C₅×#35348 #11958068

order	1280
nilpotency class	2
isoclinism	isoclinic class of #35346
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₅ · Schur multiplier (H₂) = C₂⁹

Aliases

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

4922 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 160

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 28336);