C₅×#9931 #11932651

order	1280
nilpotency class	3
isoclinism	isoclinic class of #9930
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂⁴

Aliases

	subgroup	G/H
center, socle	C₂²×C₅	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₅
prime radical	C₅×#3006	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂³×C₄×C₅ ◁ G

792 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 792 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 2919);