C₅×#2397 #10615992

order	640
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅ · Schur multiplier (H₂) = C₂⁶

Aliases

	subgroup	G/H
center	C₂²×C₄×C₅	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁴×C₅
socle	C₂³×C₅	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ G

840 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)(6,7,8,9)(14,15,17,18)(16,19,20,21);(7,9)(10,11)(12,13)(15,18)(19,21);(7,9)(11,13);(14,16,17,20)(15,19,18,21)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(640, 18074);