#4147⋊C₃ #91964

order	480
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, Frattini	C₂	C₂×D₅×A₄
commutator, cosocle, hypocenter	C₅×Q₈	C₂²×C₃
Fitting	C₂×C₅×Q₈	C₂×C₃
socle	C₂×C₅	C₂²×A₄
hypercenter	C₂²	D₅×A₄
LCS	G ▷ C₅×Q₈
UCS	C₁ ◁ C₂ ◁ C₂²

92 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:

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

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1040);