C₅⋊(#126⋊C₃) #91187

order	480
isoclinism	isoclinic class of C₅⋊(#126⋊C₃)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₂

Aliases

unambiguous semidirect product	C₅⋊(#126⋊C₃)
unambiguous semidirect product	#4022⋊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

40 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 80

A minimal faithful permutation representation — 2 generators on 21 points:

(2,3)(4,5)(7,18,20,11,12,16)(8,14,21,15,13,19)(9,10,17);(1,2,4,5,3)(6,19,17,12)(7,16,11,15)(8,14,20,13)(9,21,10,18)

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 263);