C₇×Dic₁₃ #67241

order	364
isoclinism	isoclinic class of D₁₃
automorphism	Aut(G) = C₂²×C₃×AGL(1,𝔽₁₃) (order 1872) · Inn(G) = D₁₃ · Out(G) = C₂³×C₃²
homology	Abelianization (H₁) = C₄×C₇ · Schur multiplier (H₂) = C₁

Aliases

C₇×Dic₁₃

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

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 364

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(364, 2);