C₅²×#547 #13107405

order	1600
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅² · Schur multiplier (H₂) = C₂⁵×C₅

Aliases

	subgroup	G/H
center, socle	C₂²×C₅²	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₅²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅² ◁ G

1168 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 4 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 9757);