C₂×#3828 #64358

order	288
isoclinism	isoclinic class of #634
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵×C₃

Aliases

Fitting	C₂²×C₃²×C₄ ⋊ C₂
Sylow	C₃² ⋊ C₂×#41

492 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 4 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 1006);