C₃×D₃×Q₈ #3821

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

C₃×D₃×Q₈

Fitting	C₃²×Q₈ ⋊ C₂
Sylow	C₃² ⋊ C₂×Q₈

82 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(144, 164);