C₃⋊#3874 #90656

order	450
isoclinism	isoclinic class of C₃⋊#3874
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₃

Aliases

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

32 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 18 points:

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

Polycyclic presentation:

2,3^2,5^2|b^a=b^2,c^a=c^2,e^a=d^4e^4,d^b=de^3,e^b=d^4e^3

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(450, 21);