Finite Group Databasebeta

← Group #72339063

Character table — Group #72339063

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11222444444888816161616161616161616323232323232323232323232326464646464646464646464646464128128128128
order12222224444444422224444442244444888888244444444448884488
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1
χ31111111111111111111111111-11-11-1-11-1-1-1-1-1-11-1-11111-1-1-1-111-111-1-1
χ41111111111111111111111111-11-11-1-11-1-1-1-1-1-11-1-1-1-1-1-1111111-1-1-111
χ51111111111111111-1-1-11-111111-11111-11111-1-1-1-1-1ii−i−iii−i−i-11-1i−ii−i
χ61111111111111111-1-1-11-111111-11111-11111-1-1-1-1-1−i−iii−i−iii-11-1−ii−ii
χ71111111111111111-1-1-11-11111-1-1-11-1-1-1-1-1-1-111-111ii−i−i−i−iii-111i−i−ii
χ81111111111111111-1-1-11-11111-1-1-11-1-1-1-1-1-1-111-111−i−iiiii−i−i-111−iii−i
χ911111111111-1-1-1-111111111-1-11111-1-1111-1-111-11-11111-1-1-1-1-1-1-1-1-111
χ1011111111111-1-1-1-111111111-1-11111-1-1111-1-111-11-1-1-1-1-11111-1-1-111-1-1
χ1111111111111-1-1-1-111111111-1-1-11-11111-1-111-1-1-1-1111111111-1-11-1-1-1-1
χ1211111111111-1-1-1-111111111-1-1-11-11111-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-111111
χ1311111111111-1-1-1-11-1-1-11-111-1-11-111-1-1-111-1-1-1-11-11ii−i−i−i−iii1-11−iii−i
χ1411111111111-1-1-1-11-1-1-11-111-1-11-111-1-1-111-1-1-1-11-11−i−iiiii−i−i1-11i−i−ii
χ1511111111111-1-1-1-11-1-1-11-111-1-1-1-1-1111-1-1-1111111-1ii−i−iii−i−i1-1-1−ii−ii
χ1611111111111-1-1-1-11-1-1-11-111-1-1-1-1-1111-1-1-1111111-1−i−iii−i−iii1-1-1i−ii−i
χ17222222222220000222222-2-2000-20-222-200-2-2000020000000000-20000
χ18222222222220000222222-2-2000-20-2-2-2-200220000-2000000000020000
χ192222222222200002-2-2-22-2-2-200020-222200-2-20000-2000000000020000
χ202222222222200002-2-2-22-2-2-200020-2-2-220022000020000000000-20000
χ21222222222220000-222-2-2-2-2-2002-222002-2-200-2-2020000000000000000
χ22222222222220000-222-2-2-2-2-200-2-2-220022200220-20000000000000000
χ23222222222220000-2-2-22-22-2-200222200-2-2-200220-20000000000000000
χ24222222222220000-2-2-22-22-2-200-22-2200-22200-2-2020000000000000000
χ25222222222222222-222-2-2-22222020-200-200000020000000000-2-200000
χ26222222222222222-2-2-22-2222220-20-2002000000-200000000002-200000
χ2722222222222-2-2-2-2-222-2-2-222-2-2020-200-2000000-200000000002200000
χ2822222222222-2-2-2-2-2-2-22-2222-2-20-20-200200000020000000000-2200000
χ294444444-4-4-4-4000004-4000000000000000000000002i−2i2i−2i00000000000
χ304444444-4-4-4-4000004-400000000000000000000000−2i2i−2i2i00000000000
χ314444444-4-4-4-400000-44000000000000000000000002-2-2200000000000
χ324444444-4-4-4-400000-4400000000000000000000000-222-200000000000
χ3344444-4-444-4-400004000-40000000004i−4i0000000000000000000000000
χ3444444-4-444-4-400004000-4000000000−4i4i0000000000000000000000000
χ3544444-4-444-4-40000-40004000000000000004i−4i00000000000000000000
χ3644444-4-444-4-40000-4000400000000000000−4i4i00000000000000000000
χ3744444-4-4-4-444000000040-40000000000000000000000002-22-20000000
χ3844444-4-4-4-444000000040-4000000000000000000000000-22-220000000
χ3944444-4-4-4-4440000000-4040000000000000000000000002i−2i−2i2i0000000
χ4044444-4-4-4-4440000000-404000000000000000000000000−2i2i2i−2i0000000
χ41888-8-800008-80000000000000040-40000000000000000000000000000
χ42888-8-800008-800000000000000-4040000000000000000000000000000
χ43888-8-80000-88444400000000-4-40000000000000000000000000000000
χ44888-8-80000-88-4-4-4-400000000440000000000000000000000000000000
χ4588-88-8008-80000000000000000000000000004-4000000000000000000
χ4688-88-8008-8000000000000000000000000000-44000000000000000000
χ4788-88-800-880044-4-4000000004-40000000000000000000000000000000
χ4888-88-800-8800-4-44400000000-440000000000000000000000000000000
χ4988-8-888-800000000000000000000000004-40000000000000000000000
χ5088-8-888-80000000000000000000000000-440000000000000000000000
χ5188-8-88-88000044-4-400000000-440000000000000000000000000000000
χ5288-8-88-880000-4-444000000004-40000000000000000000000000000000
χ5316-16000000000008-80000004-4000000000000000000000000000000000
χ5416-1600000000000-880000004-4000000000000000000000000000000000
χ5516-160000000008-800000000-44000000000000000000000000000000000
χ5616-16000000000-8800000000-44000000000000000000000000000000000

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