C₂×C₅²×SD₃₂ #13103243

order	1600
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅² · Schur multiplier (H₂) = C₂²×C₅

Aliases

C₂×C₅²×SD₃₂

	subgroup	G/H
center, socle	C₂²×C₅²	D₈
commutator, Frattini, cosocle	C₈	C₂³×C₅²
prime radical	C₂×C₅²×D₈	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅² ◁ C₂×C₄×C₅² ◁ C₂×C₅²×C₈ ◁ G

360 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 800

A minimal faithful permutation representation — 3 generators on 28 points:

(1,2)(19,20,21,22,23);(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18)(24,25,26,27,28);(4,10)(5,17)(6,8)(7,15)(9,13)(12,18)(14,16)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 5595);