C₃×#1035 #64462

order	300
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) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

Fitting, Hall	C₃×C₂₅ ⋊ C₄
derived, Sylow	C₂₅ ⋊ C₃×C₄

18 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 75

A minimal faithful permutation representation — 2 generators on 28 points:

(2,10,5,4)(3,20,9,8)(6,19,15,14)(7,11,18,17)(12,25,23,22)(13,24,21,16)(26,27,28);(1,2,6,16,13,3,7,4,11,22,8,19,12,23,14,20,25,17,10,18,9,21,24,15,5)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(300, 5);