C₂×#1044 #6061

order	200
isoclinism	isoclinic class of #1044
automorphism	Aut(G) = C₂×AGL(1,𝔽₅)²⋊C₂ (order 1600) · Inn(G) = #1044 · Out(G) = C₂²×C₄
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂×C₅

Aliases

Fitting, socle	C₂×C₅² ⋊ C₄
derived, Sylow	C₅² ⋊ C₂×C₄

42 conjugacy classes of subgroups.

minimal degree	μ(G) = 12
transitive degree	μ_t(G) = 20

A minimal faithful permutation representation — 2 generators on 12 points:

(4,5,6,7)(9,10,11,12);(1,2)(3,4,5,7,6)(8,9,12,10,11)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(200, 48);