C₁₁×#4062 #13183129

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

Aliases

direct product

C₁₁×#4062

Splittings

Fitting	C₅×C₁₁×SD₁₆ ⋊ C₂
Hall	C₅×C₁₁ ⋊ #135
Sylow	C₅ ⋊ C₁₁×#135

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
hypercenter	C₁₁×SD₁₆	D₅
hypocenter	C₅	C₁₁×#135
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₁₁ ◁ C₄×C₁₁ ◁ C₁₁×SD₁₆

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

normal subgroups only

This group has 124 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)(17,19,21,27)(18,23,22,25)(20,29,28,26)(24,31,30,32);(18,22)(19,26)(20,28)(23,31)(25,32)(27,29);(13,14)(15,16)(17,18)(19,25)(20,24)(21,22)(23,27)(26,31)(28,30)(29,32)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 938);