# Capable group of order 32

A group that can be written as $G/Z(G)$ for some group $G$ is called capable. Can someone list the capable groups of order 32?

• What did you tried to do? Do you know which groups of order $32$ exist at all? – Ofir Schnabel Jan 8 '15 at 7:58
• I want to know if the following groups of order 32 are capable? smallgroup(32,6), smallgroup(32,7), smallgroup(32,8), smallgroup(32,43), smallgroup(32,44). Also we know that $D_{32}$ is capable. – M. R. Jan 8 '15 at 9:00
• The quaternion group $Q_{32}$ is not capable. For criteria see also here. – Dietrich Burde Jan 8 '15 at 10:04
• @ Dietrich Burde: What about the other groups? – M. R. Sep 2 '15 at 6:28