C₅⋊(#127⋊C₃) #91186

order	480
isoclinism	isoclinic class of C₅⋊(#127⋊C₃)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₄

Aliases

unambiguous semidirect product	C₅⋊(#127⋊C₃)
unambiguous semidirect product	#4020⋊C₃

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₄²×C₅	C₂×C₃
Frattini	C₂²	D₅×A₄
socle	C₂²×C₅	C₂×A₄
LCS	G ▷ C₄²×C₅
UCS	C₁

56 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 60

A minimal faithful permutation representation — 2 generators on 17 points:

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

Polycyclic presentation:

2,3,2^2,5,2^2|c^2=fg,d^2=g,c^a=cfg,d^a=dg,e^a=e^4,c^b=cd,d^b=cg,f^b=g,g^b=fg

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 262);