C₂×C₅²×H(5,𝔽₂) #13107899

order	1600
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₅² · Schur multiplier (H₂) = C₂⁹×C₅

Aliases

	subgroup	G/H
center, socle	C₂²×C₅²	C₂⁴
commutator, Frattini, cosocle	C₂	C₂⁵×C₅²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅² ◁ G

3592 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 400

A minimal faithful permutation representation — 5 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 10251);