#1039⋊C₃ #64471

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

Aliases

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

18 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 60

A minimal faithful permutation representation — 2 generators on 19 points:

(1,2,4)(3,6,10,7,5,12)(8,13,15,14,11,9)(16,17,18,19);(1,3,8,14,7)(2,5,11,13,6)(4,9,10,12,15)

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(300, 14);