C₂²×C₅×#451 #11983070

order	1280
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₅ · Schur multiplier (H₂) = C₂¹⁰

Aliases

C₂²×C₅×#451

	subgroup	G/H
center, socle	C₂⁴×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
prime radical	C₂⁵×C₅	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₅ ◁ C₂⁴×C₄×C₅ ◁ G

4982 conjugacy classes of subgroups.

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 640

A minimal faithful permutation representation — 5 generators on 29 points:

(1,2)(25,26,27,28,29);(3,4);(5,6)(7,8)(9,10,13,16)(11,17,19,24)(12,20,22,15)(14,21,23,18);(9,11,13,19)(10,14,16,23)(12,21,22,18)(15,24,20,17);(6,8)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 53338);