C₂×C₅×#535 #10619231

order	640
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₅ · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₅
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

1896 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 160

A minimal faithful permutation representation — 5 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(640, 21313);