Group 
GAP ID (second part) 
Order of automorphism group 
Iso. class of automorphism group 
Log_2 of largest power of 2 dividing automorphism group 
Iso. class of 2Sylow subgroup of automorphism group 
Log_2 of order of 2core 
Iso. class of 2core 
Log_2 of order of inner automorphism group 
Iso. class of inner automorphism group

cyclic group:Z16 
1 
8 
direct product of Z4 and Z2 
3 
direct product of Z4 and Z2 
3 
direct product of Z4 and Z2 
0 
trivial group

direct product of Z4 and Z4 
2 
96 
general linear group:GL(2,Z4) 
5 
SmallGroup(32,27) 
4 
elementary abelian group:E16 
0 
trivial group

SmallGroup(16,3) 
3 
32 
SmallGroup(32,27) 
5 
SmallGroup(32,27) 
5 
SmallGroup(32,27) 
2 
Klein fourgroup

nontrivial semidirect product of Z4 and Z4 
4 
32 
SmallGroup(32,27) 
5 
SmallGroup(32,27) 
5 
SmallGroup(32,27) 
2 
Klein fourgroup

direct product of Z8 and Z2 
5 
16 
direct product of D8 and Z2 
4 
direct product of D8 and Z2 
4 
direct product of D8 and Z2 
0 
trivial group

M16 
6 
16 
direct product of D8 and Z2 
4 
direct product of D8 and Z2 
4 
direct product of D8 and Z2 
2 
Klein fourgroup

dihedral group:D16 
7 
32 
holomorph of Z8 
5 
holomorph of Z8 
5 
holomorph of Z8 
3 
dihedral group:D8

semidihedral group:SD16 
8 
16 
direct product of D8 and Z2 
4 
direct product of D8 and Z2 
4 
direct product of D8 and Z2 
3 
dihedral group:D8

generalized quaternion group:Q16 
9 
32 
holomorph of Z8 
5 
holomorph of Z8 
5 
holomorph of Z8 
3 
dihedral group:D8

direct product of Z4 and V4 
10 
192 
SmallGroup(192,1493) 
6 
Uppertriangular unipotent matrix group:U(4,2) 
5 
inner holomorph of D8 (one of the extraspecial groups of order 32) 
0 
trivial group

direct product of D8 and Z2 
11 
64 
Uppertriangular unipotent matrix group:U(4,2) 
6 
Uppertriangular unipotent matrix group:U(4,2) 
6 
Uppertriangular unipotent matrix group:U(4,2) 
2 
Klein fourgroup

direct product of Q8 and Z2 
12 
192 
SmallGroup(192,955) 
6 
Uppertriangular unipotent matrix group:U(4,2) 
5 
SmallGroup(32,27) 
2 
Klein fourgroup

central product of D8 and Z4 
13 
48 
direct product of S4 and Z2 
4 
direct product of D8 and Z2 
3 
elementary abelian group:E8 
2 
Klein fourgroup

elementary abelian group:E16 
14 
20160 
alternating group:A8 
6 
Uppertriangular unipotent matrix group:U(4,2) 
0 
trivial group 
0 
trivial group
