C₂²×C₅×#496 #11983353

order	1280
nilpotency class	3
isoclinism	isoclinic class of #468
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₅ · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

C₂²×C₅×#496

	subgroup	G/H
center, socle	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

4038 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 640

A minimal faithful permutation representation — 5 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 53621);