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D₅⋊(C₉⋊C₈) #10623649

order	720
isoclinism	isoclinic class of C₉⋊AGL(1,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

unambiguous semidirect product

D₅⋊(C₉⋊C₈)

Splittings

derived, Hall	C₅×C₉ ⋊ C₂×C₈
Sylow	C₉ ⋊ D₅⋊C₈
Sylow	C₅ ⋊ C₂×C₉⋊C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₄	C₉⋊AGL(1,𝔽₅)
commutator, hypocenter	C₅×C₉	C₂×C₈
Frattini	C₂×C₃	C₂×ΓL(1,𝔽₁₆)
Fitting	C₄×C₅×C₉	C₄
socle	C₂×C₃×C₅	C₂×Dic₃
prime radical	C₂×C₃×D₅	Dic₃
cosocle	C₉×Dic₅	C₂²
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₄

66 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 360

Polycyclic presentation:

2^4,3,5,3|a^2=c,b^2=d,c^2=d,e^3=g,e^a=e^2g^2,f^a=f^3,g^a=g^2,f^c=f^4

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	AGL(1,𝔽₅)×C₉⋊C₈, #13083911, #13083916, …
maximal normal subgroup of	AGL(1,𝔽₅)×C₉⋊C₈, #13083911, #13083916, …
maximal quotient of	D₅⋊(C₉⋊C₁₆), #13083978, C₄×C₉⋊#170, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(720, 118);