C₂³×C₅×#41 #10619448

order	640
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₅ · Schur multiplier (H₂) = C₂¹⁴

Aliases

C₂³×C₅×#41

	subgroup	G/H
center	C₂³×C₄×C₅	C₂²
commutator, Frattini, cosocle	C₂	C₂⁶×C₅
socle	C₂⁴×C₅	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₅ ◁ G

6520 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 320

A minimal faithful permutation representation — 6 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(640, 21530);