C₅×#60558 #11983278

order	1280
nilpotency class	3
isoclinism	isoclinic class of #3003
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₅ · Schur multiplier (H₂) = C₂⁸

Aliases

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
socle	C₂²×C₅	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄²×C₅ ◁ G

2570 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)(6,7)(8,11)(9,10)(12,13)(14,15)(16,18)(17,19)(20,21);(7,10)(11,13);(15,18)(16,21)(19,20);(6,8,9,12)(7,11,10,13);(15,19)(18,20)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 53546);