C₅×#10501 #11933221

order	1280
nilpotency class	3
isoclinism	isoclinic class of #10500
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂²

Aliases

	subgroup	G/H
center, socle	C₂²×C₅	#394
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₅
prime radical	C₅×#532	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

440 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 320

A minimal faithful permutation representation — 3 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 3489);