C₂×#826 #5146

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) = C₂³

Aliases

Fitting	C₂×C₃×D₈ ⋊ C₂
Sylow	C₃ ⋊ C₂×D₁₆

98 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)(7,11)(8,15)(9,16)(12,13)(14,20)(17,21)(18,19);(4,5)(6,7)(8,11)(9,18)(10,14)(12,15)(13,16)(17,20)(19,21);(1,2)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 705);