C₅×#10437 #11933157

order	1280
nilpotency class	3
isoclinism	isoclinic class of #10046
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂²

Aliases

	subgroup	G/H
center, socle, prime radical	C₂³×C₅	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₅
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ G

478 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.

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

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 1280

A minimal faithful permutation representation — 3 generators on 25 points:

(1,2,3,4,5)(7,8)(10,11,13,16)(12,14,17,15);(6,7)(8,9)(18,19,21,24)(20,22,25,23);(6,8,9,7)(11,14)(12,17)(15,16)(19,22)(20,25)(23,24)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 3425);