C₅×#3373 #10616968

order	640
nilpotency class	3
isoclinism	isoclinic class of #3264
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅ · Schur multiplier (H₂) = C₂⁴

Aliases

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₅
prime radical	C₅×#459	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄×C₅×Q₈ ◁ G

384 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)(7,10)(11,12)(14,15,18,21)(16,19,17,20);(6,7,9,10)(8,12,13,11)(14,16,18,17)(15,19,21,20);(15,20)(16,17)(19,21);(6,8,9,13)(7,11,10,12)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(640, 19050);