Oracle - Find the group of most consecutive occurrence of a value in a column

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I have a table structure called test_table like this:

Timestamp Value
08:45:45 C 
08:45:59 E 
08:46:52 V 
08:46:59 C 
08:47:09 C 
08:48:00 C 
08:48:30 C 
08:48:55 C 
08:49:45 E 
08:50:45 E 
08:41:45 V 

and so on..

It is a large table and has about 3000 rows. I want to find the section of the table (start and end timestamp) for the longest running occurrence of "C" values. For example in the above case it would be 8:46:59 to 8:48:55. Is there an oracle query to extract that longest set of data from the large table?

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