Its just computing the order of a matrix group over integers mod 20 got 
slower, I think:

 ┌───────┐   GAP, Version 4.5.7 of 14-Dec-2012 (free software, GPL)
 │  GAP  │   http://www.gap-system.org
 └───────┘   Architecture: x86_64-unknown-linux-gnu-gcc-default64
 Libs used:  gmp
 Loading the library and packages ...
 Packages:   GAPDoc 1.5.1
 Try '?help' for help. See also  '?copyright' and  '?authors'
gap> M := [
>   [19, 12, 19, 0, 11, 18], 
>   [17, 4, 0, 9, 14, 10], 
>   [11, 5, 14, 0, 11, 17], 
>   [12, 2, 17, 4, 9, 1], 
>   [10, 3, 11, 16, 17, 6], 
>   [7, 8, 10, 6, 2, 2]];;
gap> G := Group([ M*One(ZmodnZ(20)) ]);
<matrix group with 1 generators>
gap> Order(G);
13020
gap> time;
20468


[vbraun@volker-desktop sage-5.5]$ ./sage -gap
    
            #########           ######         ###########           ###  
         #############          ######         ############         ####  
        ##############         ########        #############       #####  
       ###############         ########        #####   ######      #####  
      ######         #         #########       #####    #####     ######  
     ######                   ##########       #####    #####    #######  
     #####                    ##### ####       #####   ######   ########  
     ####                    #####  #####      #############   ###  ####  
     #####     #######       ####    ####      ###########    ####  ####  
     #####     #######      #####    #####     ######        ####   ####  
     #####     #######      #####    #####     #####         #############
      #####      #####     ################    #####         #############
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      ################    ##################   #####                ####  
       ###############    #####        #####   #####                ####  
         #############    #####        #####   #####                ####  
          #########      #####          #####  #####                ####  
                                                                          
     Information at:  http://www.gap-system.org
     Try '?help' for help. See also  '?copyright' and  '?authors'
    
   Loading the library. Please be patient, this may take a while.
GAP4, Version: 4.4.12 of 17-Dec-2008, x86_64-unknown-linux-gnu-gcc
gap> M := [
>   [19, 12, 19, 0, 11, 18], 
>   [17, 4, 0, 9, 14, 10], 
>   [11, 5, 14, 0, 11, 17], 
>   [12, 2, 17, 4, 9, 1], 
>   [10, 3, 11, 16, 17, 6], 
>   [7, 8, 10, 6, 2, 2]];;
gap> G := Group([ M*One(ZmodnZ(20)) ]);
<matrix group with 1 generators>
gap> Order(G);
13020
gap> time;
7566




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