C₂×C₅×#1658 #11941708

order	1280
nilpotency class	3
isoclinism	isoclinic class of #1655
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂×C₅×#1658

Subgroups

	subgroup	G/H
center, socle	C₂³×C₅	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₂×C₅×#127	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ G

882 conjugacy classes of subgroups; only the 238 normal subgroups are shown.

normal subgroups only

This group has 882 conjugacy classes of subgroups — too many to draw. Only its 238 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) = 39
transitive degree	μ_t(G) = 640

A minimal faithful permutation representation — 4 generators on 39 points:

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

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, 11976);