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C₅×#4296 #11719989

order	855
isoclinism	isoclinic class of #4296
automorphism	?
homology	Abelianization (H₁) = C₅×C₉ · Schur multiplier (H₂) = C₁

Aliases

Splittings

Fitting, socle, Hall	C₅×C₁₉ ⋊ C₉
derived, Sylow	C₁₉ ⋊ C₅×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₅	#4296
commutator, hypocenter	C₁₉	C₅×C₉
Frattini	C₁	G
Fitting, socle	C₅×C₁₉	C₉
prime radical	C₅×C₁₉⋊C₃	C₃
cosocle	C₁₉⋊C₃	C₃×C₅
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₅

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 95

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

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

Conjugacy classes & character table

55 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×AGL(1,𝔽₁₉), D₅×#4296, C₅⋊AGL(1,𝔽₁₉), …
maximal normal subgroup of	C₅×AGL(1,𝔽₁₉), D₅×#4296, C₅⋊AGL(1,𝔽₁₉), …
maximal quotient of	C₂×C₅×#4296, C₅×C₂²⋊#4296, C₂₅×#4296, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(855, 3);