Dic₃⋊C₄ #210

order	48
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = C₂⁴×D₃ (order 96) · Inn(G) = C₂×D₃ · Out(G) = C₂³
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

Dic₃⋊C₄

C₃ ⋊ C₄⋊C₄

26 conjugacy classes of subgroups.

minimal degree	μ(G) = 11
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 2 generators on 11 points:

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

Polycyclic presentation:

2^4,3|a^2=d,b^2=c,b^a=bd,e^a=e^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(48, 12);