C₃×#208 #3732

order	144
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = C₂²×D₃×D₄ (order 192) · Inn(G) = C₂×D₃ · Out(G) = C₂⁴
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

C₃² ⋊ M₁₆

48 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 24

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(144, 75);