C₅×#10430 #11933150

order	1280
nilpotency class	3
isoclinism	isoclinic class of #10046
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂⁴

Aliases

	subgroup	G/H
center, socle	C₂³×C₅	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₅
prime radical	C₅×#2537	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ G

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

normal subgroups only

This group has 630 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) = 640

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

(1,2,3,4,5)(7,8)(10,11)(12,14)(13,16)(15,17);(6,7)(8,9)(18,19)(20,22)(21,24)(23,25);(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, 3418);