How to group list and split every n records?

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C#

LINQ

I would like to know how to group item and split every N record by using LINQ

I have this table contains 22 ITEM01 and each quantity is 10, 2 ITEM02 with quantity 50 for each

# |ITEM  |QUANTITY
==================
1 |ITEM01| 10
2 |ITEM01| 10
3 |ITEM01| 10
.     .     .
.     .     .
22|ITEM01| 10
23|ITEM02| 50
24|ITEM02| 50

How to get the expected result below by using LINQ? (Group by item if count >10, if not, let it shows one by one.

ITEM  |QUANTITY
=================
ITEM01 | 100
ITEM01 | 100
ITEM01 | 10
ITEM01 | 10
ITEM01 | 10
ITEM02 | 50
ITEM02 | 50

I've tried following code, but it cannot achieve

var query =
    items.GroupBy(item => item.Name)
         .SelectMany(g => g.Select((item, index) => new { item, index })
                           .GroupBy(x => x.index / 10)
                           .Select(batch => new Item {
                                 Name = batch.First().item.Name,
                                 Quantity = batch.Sum(x => x.item.Quantity)
                            })).OrderBy(item => item.Name);

Thanks for your help