000200000
χ292222-2-222200-2000-202i−2i2i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00200-2002i−2i1+i−1−i1−i−1+i000001+i−1−i1−i−1+i0000000
χ302222-2-222200-2000-202i−2i2i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00-200200−2i2i1+i−1−i1−i−1+i00000−1−i1+i−1+i1−i0000000
χ312222-2-222200-2000-202i−2i2i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00200-2002i−2i−1−i1+i−1+i1−i00000−1−i1+i−1+i1−i0000000
χ322222-2-222200-2000-202i−2i2i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00-200200−2i2i−1−i1+i−1+i1−i000001+i−1−i1−i−1+i0000000
χ332222-2-222200-2000-20−2i2i−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00200-200−2i2i1−i−1+i1+i−1−i000001−i−1+i1+i−1−i0000000
χ342222-2-222200-2000-20−2i2i−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00-2002002i−2i1−i−1+i1+i−1−i00000−1+i1−i−1−i1+i0000000
χ352222-2-222200-2000-20−2i2i−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00200-200−2i2i−1+i1−i−1−i1+i00000−1+i1−i−1−i1+i0000000
χ362222-2-222200-2000-20−2i2i−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00-2002002i−2i−1+i1−i−1−i1+i000001−i−1+i1+i−1−i0000000
χ3744444400-400-444-4000000222222220000000000-2-2-2-20000000000000000
χ3844444400-400-444-4000000-2-2-2-2-2-2-2-2000000000022220000000000000000
χ3944444400-400-4-4-440000002i2i2i2i−2i−2i−2i−2i0000000000−2i−2i2i2i0000000000000000
χ4044444400-400-4-4-44000000−2i−2i−2i−2i2i2i2i2i00000000002i2i−2i−2i0000000000000000
χ414444-4-400-44440000-4000022-2-222-2-20000000000-22-220000000000000000
χ424444-4-400-44440000-40000-2-222-2-22200000000002-22-20000000000000000
χ434444-4-400-4-4-440000400002i2i−2i−2i−2i−2i2i2i0000000000−2i2i2i−2i0000000000000000
χ444444-4-400-4-4-44000040000−2i−2i2i2i2i2i−2i−2i00000000002i−2i−2i2i0000000000000000
χ454444-4-4-4-4400-4000404i−4i−4i4i00000000000000000000000000000000000000
χ464444-4-4-4-4400-400040−4i4i4i−4i00000000000000000000000000000000000000
χ47888-88-800000000000000000000000400-400000000000000000000000000
χ48888-88-800000000000000000000000-400400000000000000000000000000
χ49888-8-88000000000000000000000000400-40000000000000000000000000
χ50888-8-88000000000000000000000000-40040000000000000000000000000
χ5188-80004-404-404-40000000004i−4i004i−4i000000000000000000000000000000
χ5288-80004-404-404-4000000000−4i4i00−4i4i000000000000000000000000000000
χ5388-80004-40-440-440000000004-400-44000000000000000000000000000000
χ5488-80004-40-440-44000000000-44004-4000000000000000000000000000000
χ5588-8000-4404-40-4400000004-4004-400000000000000000000000000000000
χ5688-8000-4404-40-440000000-4400-4400000000000000000000000000000000
χ5788-8000-440-4404-400000004i−4i00−4i4i00000000000000000000000000000000
χ5888-8000-440-4404-40000000−4i4i004i−4i00000000000000000000000000000000
χ5932-32000000000000000000000000000000000000000000000000000000000

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