C₅×#23430 #11946150

order	1280
nilpotency class	3
isoclinism	isoclinic class of #23391
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅ · Schur multiplier (H₂) = C₂⁷

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 ◁ C₂²×C₄²×C₅ ◁ G

2706 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)(16,19)(17,20)(18,21);(7,9)(10,11)(12,13)(15,19)(16,17)(20,21);(11,13)(15,20)(16,17)(19,21);(14,16,18,17)(15,19,21,20)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 16418);