C₅×#10192 #11932912

order	1280
nilpotency class	3
isoclinism	isoclinic class of #10192
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂⁴

Aliases

	subgroup	G/H
center, socle	C₂²×C₅	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₅
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

678 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 3180);