C₃⋊#1042 #64490

order	300
isoclinism	isoclinic class of C₃⋊#1042
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

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

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:

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

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(300, 33);