C₂×C₅×B(4,𝔽₂) #10616618

order	640
nilpotency class	3
isoclinism	isoclinic class of B(4,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅ · Schur multiplier (H₂) = C₂⁷

Aliases

	subgroup	G/H
center, socle	C₂²×C₅	#120
commutator, Frattini, cosocle	C₂³	C₂⁴×C₅
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂⁴×C₅ ◁ G

1018 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 80

A minimal faithful permutation representation — 4 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(640, 18700);