C₃×Dic₃×A₄ #88977

order	432
isoclinism	isoclinic class of D₃×A₄
automorphism	Aut(G) = C₂×D₃²×S₄ (order 1728) · Inn(G) = D₃×A₄ · Out(G) = C₂²×D₃
homology	Abelianization (H₁) = C₃²×C₄ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₃×Dic₃×A₄
unambiguous semidirect product	C₃⋊(C₃×C₄×A₄)
unambiguous semidirect product	(C₂²×Dic₃)⋊C₃²
unambiguous semidirect product	(C₂²×C₃×Dic₃)⋊C₃

C₂²×C₃ ⋊ C₃²×C₄

136 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 36

A minimal faithful permutation representation — 2 generators on 14 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 624);