C₅×#3488 #10619273

order	640
nilpotency class	2
isoclinism	isoclinic class of #3484
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₅ · Schur multiplier (H₂) = C₂⁹

Aliases

	subgroup	G/H
center, socle	C₂²×C₅	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₅
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ G

1658 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 160

A minimal faithful permutation representation — 5 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(640, 21355);