C₅×#10476 #11933196

order	1280
nilpotency class	3
isoclinism	isoclinic class of #10260
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂³

Aliases

	subgroup	G/H
center, socle	C₂³×C₅	#121
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₅
prime radical	C₂²×C₅×D₄	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ G

506 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 640

A minimal faithful permutation representation — 3 generators on 25 points:

(1,2,3,4,5)(10,11)(12,14)(13,16)(15,17)(18,19,22,24)(20,25,23,21);(6,7)(8,9)(19,20)(21,25)(23,24);(7,9)(11,14)(12,17)(15,16)(18,20,21,19,22,23,25,24)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 3464);