order	192
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	Aut(G) = C₂⁵×D₄ (order 256) · Inn(G) = D₄ · Out(G) = C₂⁵
homology	Abelianization (H₁) = C₂×C₃×C₈ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₃×D₄⋊C₈
unambiguous semidirect product	D₄⋊(C₃×C₈)

Subgroups

82 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 2 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 131);