C₂×#828 #5178

order	192
isoclinism	isoclinic class of #826
automorphism	Aut(G) = D₃×#10576928 (order 3072) · Inn(G) = #213 · Out(G) = C₂²×#41
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

Fitting	C₂×C₃×Q₁₆ ⋊ C₂
Sylow	C₃ ⋊ C₂×SD₃₂

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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 737);