C₅×#24277 #11946997

order	1280
nilpotency class	3
isoclinism	isoclinic class of #24274
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

1608 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 320

A minimal faithful permutation representation — 4 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 17265);