C₅×#2434 #10616029

order	640
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅ · Schur multiplier (H₂) = C₂⁶

Aliases

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

800 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 320

A minimal faithful permutation representation — 4 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(640, 18111);