C₂×#3743 #64109

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

Aliases

Fitting	C₂×C₃²×C₈ ⋊ C₂
Sylow	C₃² ⋊ C₂×M₁₆

204 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)(9,10,11,14,12,13,15,16);(1,2)(4,5)(7,8)(10,13)(14,16);(1,2)(6,7,8)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 757);