C₅⋊#1020 #92125

order	480
isoclinism	isoclinic class of C₅⋊#1020
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₂³

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₅×C₂²⋊A₄	C₂
Fitting, socle	C₂⁴×C₅	D₃
LCS	G ▷ C₅×C₂²⋊A₄
UCS	C₁

112 conjugacy classes of subgroups.

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 40

A minimal faithful permutation representation — 2 generators on 13 points:

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

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1201);