C₃×#3624 #87968

order	408
isoclinism	isoclinic class of #595
automorphism	Aut(G) = C₂²×AGL(1,𝔽₁₇) (order 1088) · Inn(G) = #595 · Out(G) = C₂²×C₄
homology	Abelianization (H₁) = C₃×C₈ · Schur multiplier (H₂) = C₁

Aliases

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

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 408

A minimal faithful permutation representation — 2 generators on 28 points:

(2,6,4,3)(5,13,9,8)(7,11,10,12)(14,15,17,16)(18,22,24,19,21,25,20,23)(26,27,28);(1,2,5,10,6,11,15,17,13,8,14,16,12,3,7,9,4)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(408, 5);