C₂×#3752 #64136

order	288
isoclinism	isoclinic class of #634
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂⁴×C₃

Aliases

Fitting	C₂²×C₃²×C₄ ⋊ C₂
Sylow	C₃² ⋊ C₂×C₂²⋊C₄

396 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 3 generators on 16 points:

(3,4,5)(10,12)(13,14,15,16);(1,2)(4,5)(7,8)(9,10)(11,12);(1,2)(6,7,8)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 784);