C₅×#9983 #11932703

order	1280
nilpotency class	3
isoclinism	isoclinic class of #9980
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₅×#9983

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₅
prime radical	C₅×#2815	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂³×C₄×C₅ ◁ G

602 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 37
transitive degree	μ_t(G) = 160

A minimal faithful permutation representation — 3 generators on 37 points:

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 2971);