C₂²×C₅×#501 #11983376

order	1280
nilpotency class	3
isoclinism	isoclinic class of #468
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₅ · Schur multiplier (H₂) = C₂⁸

Aliases

C₂²×C₅×#501

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₅ ◁ C₂²×C₄²×C₅ ◁ G

2142 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 5 generators on 25 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 53644);