C₂×#1035 #6025

order	200
isoclinism	isoclinic class of #1035
automorphism	Aut(G) = C₂×AGL(1,ℤ/25) (order 1000) · Inn(G) = #1035 · Out(G) = C₂×C₅
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×#1035
unambiguous semidirect product	D₂₅⋊C₄

Fitting	C₂×C₂₅ ⋊ C₄
derived, Sylow	C₂₅ ⋊ C₂×C₄

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 50

A minimal faithful permutation representation — 2 generators on 27 points:

(4,6,7,12)(5,10,11,22)(8,16,17,21)(9,19,20,13)(14,24,25,27)(15,18,23,26);(1,2)(3,4,8,18,15,5,9,6,13,24,10,21,14,25,16,22,27,19,12,20,11,23,26,17,7)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(200, 12);