C₅×#10082 #11932802

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

Aliases

direct product

C₅×#10082

Subgroups

	subgroup	G/H
center, socle	C₂³×C₅	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₅
prime radical	C₂²×C₅×D₄	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ G

590 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 590 conjugacy classes of subgroups — too many to draw. Only its 114 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 — 3 generators on 33 points:

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

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, 3070);