C₅×#11669 #11934389

order	1280
nilpotency class	4
isoclinism	isoclinic class of #11669
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅×#11669

Subgroups

	subgroup	G/H
center	C₄×C₅	#418
commutator	C₂×C₈	C₂²×C₄×C₅
Frattini, cosocle	C₄×C₈	C₂³×C₅
socle	C₂×C₅	#1490
prime radical	C₅×#575	C₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₅ ◁ C₂×C₅×C₈ ◁ C₄×C₅×M₁₆ ◁ G

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

normal subgroups only

This group has 360 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.

Full subgroup data →

Presentation

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 80

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

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

Conjugacy classes & character table

230 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	AGL(1,𝔽₅)×#11669
maximal subgroup of	D₅×#11669, C₅×#489347
maximal normal subgroup of	D₅×#11669, C₅×#489347

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 4657);