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AGL(1,𝔽₅)×Dic₉ #10623630

order	720
isoclinism	isoclinic class of D₉×AGL(1,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₄

Aliases

direct product	AGL(1,𝔽₅)×Dic₉
unambiguous semidirect product	(C₉×AGL(1,𝔽₅))⋊C₄
unambiguous semidirect product	(C₉⋊AGL(1,𝔽₅))⋊C₄

Splittings

derived, Hall	C₅×C₉ ⋊ C₄²
Sylow	C₉ ⋊ C₄×AGL(1,𝔽₅)
Sylow	C₅ ⋊ C₄×Dic₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₉×AGL(1,𝔽₅)
commutator, hypocenter	C₅×C₉	C₄²
Frattini	C₂×C₃	D₃×AGL(1,𝔽₅)
Fitting	C₂×C₅×C₉	C₂×C₄
socle	C₂×C₃×C₅	C₄×D₃
prime radical	C₂×C₃×D₅	C₂×D₃
cosocle	C₂×C₉×D₅	C₂²
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₂

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 180

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	AGL(1,𝔽₅)×Dic₁₈, #13085170, (C₉⋊AGL(1,𝔽₅))⋊Q₈, …
maximal normal subgroup of	AGL(1,𝔽₅)×Dic₁₈, #13085170, (C₉⋊AGL(1,𝔽₅))⋊Q₈, …
maximal quotient of	AGL(1,𝔽₅)×C₉⋊C₈, #13083911, (C₉⋊AGL(1,𝔽₅))⋊C₈, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(720, 99);