C₅×#19747 #11942467

order	1280
nilpotency class	3
isoclinism	isoclinic class of #19745
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅ · Schur multiplier (H₂) = C₂³×C₄

Aliases

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

908 conjugacy classes of subgroups.

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 12735);