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C₁₁×#704 #11724972

order	880
isoclinism	isoclinic class of #700
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

Splittings

Hall	C₅×C₁₁ ⋊ M₁₆
Sylow	C₅ ⋊ C₁₁×M₁₆

Subgroups

	subgroup	G/H
center	C₂×C₁₁	C₂×AGL(1,𝔽₅)
commutator	C₂×C₅	C₂×C₄×C₁₁
Frattini	C₂	C₂×C₁₁×AGL(1,𝔽₅)
Fitting, prime radical	C₂²×C₅×C₁₁	C₄
socle	C₂×C₅×C₁₁	C₂×C₄
cosocle	Dic₅	C₂²×C₁₁
hypercenter	C₂²×C₁₁	AGL(1,𝔽₅)
hypocenter	C₅	C₁₁×M₁₆
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂²×C₁₁

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 440

A minimal faithful permutation representation — 2 generators on 24 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,16,15)(18,21)(22,24);(13,14,15,16)(17,18,19,22,20,21,23,24)

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#13182582, #13182583, C₁₁×#4005, …
maximal normal subgroup of	#13182582, #13182583, C₁₁×#4005, …
maximal quotient of	C₁₁×#4002, C₁₁×#4004, C₁₁×C₂²⋊#170, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(880, 140);