gap> G:=SmallGroup(1024,1);
<pc group of size 1024 with 10 generators>
gap> Rank(G);
1
gap> PClassPGroup(G);
10
gap> GRPS1024_Heritage(G);
[ 512, 1, 1 ]
gap> H:=SmallGroup(1024,3568); #this is a partially constructed group
<pc group with 0 generators>
gap> PClassPGroup(H);
2
gap> RankPGroup(H);
5
gap> GRPS1024_Heritage(H);
[ 32, 51, 1 ]
gap> K:=SmallGroup(1024,3569); #this is a partially constructed group
<pc group with 0 generators>
gap> PClassPGroup(K);
2
gap> RankPGroup(K);
5
gap> GRPS1024_Heritage(K);
[ 32, 51, 2 ]
#notice that H,K have the same parent group but their age differs

gap> Groups1024Information();
##################  Groups Information  #########################
There are 49487367289 groups of order 1024
They are sorted by rank, p-class, parent group and then age

Group  1				has rank 1 and pclass 10
Group  2				has rank 2 and pclass 3
Groups 3-1912				have rank 2 and pclass 4
Groups 1913-6569			have rank 2 and pclass 5
Groups 6570-8638			have rank 2 and pclass 6
Groups 8639-9077			have rank 2 and pclass 7
Groups 9078-9117			have rank 2 and pclass 8
Groups 9118-9122			have rank 2 and pclass 9
Groups 9123-319435			have rank 3 and pclass 3
Groups 319436-708057			have rank 3 and pclass 4
Groups 708058-781241			have rank 3 and pclass 5
Groups 781242-789631			have rank 3 and pclass 6
Groups 789632-789820			have rank 3 and pclass 7
Groups 789821-789829			have rank 3 and pclass 8
Groups 789830-793395			have rank 4 and pclass 2
Groups 793396-7180625			have rank 4 and pclass 3
Groups 7180626-8792073			have rank 4 and pclass 4
Groups 8792074-8843732			have rank 4 and pclass 5
Groups 8843733-8844822			have rank 4 and pclass 6
Groups 8844823-8844836			have rank 4 and pclass 7
Groups 8844837-387473667		have rank 5 and pclass 2 ## Not Available ##
Groups 387473668-752623856		have rank 5 and pclass 3
Groups 752623857-754063194		have rank 5 and pclass 4
Groups 754063195-754066166		have rank 5 and pclass 5
Groups 754066167-754066184		have rank 5 and pclass 6
Groups 754066185-48452082590		have rank 6 and pclass 2 ## Not Available ##
Groups 48452082591-48760455837	        have rank 6 and pclass 3
Groups 48760455838-48760467931	        have rank 6 and pclass 4
Groups 48760467932-48760467954	        have rank 6 and pclass 5
Groups 48760467955-49487311927	        have rank 7 and pclass 2 ## Not Available ##
Groups 49487311928-49487364283	        have rank 7 and pclass 3
Groups 49487364284-49487364310	        have rank 7 and pclass 4
Groups 49487364311-49487367243	        have rank 8 and pclass 2
Groups 49487367244-49487367275	        have rank 8 and pclass 3
Groups 49487367276-49487367288	        have rank 9 and pclass 2 ## Not Available ##
Group  49487367289                      has rank 10 and pclass 1
This library was created by David Burrell (2022).