C₇×#595 #90913

order	476
isoclinism	isoclinic class of #595
automorphism	Aut(G) = C₂×C₃×AGL(1,𝔽₁₇) (order 1632) · Inn(G) = #595 · Out(G) = C₂×C₃×C₄
homology	Abelianization (H₁) = C₄×C₇ · Schur multiplier (H₂) = C₁

Aliases

Fitting, socle, Hall	C₇×C₁₇ ⋊ C₄
derived, Sylow	C₁₇ ⋊ C₄×C₇

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 119

A minimal faithful permutation representation — 2 generators on 24 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(476, 5);