C₃×#1044 #64488

order	300
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) = C₃×C₄ · Schur multiplier (H₂) = C₅

Aliases

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

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 30

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(300, 31);