C₃×#3633 #87996

order	408
isoclinism	isoclinic class of #3633
automorphism	Aut(G) = C₂×AGL(1,𝔽₁₇) (order 544) · Inn(G) = #3633 · Out(G) = C₂²
homology	Abelianization (H₁) = C₃×C₈ · Schur multiplier (H₂) = C₁

Aliases

Fitting, socle, Hall	C₃×C₁₇ ⋊ C₈
derived, Sylow	C₁₇ ⋊ C₃×C₈

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 51

A minimal faithful permutation representation — 2 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(408, 33);