C₅×#10428 #11933148

order	1280
nilpotency class	3
isoclinism	isoclinic class of #10078
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅×#10428

Subgroups

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

386 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 41
transitive degree	μ_t(G) = 1280

A minimal faithful permutation representation — 3 generators on 41 points:

(1,2,3,4,5)(7,8)(10,11)(12,16)(13,17)(14,18)(15,19)(20,23)(21,24)(22,25)(26,27,30,34)(28,31,36,41)(29,32,38,33)(35,39,37,40);(6,7)(8,9)(10,12,15,22)(11,16,19,25)(13,21,14,20)(17,24,18,23)(26,28,30,36)(27,31,34,41)(29,37,38,35)(32,40,33,39);(6,8,9,7)(11,17)(12,20)(13,14)(18,19)(21,22)(23,24)(27,32)(29,38)(31,39)(33,34)(35,37)(40,41)

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 3416);