C₁₁×#4097 #13183164

order	1760
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#4097

Splittings

Hall	C₅×C₁₁ ⋊ #137
Sylow	C₅ ⋊ C₁₁×#137

Subgroups

	subgroup	G/H
center	C₂×C₁₁	C₂×C₂²⋊D₅
commutator, cosocle	C₄×C₅	C₂³×C₁₁
Frattini	C₄	C₂²×D₅×C₁₁
Fitting, prime radical	C₅×C₁₁×#41	C₂
socle	C₂×C₅×C₁₁	C₂×D₄
hypercenter	C₁₁×#41	D₅
hypocenter	C₅	C₁₁×#137
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₁₁×#41

120 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 58 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)(12,13,15,16,14)(18,23)(19,26)(20,28)(22,29)(24,25)(30,31);(17,19)(18,22)(20,27)(21,26)(23,31)(24,29)(25,30)(28,32);(13,14)(15,16)(17,18,21,25)(19,22,26,30)(20,23,28,24)(27,31,32,29)

Conjugacy classes & character table

341 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 973);