Finite Group Databasebeta

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C₅×#4325 #11724903

order	880
isoclinism	isoclinic class of #4323
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₁

Aliases

Splittings

Fitting	C₅×Q₈×C₁₁ ⋊ C₂
Hall	C₅×C₁₁ ⋊ SD₁₆
Sylow	C₁₁ ⋊ C₅×SD₁₆

Subgroups

	subgroup	G/H
center	C₂×C₅	C₂²⋊D₁₁
commutator, cosocle	C₄×C₁₁	C₂²×C₅
Frattini	C₄	C₂×C₅×D₁₁
Fitting	C₅×Q₈×C₁₁	C₂
socle	C₂×C₅×C₁₁	D₄
prime radical	C₅×D₄₄	C₂
hypercenter	C₅×Q₈	D₁₁
hypocenter	C₁₁	C₅×SD₁₆
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×Q₈

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

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₅×#4325, #13182921, #13182922, …
maximal normal subgroup of	D₅×#4325, #13182921, #13182922, …
maximal quotient of	C₅×#66872, C₅×#66873, C₅×#66899, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(880, 71);