A₄×D₈ #5455

order	192
automorphism	Aut(G) = S₄×AGL(1,ℤ/8) (order 768) · Inn(G) = D₄×A₄ · Out(G) = C₂³
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product	A₄×D₈
unambiguous semidirect product	(C₂²×D₈)⋊C₃

C₂²×D₈ ⋊ C₃

93 conjugacy classes of subgroups.

minimal degree	μ(G) = 12
transitive degree	μ_t(G) = 24

A minimal faithful permutation representation — 2 generators on 12 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 1014);