D₅×#226 #91895

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

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅×S₄
commutator, cosocle, hypocenter	C₅×SL(2,𝔽₃)	C₂²
Fitting	C₅×Q₈	C₂×D₃
socle	C₂×C₅	C₂×S₄
prime radical	D₅×SL(2,𝔽₃)	C₂
LCS	G ▷ C₅×SL(2,𝔽₃)
UCS	C₁ ◁ C₂

78 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 971);