C₃×#239 #3822

order	144
automorphism	Aut(G) = C₂²×D₃×S₄ (order 576) · Inn(G) = C₂²×D₃ · Out(G) = C₂²×D₃
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂²

Aliases

Fitting	C₃²×Q₈ ⋊ C₂
Sylow	C₃² ⋊ #41

86 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 3 generators on 14 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(144, 165);