C₅×#13333 #11936053

order	1280
nilpotency class	4
isoclinism	isoclinic class of #13331
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₅×#13333

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅	#459
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₅
prime radical	C₂×C₅×#135	C₂²
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

546 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 122 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)(13,29)(14,32)(15,21)(16,35)(17,22)(18,25)(19,28)(20,24)(26,38)(27,37)(30,36)(31,40)(33,39)(34,41);(7,9)(10,12,17,28)(11,18,22,36)(13,14,31,34)(15,27,16,26)(19,32,23,41)(20,38,39,37)(21,40,35,29)(24,25,33,30);(10,13,17,31)(11,19,22,23)(12,24,28,33)(14,26,34,27)(15,25,16,30)(18,20,36,39)(21,38,35,37)(29,41,40,32)

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, 6321);