C₅²×#498 #13103235

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

Aliases

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

392 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 1600

A minimal faithful permutation representation — 3 generators on 26 points:

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

maximal subgroup of	C₅⋊D₅×#498, C₅²×#1705, #72221136, …
maximal normal subgroup of	C₅⋊D₅×#498, C₅²×#1705, #72221136, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 5587);