C₂×C₅×#557 #10619261

order	640
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₅ · Schur multiplier (H₂) = C₂⁸

Aliases

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

1048 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 640

A minimal faithful permutation representation — 5 generators on 23 points:

(1,2)(19,20,21,22,23);(4,7)(8,9)(11,12,14,16)(13,17,18,15);(3,4,6,7)(5,9,10,8);(11,13,14,18)(12,15,16,17);(3,5,6,10)(4,8,7,9)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(640, 21343);