C₅×D₈×C₁₉ #13095101

order	1520
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

C₅×D₈×C₁₉

	subgroup	G/H
center, socle	C₂×C₅×C₁₉	D₄
commutator, Frattini, cosocle	C₄	C₂²×C₅×C₁₉
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₁₉ ◁ C₄×C₅×C₁₉ ◁ G

44 conjugacy classes of subgroups.

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 760

A minimal faithful permutation representation — 2 generators on 32 points:

(1,2,3,4,5)(6,7,8,9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32);(7,13)(8,12)(9,11)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1520, 85);