C₂×C₂²⋊#157 #64293

order	288
isoclinism	isoclinic class of #3788
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂⁴×C₃

Aliases

Fitting	C₂³×C₃² ⋊ C₄
Sylow	C₃² ⋊ C₂×C₂²⋊C₄

266 conjugacy classes of subgroups.

minimal degree	μ(G) = 12
transitive degree	μ_t(G) = 24

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, 941);