C₂×C₅×#3498 #11985515

order	1280
nilpotency class	2
isoclinism	isoclinic class of #3484
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₅ · Schur multiplier (H₂) = C₂¹⁴

Aliases

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₅
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

12982 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 320

A minimal faithful permutation representation — 6 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 55783);