C₂×C₄×#261 #88235

order	416
isoclinism	isoclinic class of #261
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product	C₂×C₄×#261
unambiguous semidirect product	D₁₃⋊C₄²

Fitting	C₂×C₄×C₁₃ ⋊ C₄
derived, Sylow	C₁₃ ⋊ C₂×C₄²

108 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 104

A minimal faithful permutation representation — 3 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(416, 202);