C₅²×#492 #13103229

order	1600
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅² · Schur multiplier (H₂) = C₂×C₄×C₅

Aliases

	subgroup	G/H
center, socle	C₂²×C₅²	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₅²
prime radical	C₅²×#127	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅² ◁ C₄²×C₅² ◁ G

568 conjugacy classes of subgroups.

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 5581);