order	144
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = C₂⁵×D₃ (order 192) · Inn(G) = C₂×D₃ · Out(G) = C₂⁴
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₃×(C₂×D₃)⋊C₄
unambiguous semidirect product	(C₂×D₃)⋊(C₃×C₄)

Splittings

Fitting	C₂×C₃²×C₄ ⋊ C₂
Sylow	C₃² ⋊ C₂²⋊C₄

76 conjugacy classes of subgroups.

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(144, 79);