Finite Group Databasebeta

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C₁₁×#677 #11724908

order	880
isoclinism	isoclinic class of #677
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

Splittings

Fitting	C₅×C₈×C₁₁ ⋊ C₂
Hall	C₅×C₁₁ ⋊ SD₁₆
Sylow	C₅ ⋊ C₁₁×SD₁₆

Subgroups

	subgroup	G/H
center	C₂×C₁₁	D₂₀
commutator, cosocle	C₄×C₅	C₂²×C₁₁
Frattini	C₄	C₂×D₅×C₁₁
Fitting	C₅×C₈×C₁₁	C₂
socle	C₂×C₅×C₁₁	D₄
prime radical	C₁₁×D₂₀	C₂
hypercenter	C₈×C₁₁	D₅
hypocenter	C₅	C₁₁×SD₁₆
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₁₁ ◁ C₄×C₁₁ ◁ C₈×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)(12,13,15,16,14)(17,18,19,21,20,22,23,24);(13,14)(15,16)(18,21)(19,23)(22,24)

Conjugacy classes & character table

253 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₁₁×#677, #13182666, #13182672, …
maximal normal subgroup of	D₁₁×#677, #13182666, #13182672, …
maximal quotient of	C₁₁×#3949, C₁₁×#3953, C₁₁×#3948, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(880, 76);