C₅×#16551 #11939271

order	1280
nilpotency class	2
isoclinism	isoclinic class of #16249
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅ · Schur multiplier (H₂) = C₂⁴×C₄²

Aliases

	subgroup	G/H
center, socle	C₂⁴×C₅	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₅
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₅ ◁ G

2470 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 4 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 9539);