C₃×#3874 #90655

order	450
isoclinism	isoclinic class of #3874
automorphism	Aut(G) = C₂×#64480⋊C₂ (order 1200) · Inn(G) = #3874 · Out(G) = C₂×C₄
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

	subgroup	G/H
center, hypercenter	C₃	#3874
commutator, cosocle, hypocenter	C₅²⋊C₃	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅²	D₃
LCS	G ▷ C₅²⋊C₃
UCS	C₁ ◁ C₃

26 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 45

A minimal faithful permutation representation — 2 generators on 18 points:

(1,2,3)(4,10)(5,7,9,16,8,12,15,13,14,17)(6,18);(4,5,7)(6,9,17)(8,13,11)(10,14,16)(12,18,15)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(450, 20);