order	192
automorphism	Aut(G) = S₄×B(4,𝔽₂) (order 1536) · Inn(G) = C₂×S₄ · Out(G) = #120
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

direct product	C₂×A₄⋊Q₈
unambiguous semidirect product	(C₂×A₄)⋊Q₈

Subgroups

165 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 14 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 1468);