C₂×#812 #5097

order	192
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = C₂×D₃×#3025 (order 1536) · Inn(G) = C₂×D₃ · Out(G) = C₂²×#120
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂²

Aliases

C₃ ⋊ C₂×M₃₂

90 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 3 generators on 21 points:

(1,2)(3,4,5)(7,11)(12,17)(13,18)(19,21);(4,5)(6,7,8,12,9,13,14,19,10,11,15,17,16,18,20,21);(1,2)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 656);