D₃×D₄ #236

order	48
automorphism	Aut(G) = C₂×D₃×D₄ (order 96) · Inn(G) = C₂²×D₃ · Out(G) = C₂²
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

D₃×D₄

Fitting	C₃×D₄ ⋊ C₂
Sylow	C₃ ⋊ C₂×D₄

54 conjugacy classes of subgroups.

minimal degree	μ(G) = 7
transitive degree	μ_t(G) = 12

A minimal faithful permutation representation — 3 generators on 7 points:

(2,4)(5,6,7);(1,2)(3,4);(6,7)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(48, 38);