C₂×C₅×#1662 #11941705

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×#1662

Subgroups

	subgroup	G/H
center, socle	C₂³×C₅	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₂×C₅×#562	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ G

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

normal subgroups only

This group has 958 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);(3,4,8,12)(5,13,15,18)(6,11,7,10)(9,16,17,14)(19,20,23,26)(21,27,29,34)(22,30,32,25)(24,31,33,28);(3,5)(4,9)(6,16)(7,14)(8,15)(10,18)(11,13)(12,17)(19,21,23,29)(20,24,26,33)(22,31,32,28)(25,34,30,27);(3,5)(4,9)(6,14)(7,16)(8,15)(10,13)(11,18)(12,17)(22,32)(25,30)(27,34)(28,31)

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, 11973);