C₅×#7259 #11929979

order	1280
nilpotency class	4
isoclinism	isoclinic class of #1347
automorphism	?
homology	Abelianization (H₁) = C₄²×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅×#7259

Subgroups

	subgroup	G/H
center, socle	C₂³×C₅	#102
commutator	C₂×C₈	C₄²×C₅
Frattini, cosocle	C₂³×C₈	C₂²×C₅
prime radical	C₂⁴×C₅	SD₁₆
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂³×C₄×C₅ ◁ C₂³×C₅×C₈ ◁ G

342 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 118 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) = 33
transitive degree	μ_t(G) = 640

A minimal faithful permutation representation — 2 generators on 33 points:

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

Conjugacy classes & character table

290 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 247);