C₄×#157 #3789

order	144
isoclinism	isoclinic class of #157
automorphism	Aut(G) = D₄×AΓL(1,𝔽₉) (order 1152) · Inn(G) = #157 · Out(G) = C₂²×D₄
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₃×C₄

Aliases

Fitting	C₃²×C₄ ⋊ C₄
derived, Sylow	C₃² ⋊ C₄²

46 conjugacy classes of subgroups.

minimal degree	μ(G) = 10
transitive degree	μ_t(G) = 24

A minimal faithful permutation representation — 2 generators on 10 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(144, 132);