C₅×#10104 #11932824

order	1280
nilpotency class	3
isoclinism	isoclinic class of #10104
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂³

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

642 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 642 conjugacy classes of subgroups — too many to draw. Only its 106 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)(6,7)(8,10)(9,12)(11,13)(15,18)(16,20)(19,21);(7,10)(8,13)(11,12)(16,20)(18,21);(6,7)(8,11)(9,12)(10,13)(14,15)(16,21)(17,19)(18,20)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 3092);