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C₄₁×C₅²⋊C₉ #22604335

order	9225
isoclinism	isoclinic class of C₅²⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₉×C₄₁ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₄₁×C₅²⋊C₉
unambiguous semidirect product	C₅²⋊(C₉×C₄₁)
unambiguous semidirect product	(C₅²×C₄₁)⋊C₉

Splittings

derived, Sylow	C₅² ⋊ C₉×C₄₁
Hall	C₅²×C₄₁ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₄₁	C₅²⋊C₃
commutator, hypocenter	C₅²	C₉×C₄₁
Frattini	C₃	C₄₁×C₅²⋊C₃
Fitting, socle	C₃×C₅²×C₄₁	C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃×C₄₁

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1353 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	C₄₁⋊#90646, #49146675, #90646⋊D₄₁, …
maximal subgroup of	C₄₁×#90646, C₄₁⋊#90646, C₄₁×(C₅⋊D₅)⋊C₉, …
maximal normal subgroup of	C₄₁×#90646, C₄₁⋊#90646, C₄₁×(C₅⋊D₅)⋊C₉, …
maximal quotient of	C₂×C₄₁×C₅²⋊C₉, C₄₁×C₂²⋊(C₅²⋊C₉)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9225, 7);