C₂×C₄⋊#157 #64285

order	288
isoclinism	isoclinic class of #3788
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³×C₃

Aliases

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

146 conjugacy classes of subgroups.

minimal degree	μ(G) = 12
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 3 generators on 12 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 933);