C₇×#261 #67244

order	364
isoclinism	isoclinic class of #261
automorphism	Aut(G) = C₂×C₃×AGL(1,𝔽₁₃) (order 936) · Inn(G) = #261 · Out(G) = C₂×C₃²
homology	Abelianization (H₁) = C₄×C₇ · Schur multiplier (H₂) = C₁

Aliases

Fitting, socle, Hall	C₇×C₁₃ ⋊ C₄
derived, Sylow	C₁₃ ⋊ C₄×C₇

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 91

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(364, 5);