C₅×#13483 #11936203

order	1280
nilpotency class	4
isoclinism	isoclinic class of #13304
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅×#13483

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₅	C₂×D₈
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₅
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

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

normal subgroups only

This group has 326 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) = 49
transitive degree	μ_t(G) = 1280

A minimal faithful permutation representation — 3 generators on 49 points:

(1,2,3,4,5)(6,7,8,9)(10,11)(12,15)(13,14)(16,17)(18,19)(20,24)(21,25)(22,26)(23,27)(28,42)(29,37)(30,38)(31,39)(32,40)(33,41)(34,44)(35,45)(36,46)(43,48)(47,49);(11,14)(15,17)(18,20,21,29)(19,24,25,37)(22,28,32,46)(23,35,33,31)(26,42,40,36)(27,45,41,39)(30,48,47,34)(38,43,49,44);(7,9)(10,12,13,16)(11,15,14,17)(19,25)(20,28)(22,34)(23,33)(24,36)(26,43)(29,46)(30,31)(32,48)(35,47)(37,42)(38,45)(39,49)(40,44)

Conjugacy classes & character table

260 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 6471);