C₅×#498 #65661

order	320
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₄

Aliases

	subgroup	G/H
center, socle, prime radical	C₂²×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ G

98 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 320

A minimal faithful permutation representation — 3 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 999);