C₅⋊(#120⋊C₃) #91192

order	480
isoclinism	isoclinic class of C₅⋊(#120⋊C₃)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₂²

Aliases

unambiguous semidirect product	C₅⋊(#120⋊C₃)
unambiguous semidirect product	#4099⋊C₃

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₂⁴×C₅	C₂×C₃
Frattini	C₂²	D₅×A₄
socle	C₂²×C₅	C₂×A₄
LCS	G ▷ C₂⁴×C₅
UCS	C₁

70 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)(8,11,13,12,9,10);(1,2,4,5,3)(7,12)(10,11)

Polycyclic presentation:

2,3,2^4,5|c^a=cef,d^a=df,g^a=g^4,c^b=cd,d^b=c,e^b=f,f^b=ef

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 268);