C₃×#1042 #64486

order	300
isoclinism	isoclinic class of #1042
automorphism	Aut(G) = C₂×AGL(1,𝔽₅)² (order 800) · Inn(G) = #1042 · Out(G) = C₂×C₄
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

Fitting, socle, Hall	C₃×C₅² ⋊ C₄
derived, Sylow	C₅² ⋊ C₃×C₄

26 conjugacy classes of subgroups.

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 60

A minimal faithful permutation representation — 2 generators on 13 points:

(1,2,3)(5,6)(7,8)(10,13,12,11);(4,5,7,8,6)(9,10,13,11,12)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(300, 29);