C₅×#10588 #11933308

order	1280
nilpotency class	3
isoclinism	isoclinic class of #10260
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂²

Aliases

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

386 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 1280

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 3576);