C₅×#2677 #10616272

order	640
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅ · Schur multiplier (H₂) = C₂⁵

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

544 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)(7,9)(14,15,18,20)(16,17,21,19);(11,13)(14,16,18,21)(15,19,20,17);(6,7)(8,9)(10,11)(12,13);(6,7)(8,9)(14,17,18,19)(15,16,20,21)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(640, 18354);