C₁₁×#4061 #13183128

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

Aliases

direct product

C₁₁×#4061

Splittings

Fitting	C₅×C₁₁×SD₁₆ ⋊ C₂
Hall	C₅×C₁₁ ⋊ #137
Sylow	C₅ ⋊ C₁₁×#137

Subgroups

	subgroup	G/H
center	C₂×C₁₁	D₄×D₅
commutator, cosocle	C₄×C₅	C₂³×C₁₁
Frattini	C₄	C₂²×D₅×C₁₁
Fitting	C₅×C₁₁×SD₁₆	C₂
socle	C₂×C₅×C₁₁	C₂×D₄
prime radical	C₁₁×#711	C₂
hypercenter	C₁₁×SD₁₆	D₅
hypocenter	C₅	C₁₁×#137
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₁₁ ◁ C₄×C₁₁ ◁ C₁₁×SD₁₆

120 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 54 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)(19,25)(20,28)(22,29)(26,27)(30,32);(17,19,21,27)(18,22,23,30)(20,25,28,26)(24,32,31,29);(13,14)(15,16)(17,18)(19,22)(20,24)(21,23)(25,32)(26,29)(27,30)(28,31)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 937);