SD₁₆×#108 #225751

order	512
nilpotency class	3
isoclinism	isoclinic class of D₈²
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁴

Aliases

602 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:

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

maximal subgroup of	#72309514, #72309531, #72309534, …
maximal normal subgroup of	#72309514, #72309531, #72309534, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 132947);