C₂²×#157 #3848

order	144
isoclinism	isoclinic class of #157
automorphism	Aut(G) = S₄×AΓL(1,𝔽₉) (order 3456) · Inn(G) = #157 · Out(G) = C₂²×S₄
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³×C₃

Aliases

Fitting, socle	C₂²×C₃² ⋊ C₄
derived, Sylow	C₃² ⋊ C₂²×C₄

86 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 10 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(144, 191);