how to count length of grouped array in angular or javascript?

Use .filter if you need to find the length of just one particular group name, or reduce if you need to figure out all of them:

const input = [  
  {
    name: 'hello 1',
    checked: true,
    color:'#1ac3ec',
    group:'first category'
  },
  {
    name: 'hello 2',
    checked: true,
    color:'#7dc55c',
    group:'first category'
  },
  {
    name: 'hello 3',
    checked: true,
    color:'#005073',
    group:'second category'
  },{
    name: 'hello 4',
    checked: true,
    color:'#fbb330',
    group:'second category'
    },{
    name: 'hello 4',
    checked: true,
    color:'#fbb330',
    group:'sole category'
    }
];
const groups = input.reduce((accum, { group }) => {
  accum[group] = (accum[group] || 0) + 1;
  return accum;
}, {});
console.log(groups);

You can do it with plain JavaScript. Use Array#reduce to create a group by categories and then you can simply count the number of elements statements such as:

group['first category'].length

Working demo:

const array = [  
  {
    name: 'hello 1',
    checked: true,
    color:'#1ac3ec',
    group:'first category'
  },
  {
    name: 'hello 2',
    checked: true,
    color:'#7dc55c',
    group:'first category'
  },
  {
    name: 'hello 3',
    checked: true,
    color:'#005073',
    group:'second category'
  },{
    name: 'hello 4',
    checked: true,
    color:'#fbb330',
    group:'second category'
    }
];

const group = array.reduce((acc, item) => {
  if (!acc[item.group]) {
    acc[item.group] = [];
  }
  
  acc[item.group].push(item);
  return acc;
}, {});

console.log(group['first category'].length);
console.log(group['second category'].length);

though lengthy this should be cleaner solution:

var array = [  
  {
    name: 'hello 1',
    checked: true,
    color:'#1ac3ec',
    group:'first category'
  },
  {
    name: 'hello 2',
    checked: true,
    color:'#7dc55c',
    group:'first category'
  },
  {
    name: 'hello 3',
    checked: true,
    color:'#005073',
    group:'second category'
  },{
    name: 'hello 4',
    checked: true,
    color:'#fbb330',
    group:'second category'
    }
];

var name = checked = color = group = 0;
array.forEach(function(item){
if(item.name){
    name++;
}
if(item.checked){
    checked++;
}
if(item.color){
    color++;
}
if(item.group){
    group++;
}
});
console.log(name);
console.log(checked);
console.log(color);
console.log(group);