C₅×#24116 #11946836

order	1280
nilpotency class	3
isoclinism	isoclinic class of #23848
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅ · Schur multiplier (H₂) = C₂⁶

Aliases

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄×C₅×D₄ ◁ G

1434 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 640

A minimal faithful permutation representation — 4 generators on 25 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 17104);