Finite Group Databasebeta

← Group #72315164

Character table — Group #72315164

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1122222224444444444444488888888888888888881616161616161616161616161616161616163232323232323232323232323232323264646464646464646464646464646464
order12222222222222222222222222222222222222444422224444444444444444444444444444444444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ5111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ8111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ911111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ1211111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ1311111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111
χ1411111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ1511111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ1611111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ1722222222222222222222222222222-2-2-2-2-2-2-2-22-2-2-2-20000-2-200000000000022-2-222-2-2000000000000000000000000
χ1822222222222222222222222222222-2-2-2-2-2-2-2-22-2-2-2-20000-2-2000000000000-2-222-2-222000000000000000000000000
χ19222222222222222-2-2-2-2-2-2-2-22-222-2-222222222-2-2-2-2-20000-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ20222222222222222-2-2-2-2-2-2-2-22-222-2-222222222-2-2-2-2-20000-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ21222222222222222-2-2-2-2-2-2-2-22-222-2-2-2-2-2-2-2-2-2-2-2222222-2-22222-2-2-2-2-2-2222200000000000000000000000000000000
χ22222222222222222-2-2-2-2-2-2-2-22-222-2-2-2-2-2-2-2-2-2-2-22222-2-22222-2-2222222-2-2-2-200000000000000000000000000000000
χ2322222222222-2-2-2-22222-2-2-2-22-2-2-2222222-2-2-2-2-222222222-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ2422222222222-2-2-2-22222-2-2-2-22-2-2-2222222-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ2522222222222-2-2-2-22222-2-2-2-22-2-2-222-2-2-2-22222-2-2-2-2-2000022000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2622222222222-2-2-2-22222-2-2-2-22-2-2-222-2-2-2-22222-2-2-2-2-200002200000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2722222222222-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-22-2-2-2-200002200000000000022-2-2-2-222000000000000000000000000
χ2822222222222-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-22-2-2-2-2000022000000000000-2-22222-2-2000000000000000000000000
χ29222222222-2-222-2-222222222-2-22-2-2-222-2-222-2-2-222-2-200002-20000000000000000000000000000002-2002-200000000
χ30222222222-2-222-2-222222222-2-22-2-2-222-2-222-2-2-222-2-200002-2000000000000000000000000000000-2200-2200000000
χ31222222222-2-222-2-222222222-2-22-2-2-2-2-222-2-222-2-2-2220000-2200000000000000000000000000002-2002-20000000000
χ32222222222-2-222-2-222222222-2-22-2-2-2-2-222-2-222-2-2-2220000-220000000000000000000000000000-2200-220000000000
χ33222222222-2-222-2-2-2-2-2-2-2-2-2-2-222-22222-2-222-2-22-2-2220000-220000000000000000000000000000000000002i−2i2i−2i0000
χ34222222222-2-222-2-2-2-2-2-2-2-2-2-2-222-22222-2-222-2-22-2-2220000-22000000000000000000000000000000000000−2i2i−2i2i0000
χ35222222222-2-222-2-2-2-2-2-2-2-2-2-2-222-222-2-222-2-222222-2-200002-200000000000000000000000000000000000000002i−2i2i−2i
χ36222222222-2-222-2-2-2-2-2-2-2-2-2-2-222-222-2-222-2-222222-2-200002-20000000000000000000000000000000000000000−2i2i−2i2i
χ37222222222-2-2-2-2222222-2-2-2-2-22-22-2-222-2-2-2-222222-2-20000-2200000000000000000000000000000000000000002i−2i−2i2i
χ38222222222-2-2-2-2222222-2-2-2-2-22-22-2-222-2-2-2-222222-2-20000-220000000000000000000000000000000000000000−2i2i2i−2i
χ39222222222-2-2-2-2222222-2-2-2-2-22-22-2-2-2-22222-2-22-2-22200002-20000000000000000000000000000000000002i−2i−2i2i0000
χ40222222222-2-2-2-2222222-2-2-2-2-22-22-2-2-2-22222-2-22-2-22200002-2000000000000000000000000000000000000−2i2i2i−2i0000
χ41222222222-2-2-2-222-2-2-2-22222-2-2-222222-2-2-2-222-2-2-22200002-200000000000000000000000000002-200-220000000000
χ42222222222-2-2-2-222-2-2-2-22222-2-2-222222-2-2-2-222-2-2-22200002-20000000000000000000000000000-22002-20000000000
χ43222222222-2-2-2-222-2-2-2-22222-2-2-2222-2-22222-2-2-222-2-20000-220000000000000000000000000000002-200-2200000000
χ44222222222-2-2-2-222-2-2-2-22222-2-2-2222-2-22222-2-2-222-2-20000-22000000000000000000000000000000-22002-200000000
χ452222-2-2-2-22220000000022-2-2-22000000002-22-2-22-22-200220000-2-2000022-2-200002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ462222-2-2-2-22220000000022-2-2-22000000002-22-2-22-22-200220000-2-2000022-2-20000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ472222-2-2-2-22220000000022-2-2-22000000002-22-2-22-22-200-2-20000220000-2-22200002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ482222-2-2-2-22220000000022-2-2-22000000002-22-2-22-22-200-2-20000220000-2-2220000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ492222-2-2-2-22220000000022-2-2-2200000000-22-22-2-22-22220000-2-20022-2-2000000002i−2i−2i2i00002i−2i2i−2i0000000000000000
χ502222-2-2-2-22220000000022-2-2-2200000000-22-22-2-22-22220000-2-20022-2-200000000−2i2i2i−2i0000−2i2i−2i2i0000000000000000
χ512222-2-2-2-22220000000022-2-2-2200000000-22-22-2-22-22-2-200002200-2-222000000002i−2i−2i2i0000−2i2i−2i2i0000000000000000
χ522222-2-2-2-22220000000022-2-2-2200000000-22-22-2-22-22-2-200002200-2-22200000000−2i2i2i−2i00002i−2i2i−2i0000000000000000
χ532222-2-2-2-222200000000-2-222-2-2000000002-22-22-22-22220000-2-200-2-22200002-22-200002-2-2200000000000000000000
χ542222-2-2-2-222200000000-2-222-2-2000000002-22-22-22-22220000-2-200-2-2220000-22-220000-222-200000000000000000000
χ552222-2-2-2-222200000000-2-222-2-2000000002-22-22-22-22-2-20000220022-2-200002-22-20000-222-200000000000000000000
χ562222-2-2-2-222200000000-2-222-2-2000000002-22-22-22-22-2-20000220022-2-20000-22-2200002-2-2200000000000000000000
χ572222-2-2-2-222200000000-2-222-2-200000000-22-2222-22-200220000-2-20000-2-2222-2-2200000000-222-20000000000000000
χ582222-2-2-2-222200000000-2-222-2-200000000-22-2222-22-200220000-2-20000-2-222-222-2000000002-2-220000000000000000
χ592222-2-2-2-222200000000-2-222-2-200000000-22-2222-22-200-2-2000022000022-2-22-2-22000000002-2-220000000000000000
χ602222-2-2-2-222200000000-2-222-2-200000000-22-2222-22-200-2-2000022000022-2-2-222-200000000-222-20000000000000000
χ614444-4-4-4-44-4-40000000044-4-44-4000000004-4-4444-4-4400000000000000000000000000000000000000000000000000
χ624444-4-4-4-44-4-40000000044-4-44-400000000-444-44-444-400000000000000000000000000000000000000000000000000
χ634444-4-4-4-44-4-400000000-4-44444000000004-4-44-4-444-400000000000000000000000000000000000000000000000000
χ644444-4-4-4-44-4-400000000-4-4444400000000-444-4-44-4-4400000000000000000000000000000000000000000000000000
χ6544-4-444-4-4400004400004-44-4000-44-400000000000002-22-2002-22-22-22-22-22-200000000000000000000000000000000
χ6644-4-444-4-4400004400004-44-4000-44-40000000000000-22-2200-22-22-22-22-22-2200000000000000000000000000000000
χ6744-4-444-4-440000440000-44-44000-4-4400000000000002-2-22002-2-22-22-222-22-200000000000000000000000000000000
χ6844-4-444-4-440000440000-44-44000-4-440000000000000-222-200-222-22-22-2-22-2200000000000000000000000000000000
χ6944-4-444-4-440000-4-400004-44-40004-4400000000000002-2-22002-2-222-22-2-22-2200000000000000000000000000000000
χ7044-4-444-4-440000-4-400004-44-40004-440000000000000-222-200-222-2-22-222-22-200000000000000000000000000000000
χ7144-4-444-4-440000-4-40000-44-4400044-400000000000002-22-2002-22-2-22-22-22-2200000000000000000000000000000000
χ7244-4-444-4-440000-4-40000-44-4400044-40000000000000-22-2200-22-222-22-22-22-200000000000000000000000000000000
χ7344-4-4-4-444400440044-4-44-4-4400-400000000000000002-2-2200-222-22-2-22-222-200000000000000000000000000000000
χ7444-4-4-4-444400440044-4-44-4-4400-40000000000000000-222-2002-2-22-222-22-2-2200000000000000000000000000000000
χ7544-4-4-4-4444004400-4-444-444-400-400000000000000002-22-200-22-22-222-2-222-200000000000000000000000000000000
χ7644-4-4-4-4444004400-4-444-444-400-40000000000000000-22-22002-22-22-2-222-2-2200000000000000000000000000000000
χ7744-4-4-4-444400-4-40044-4-4-444-400400000000000000002-2-2200-222-2-222-22-2-2200000000000000000000000000000000
χ7844-4-4-4-444400-4-40044-4-4-444-40040000000000000000-222-2002-2-222-2-22-222-200000000000000000000000000000000
χ7944-4-4-4-444400-4-400-4-4444-4-4400400000000000000002-22-200-22-222-2-222-2-2200000000000000000000000000000000
χ8044-4-4-4-444400-4-400-4-4444-4-440040000000000000000-22-22002-22-2-222-2-222-200000000000000000000000000000000
χ81888-88-88-8-800000000000000000000008-800000000000000000000000000000000000000000000000000000000000
χ82888-88-88-8-80000000000000000000000-8800000000000000000000000000000000000000000000000000000000000
χ83888-8-88-88-80000008-88-80000000000000000000000000000000000000000000000000000000000000000000000000
χ84888-8-88-88-8000000-88-880000000000000000000000000000000000000000000000000000000000000000000000000
χ8588-888-8-88-80000008-8-880000000000000000000000000000000000000000000000000000000000000000000000000
χ8688-888-8-88-8000000-888-80000000000000000000000000000000000000000000000000000000000000000000000000
χ8788-88-888-8-8000000000000000000008-80000000000000000000000000000000000000000000000000000000000000
χ8888-88-888-8-800000000000000000000-880000000000000000000000000000000000000000000000000000000000000
χ8916-1600000008-88-88-800000000000000000000000000000000000000000000000000000000000000000000000000000
χ9016-1600000008-8-88-8800000000000000000000000000000000000000000000000000000000000000000000000000000
χ9116-160000000-888-8-8800000000000000000000000000000000000000000000000000000000000000000000000000000
χ9216-160000000-88-888-800000000000000000000000000000000000000000000000000000000000000000000000000000

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