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 2-Sylow subgroup of automorphism group |
Log_2 of order of 2-core |
Iso. class of 2-core |
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 four-group
|
nontrivial semidirect product of Z4 and Z4 |
4 |
32 |
SmallGroup(32,27) |
5 |
SmallGroup(32,27) |
5 |
SmallGroup(32,27) |
2 |
Klein four-group
|
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 four-group
|
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 |
Upper-triangular 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 |
Upper-triangular unipotent matrix group:U(4,2) |
6 |
Upper-triangular unipotent matrix group:U(4,2) |
6 |
Upper-triangular unipotent matrix group:U(4,2) |
2 |
Klein four-group
|
direct product of Q8 and Z2 |
12 |
192 |
SmallGroup(192,955) |
6 |
Upper-triangular unipotent matrix group:U(4,2) |
5 |
SmallGroup(32,27) |
2 |
Klein four-group
|
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 four-group
|
elementary abelian group:E16 |
14 |
20160 |
alternating group:A8 |
6 |
Upper-triangular unipotent matrix group:U(4,2) |
0 |
trivial group |
0 |
trivial group
|