C₄×#208 #4922

order	192
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = D₃×#72219157 (order 6144) · Inn(G) = C₂×D₃ · Out(G) = #4928938
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂×C₄

Aliases

C₃ ⋊ C₄×M₁₆

142 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 3 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 481);