C₅×#24464 #11947184

order	1280
nilpotency class	3
isoclinism	isoclinic class of #24464
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅ · Schur multiplier (H₂) = C₂⁶

Aliases

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂³×C₄×C₅ ◁ G

1600 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 160

A minimal faithful permutation representation — 4 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 17452);