C₄²×D₁₃ #88125

order	416
isoclinism	isoclinic class of D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂²×C₄

Aliases

C₄²×D₁₃

Fitting	C₄²×C₁₃ ⋊ C₂
derived, Sylow	C₁₃ ⋊ C₂×C₄²

108 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 208

A minimal faithful permutation representation — 3 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(416, 92);