C₅×#13439 #11936159

order	1280
nilpotency class	4
isoclinism	isoclinic class of #13313
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₅×#13439

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅	#466
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₅
prime radical	C₂²×C₅×D₁₆	C₂
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#405 ◁ G

418 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 110 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) = 41
transitive degree	μ_t(G) = 320

A minimal faithful permutation representation — 3 generators on 41 points:

(1,2,3,4,5)(6,7)(8,9)(10,11)(12,23)(13,17)(14,29)(15,32)(16,22)(18,24)(19,27)(20,30)(21,28)(25,40)(26,36)(31,35)(33,38)(34,41)(37,39);(11,17)(12,24)(13,27)(14,30)(15,28)(19,21)(20,32)(22,29)(23,33)(25,41)(26,31)(34,37)(36,40)(38,39);(7,9)(10,12,13,24,28,38,30,41,16,26,14,31,15,25,27,39)(11,18,19,23,32,37,29,40,22,35,20,36,21,34,17,33)

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 6427);