SD₁₆×M₃₂ #483529

order	512
nilpotency class	3
isoclinism	isoclinic class of D₄×D₈
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈ · Schur multiplier (H₂) = C₂⁴

Aliases

SD₁₆×M₃₂

496 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);(2,4)(3,7)(6,8);(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24);(10,18)(12,20)(14,22)(16,24)

maximal subgroup of	#72309514, #72309529, #72309533, …
maximal normal subgroup of	#72309514, #72309529, #72309533, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 390725);