C₂×#216 #943

order	96
isoclinism	isoclinic class of #213
automorphism	Aut(G) = D₃×#3484 (order 768) · Inn(G) = #67 · Out(G) = C₂²×D₄
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

C₃ ⋊ C₂×Q₁₆

60 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(96, 150);