C₂×#1043 #6060

order	200
isoclinism	isoclinic class of #1043
automorphism	Aut(G) = C₂×AGL(2,𝔽₅) (order 24000) · Inn(G) = #1043 · Out(G) = C₂×S₅
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

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

64 conjugacy classes of subgroups.

minimal degree	μ(G) = 12
transitive degree	μ_t(G) = 50

A minimal faithful permutation representation — 3 generators on 12 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(200, 47);