C₅⋊(D₁₃⋊C₃) #87610

order	390
isoclinism	isoclinic class of C₅⋊(D₁₃⋊C₃)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	C₅⋊(D₁₃⋊C₃)
unambiguous semidirect product	(C₁₃⋊C₃)⋊D₅
unambiguous semidirect product	D₆₅⋊C₃

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₃	C₂×C₃
LCS	G ▷ C₅×C₁₃
UCS	C₁

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 65

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

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

Polycyclic presentation:

2,3,5,13|c^a=c^4,d^a=d^12,d^b=d^3

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(390, 3);