order	192
automorphism	Aut(G) = C₂×D₃×#23900 (order 3072) · Inn(G) = C₂²×D₃ · Out(G) = C₂×D₄²
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂×C₄

Aliases

Dic₃×M₁₆

Splittings

C₃ ⋊ C₄×M₁₆

142 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 3 generators on 15 points:

(6,9)(10,12)(13,14,15);(5,6,7,10,8,9,11,12);(1,2,3,4)(14,15)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 676);