C₅²×#392 #13103129

order	1600
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅² · Schur multiplier (H₂) = C₂⁵×C₅

Aliases

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

1288 conjugacy classes of subgroups; only the 344 normal subgroups are shown.

normal subgroups only

This group has 1288 conjugacy classes of subgroups — too many to draw. Only its 344 normal subgroups are shown.

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

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 800

A minimal faithful permutation representation — 3 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 5481);