C₅×#13419 #11936139

order	1280
nilpotency class	4
isoclinism	isoclinic class of #13343
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂⁴

Aliases

	subgroup	G/H
center, socle	C₂²×C₅	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂²×D₄	C₂³×C₅
prime radical	C₅×#2679	C₂
LCS	G ▷ C₂²×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂³×C₅ ◁ C₂²×C₅×D₄ ◁ G

776 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 776 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

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

A minimal faithful permutation representation — 3 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 6407);