M₁₆×SD₃₂ #484065

order	512
nilpotency class	4
isoclinism	isoclinic class of D₄×D₁₆
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁴

Aliases

M₁₆×SD₃₂

483 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 4 generators on 24 points:

(1,2,3,4,5,6,7,8);(2,6)(4,8);(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24);(10,16)(11,23)(12,14)(13,21)(15,19)(18,24)(20,22)

maximal subgroup of	#72260298, #72260313, #72260414, …
maximal normal subgroup of	#72260298, #72260313, #72260414, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 391261);