C₁₁×#689 #11724920

order	880
isoclinism	isoclinic class of #686
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₁×#689

Splittings

Hall	C₅×C₁₁ ⋊ Q₁₆
Sylow	C₅ ⋊ C₁₁×Q₁₆

Subgroups

	subgroup	G/H
center	C₂×C₁₁	C₂²⋊D₅
commutator, cosocle	C₄×C₅	C₂²×C₁₁
Frattini	C₄	C₂×D₅×C₁₁
Fitting	C₅×Q₈×C₁₁	C₂
socle, prime radical	C₂×C₅×C₁₁	D₄
hypercenter	Q₈×C₁₁	D₅
hypocenter	C₅	C₁₁×Q₁₆
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₁₁ ◁ C₄×C₁₁ ◁ Q₈×C₁₁

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 880

A minimal faithful permutation representation — 2 generators on 32 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,16,14)(17,19,21,27)(18,22,24,31)(20,29,30,26)(23,32,28,25);(13,14)(15,16)(17,18,21,24)(19,25,27,32)(20,28,30,23)(22,29,31,26)

Conjugacy classes & character table

187 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₁₁×#689, #13182925, #13182928, …
maximal normal subgroup of	D₁₁×#689, #13182925, #13182928, …
maximal quotient of	C₁₁×#3939, C₁₁×#3942, C₁₁×#3967, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(880, 88);

C11×#689 #11724920

Aliases

Splittings

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₁×#689 #11724920