C₅²×#453 #13103190

order	1600
nilpotency class	3
isoclinism	isoclinic class of #453
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅² · Schur multiplier (H₂) = C₂³×C₅

Aliases

	subgroup	G/H
center, socle	C₂×C₅²	#120
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₅²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅² ◁ C₂×C₄×C₅² ◁ G

672 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.

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

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 200

A minimal faithful permutation representation — 3 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 5542);