C₂×C₅×H(5,𝔽₂) #66294

order	320
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₅ · Schur multiplier (H₂) = C₂⁹

Aliases

	subgroup	G/H
center, socle	C₂²×C₅	C₂⁴
commutator, Frattini, cosocle	C₂	C₂⁵×C₅
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ G

898 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 5 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 1632);