Finite Group Databasebeta

← Group #72315022

Character table — Group #72315022

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size112222222444444888888888888888888816161616161616161616161616161616161616161616161632323232323232323232323232323232323232323232646464646464646464646464
order12222222222222222222222222444444442222444444444444444444442444444444444444444444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111
χ911111111111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1
χ1011111111111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-111
χ1111111111111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1-1-11111
χ1211111111111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1111111-1-1-1-1
χ1311111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-1-1-1
χ1411111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-111-1-1-1-11111
χ1511111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111
χ1611111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-11111-1-1
χ17222222222222222222-2-22222-2-2-2-22222-2-200000000-2-2-2-20000000000000000000000000022-2-222-2-2000000000000
χ18222222222222222222-2-22222-2-2-2-22222-2-200000000-2-2-2-200000000000000000000000000-2-222-2-222000000000000
χ19222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000022220000000000000000000000000022-2-2-2-222000000000000
χ20222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000222200000000000000000000000000-2-22222-2-2000000000000
χ2122222222222-222-2-2-2-22-222-2-22-22-222-2-22-20000000022-2-2000000000000000022-2-2000000000000002-20000000000
χ2222222222222-222-2-2-2-22-222-2-22-22-222-2-22-20000000022-2-20000000000000000-2-22200000000000000-220000000000
χ2322222222222-222-2-2-2-22-2-2-2222-22-2-2-2222-200000000-2-222000000000000000022-2-200000000000000-220000000000
χ2422222222222-222-2-2-2-22-2-2-2222-22-2-2-2222-200000000-2-2220000000000000000-2-222000000000000002-20000000000
χ2522222222222-222-2-2-2-2-2222-2-2-22-2222-2-2-2200000000-2-22200000000000022-2-2000000000000000000002-200000000
χ2622222222222-222-2-2-2-2-2222-2-2-22-2222-2-2-2200000000-2-222000000000000-2-22200000000000000000000-2200000000
χ2722222222222-222-2-2-2-2-22-2-222-22-22-2-222-220000000022-2-200000000000022-2-200000000000000000000-2200000000
χ2822222222222-222-2-2-2-2-22-2-222-22-22-2-222-220000000022-2-2000000000000-2-222000000000000000000002-200000000
χ29222222222-2-2-2-2-2-222-22-200002-2-220000-22220022000000-2-2-2-200000000000000002i−2i002i−2i00002i−2i2i−2i000000000000
χ30222222222-2-2-2-2-2-222-22-200002-2-220000-22220022000000-2-2-2-20000000000000000−2i2i00−2i2i0000−2i2i−2i2i000000000000
χ31222222222-2-2-2-2-2-222-22-200002-2-220000-22-2-200-2-2000000222200000000000000002i−2i002i−2i0000−2i2i−2i2i000000000000
χ32222222222-2-2-2-2-2-222-22-200002-2-220000-22-2-200-2-200000022220000000000000000−2i2i00−2i2i00002i−2i2i−2i000000000000
χ33222222222-2-2-2-2-2-222-2-220000-222-200002-20022002200000000-2-2-2-22i2i−2i−2i00000000002i−2i0000002i−2i−2i2i000000000000
χ34222222222-2-2-2-2-2-222-2-220000-222-200002-20022002200000000-2-2-2-2−2i−2i2i2i0000000000−2i2i000000−2i2i2i−2i000000000000
χ35222222222-2-2-2-2-2-222-2-220000-222-200002-200-2-200-2-20000000022222i2i−2i−2i00000000002i−2i000000−2i2i2i−2i000000000000
χ36222222222-2-2-2-2-2-222-2-220000-222-200002-200-2-200-2-2000000002222−2i−2i2i2i0000000000−2i2i0000002i−2i−2i2i000000000000
χ37222-2-22-2-2222-2-2-2-22-22220000-2-2-2-20000222-2002-200000022-2-200002i2i−2i−2i0000000000−2i2i002i−2i2i−2i0000000000000000
χ38222-2-22-2-2222-2-2-2-22-22220000-2-2-2-20000222-2002-200000022-2-20000−2i−2i2i2i00000000002i−2i00−2i2i−2i2i0000000000000000
χ39222-2-22-2-2222-2-2-2-22-22220000-2-2-2-2000022-2200-22000000-2-22200002i2i−2i−2i0000000000−2i2i00−2i2i−2i2i0000000000000000
χ40222-2-22-2-2222-2-2-2-22-22220000-2-2-2-2000022-2200-22000000-2-2220000−2i−2i2i2i00000000002i−2i002i−2i2i−2i0000000000000000
χ41222-2-22-2-2222-2-2-2-22-22-2-2000022220000-2-2002-2002-20000000022-2-20000000000002i−2i00−2i2i2i−2i−2i2i0000000000000000
χ42222-2-22-2-2222-2-2-2-22-22-2-2000022220000-2-2002-2002-20000000022-2-2000000000000−2i2i002i−2i−2i2i2i−2i0000000000000000
χ43222-2-22-2-2222-2-2-2-22-22-2-2000022220000-2-200-2200-2200000000-2-2220000000000002i−2i00−2i2i−2i2i2i−2i0000000000000000
χ44222-2-22-2-2222-2-2-2-22-22-2-2000022220000-2-200-2200-2200000000-2-222000000000000−2i2i002i−2i2i−2i−2i2i0000000000000000
χ45222-2-22-2-22-2-222222-2-22-22222-222-2-2-2-2-2-222-2-222-2-222-22-2-2-22222-2-200000000000000000000000000000000000000
χ46222-2-22-2-22-2-222222-2-22-22222-222-2-2-2-2-2-22-222-2-222-22-22-222-2-2-2-22200000000000000000000000000000000000000
χ47222-2-22-2-22-2-222222-2-22-2-2-2-2-2-222-22222-222-22-22-22-2-22-22-2-222-2-22200000000000000000000000000000000000000
χ48222-2-22-2-22-2-222222-2-22-2-2-2-2-2-222-22222-22-22-22-22-22-22-2222-2-222-2-200000000000000000000000000000000000000
χ49222-2-22-2-22-2-222222-2-2-2222222-2-22-2-2-2-22-200000000-22-2200000000222200000000-2-2-2-22200000000000000000000
χ50222-2-22-2-22-2-222222-2-2-2222222-2-22-2-2-2-22-200000000-22-2200000000-2-2-2-2000000002222-2-200000000000000000000
χ51222-2-22-2-22-2-222222-2-2-22-2-2-2-22-2-2222222-2000000002-22-20000000022220000000022-2-2-2-200000000000000000000
χ52222-2-22-2-22-2-222222-2-2-22-2-2-2-22-2-2222222-2000000002-22-200000000-2-2-2-200000000-2-2222200000000000000000000
χ53222-2-22-2-22-2-2-222-2-2222222-2-2-2-222-2-222-2-2000000002-2-2200000000000000000000000000000000000000002i−2i002i−2i
χ54222-2-22-2-22-2-2-222-2-2222222-2-2-2-222-2-222-2-2000000002-2-220000000000000000000000000000000000000000−2i2i00−2i2i
χ55222-2-22-2-22-2-2-222-2-22222-2-222-2-22222-2-2-2-200000000-222-200000000000000000000000000000000000000002i−2i00−2i2i
χ56222-2-22-2-22-2-2-222-2-22222-2-222-2-22222-2-2-2-200000000-222-20000000000000000000000000000000000000000−2i2i002i−2i
χ57222-2-22-2-22-2-2-222-2-222-2-222-2-222-2-2-2-2222200000000-222-2000000000000000000000000000000000000002-2002-200
χ58222-2-22-2-22-2-2-222-2-222-2-222-2-222-2-2-2-2222200000000-222-200000000000000000000000000000000000000-2200-2200
χ59222-2-22-2-22-2-2-222-2-222-2-2-2-22222-2-222-2-222000000002-2-22000000000000000000000000000000000000002-200-2200
χ60222-2-22-2-22-2-2-222-2-222-2-2-2-22222-2-222-2-222000000002-2-2200000000000000000000000000000000000000-22002-200
χ61444444444-4-44-4-44-4-4444000044-4-40000-4-40000000000000000000000000000000000000000000000000000000000
χ62444444444-4-44-4-44-4-44-4-40000-4-4440000440000000000000000000000000000000000000000000000000000000000
χ63444-4-44-4-44444-4-44-44-44-40000-44-4400004-40000000000000000000000000000000000000000000000000000000000
χ64444-4-44-4-44444-4-44-44-4-4400004-44-40000-440000000000000000000000000000000000000000000000000000000000
χ6544-44-4-44-444-404-4000000004-40000004-400222-2-2-2-2200002-22-22-22-200000000000000000000000000000000000000
χ6644-44-4-44-444-404-4000000004-40000004-400-2-2-22222-20000-22-22-22-2200000000000000000000000000000000000000
χ6744-44-4-44-444-404-400000000-44000000-440022-22-2-22-200002-22-2-22-2200000000000000000000000000000000000000
χ6844-44-4-44-444-404-400000000-44000000-4400-2-22-222-220000-22-222-22-200000000000000000000000000000000000000
χ6944-44-4-44-44-440-440000004-40000004-40000222-2-2-2-220000-22-22-22-2200000000000000000000000000000000000000
χ7044-44-4-44-44-440-440000004-40000004-40000-2-2-22222-200002-22-22-22-200000000000000000000000000000000000000
χ7144-44-4-44-44-440-44000000-44000000-44000022-22-2-22-20000-22-222-22-200000000000000000000000000000000000000
χ7244-44-4-44-44-440-44000000-44000000-440000-2-22-222-2200002-22-2-22-2200000000000000000000000000000000000000
χ7344-4-44-4-4444-40-440000004-4000000-4400002-2-2-2-222200002-2-22-222-200000000000000000000000000000000000000
χ7444-4-44-4-4444-40-440000004-4000000-440000-22222-2-2-20000-222-22-2-2200000000000000000000000000000000000000
χ7544-4-44-4-4444-40-44000000-440000004-400002-222-22-2-200002-2-222-2-2200000000000000000000000000000000000000
χ7644-4-44-4-4444-40-44000000-440000004-40000-22-2-22-2220000-222-2-222-200000000000000000000000000000000000000
χ7744-4-44-4-444-4404-4000000004-4000000-44002-2-2-2-22220000-222-22-2-2200000000000000000000000000000000000000
χ7844-4-44-4-444-4404-4000000004-4000000-4400-22222-2-2-200002-2-22-222-200000000000000000000000000000000000000
χ7944-4-44-4-444-4404-400000000-440000004-4002-222-22-2-20000-222-2-222-200000000000000000000000000000000000000
χ8044-4-44-4-444-4404-400000000-440000004-400-22-2-22-22200002-2-222-2-2200000000000000000000000000000000000000
χ8188888-8-8-8-8000000000000000000000000000000000000000000000000000004i−4i0000000000000000000000000000
χ8288888-8-8-8-800000000000000000000000000000000000000000000000000000−4i4i0000000000000000000000000000
χ83888-8-8-888-800000000000000000000000000000000000000000000000000000004-400000000000000000000000000
χ84888-8-8-888-80000000000000000000000000000000000000000000000000000000-4400000000000000000000000000
χ8588-88-88-88-80000000000000000000000000000000000000000000000000004-4000000000000000000000000000000
χ8688-88-88-88-8000000000000000000000000000000000000000000000000000-44000000000000000000000000000000
χ8788-8-8888-8-800000000000000000000000000000000000000000000000004-400000000000000000000000000000000
χ8888-8-8888-8-80000000000000000000000000000000000000000000000000-4400000000000000000000000000000000
χ8916-16000000000800-80000000000000000000000000000000000000004i−4i4i−4i0000000000000000000000000000000000
χ9016-16000000000800-8000000000000000000000000000000000000000−4i4i−4i4i0000000000000000000000000000000000
χ9116-16000000000-80080000000000000000000000000000000000000004-4-440000000000000000000000000000000000
χ9216-16000000000-8008000000000000000000000000000000000000000-444-40000000000000000000000000000000000

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