C₅×#10435 #11933155

order	1280
nilpotency class	3
isoclinism	isoclinic class of #10046
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂³

Aliases

	subgroup	G/H
center, socle	C₂³×C₅	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₅
prime radical	C₂²×C₅×D₄	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ G

546 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 25 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 3423);