C₅×C₁₁×#137 #13183276

order	1760
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅×C₁₁×#137

Subgroups

	subgroup	G/H
center, socle	C₂×C₅×C₁₁	C₂×D₄
commutator, Frattini, cosocle	C₄	C₂³×C₅×C₁₁
prime radical	C₅×C₁₁×#41	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₁₁ ◁ C₂×C₄×C₅×C₁₁ ◁ G

120 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 80 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) = 32
transitive degree	μ_t(G) = 880

A minimal faithful permutation representation — 3 generators on 32 points:

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

Conjugacy classes & character table

605 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 1085);