C₃⋊#1039 #64477

order	300
isoclinism	isoclinic class of C₃⋊(C₅⋊D₅)
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₅

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊(C₅⋊D₅)
commutator, hypocenter	C₃×C₅²	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₅²	C₂
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₂

48 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 300

A minimal faithful permutation representation — 3 generators on 17 points:

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

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(300, 20);