order	192
isoclinism	isoclinic class of #204
automorphism	Aut(G) = C₂²×D₃×#3003 (order 3072) · Inn(G) = D₁₂ · Out(G) = C₂⁴×D₄
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

C₄×Dic₁₂

Splittings

C₃ ⋊ C₄×Q₁₆

110 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 192

A minimal faithful permutation representation — 3 generators on 23 points:

(1,2,3)(8,10,17,21,12,19,11,18)(9,13,20,23,15,22,14,16);(2,3)(8,9,12,15)(10,16,19,23)(11,20,17,14)(13,21,22,18);(4,5,6,7)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 257);