C₁₁×#4096 #13183163

order	1760
isoclinism	isoclinic class of #686
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#4096

Splittings

Fitting	C₅×C₁₁×#41 ⋊ C₂
Hall	C₅×C₁₁ ⋊ #135
Sylow	C₅ ⋊ C₁₁×#135

Subgroups

	subgroup	G/H
center	C₄×C₁₁	C₂²⋊D₅
commutator, cosocle	C₄×C₅	C₂³×C₁₁
Frattini	C₄	C₂²×D₅×C₁₁
Fitting	C₅×C₁₁×#41	C₂
socle	C₂×C₅×C₁₁	C₂×D₄
hypercenter	C₁₁×#41	D₅
hypocenter	C₅	C₁₁×#135
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₁₁×#41

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

normal subgroups only

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 972);