C₅×#13665 #11936385

order	1280
nilpotency class	5
isoclinism	isoclinic class of #13661
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₅×#13665

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₅
prime radical	C₂³×C₅	D₁₆
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×C₈ ◁ C₂²×C₅×C₁₆ ◁ G

284 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 82 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) = 73
transitive degree	μ_t(G) = 640

A minimal faithful permutation representation — 3 generators on 73 points:

(1,2,3,4,5)(6,7)(8,9)(10,11,16,21)(12,22,26,53)(13,27,32,51)(14,33,36,67)(15,37,35,20)(17,39,42,23)(18,43,46,30)(19,47,49,29)(24,55,56,72)(25,57,38,52)(28,48,62,73)(31,65,64,59)(34,44,68,71)(40,66,69,61)(41,54,50,60)(45,63,58,70);(10,12,16,26)(11,17,21,42)(13,28,32,62)(14,34,36,68)(15,38,35,25)(18,44,46,71)(19,48,49,73)(20,50,37,41)(22,51,53,27)(23,43,39,30)(24,47,56,29)(31,66,64,61)(33,40,67,69)(45,72,58,55)(52,59,57,65)(54,63,60,70);(7,9)

Conjugacy classes & character table

245 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 6653);