C₂×C₅×#124 #66190

order	320
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

	subgroup	G/H
center, socle	C₂³×C₅	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁴×C₅
prime radical	C₂²×C₅×D₄	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

330 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 160

A minimal faithful permutation representation — 4 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 1528);