C₃⋊#3928 #90930

order	480
isoclinism	isoclinic class of ΓL(1,𝔽₁₆)
automorphism	Aut(G) = D₃×C₈×AGL(1,𝔽₅) (order 960) · Inn(G) = ΓL(1,𝔽₁₆) · Out(G) = C₂×C₈
homology	Abelianization (H₁) = C₃₂ · Schur multiplier (H₂) = C₁

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₈	ΓL(1,𝔽₁₆)
commutator, hypocenter	C₃×C₅	C₃₂
Fitting	C₃×C₅×C₈	C₄
socle, prime radical	C₂×C₃×C₅	C₁₆
cosocle	C₃×#672	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₈

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 2 generators on 40 points:

(2,3,4,5)(7,8)(9,10,11,15,12,16,19,25,13,17,20,26,22,28,31,35,14,18,21,27,23,29,32,36,24,30,33,37,34,38,39,40);(1,2,5,3,4)(6,7,8)

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 6);