C₅×#18145 #11940865

order	1280
nilpotency class	3
isoclinism	isoclinic class of #18132
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅ · Schur multiplier (H₂) = C₂⁶

Aliases

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂³×C₄×C₅ ◁ G

1382 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 160

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 11133);