C₁₁×#4064 #13183131

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

Aliases

direct product

C₁₁×#4064

Splittings

Fitting	C₅×C₁₁×Q₁₆ ⋊ 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×Q₁₆	C₂
socle	C₂×C₅×C₁₁	C₂×D₄
prime radical	C₁₁×#713	C₂
hypercenter	C₁₁×Q₁₆	D₅
hypocenter	C₅	C₁₁×#137
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₁₁ ◁ C₄×C₁₁ ◁ C₁₁×Q₁₆

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

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, 940);