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C₉×D₃₂₅ #19154292

order	5850
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₃₂₅
unambiguous semidirect product	C₂₅⋊(C₉×D₁₃)

Splittings

Fitting, Hall	C₉×C₁₃×C₂₅ ⋊ C₂
derived, Hall	C₁₃×C₂₅ ⋊ C₂×C₉
Hall	C₉×C₂₅ ⋊ D₁₃
Hall	C₉×C₁₃ ⋊ D₂₅
Sylow	C₂₅ ⋊ C₉×D₁₃
Sylow	C₁₃ ⋊ C₉×D₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₃₂₅
commutator, hypocenter	C₁₃×C₂₅	C₂×C₉
Frattini	C₃×C₅	C₃×D₆₅
Fitting	C₉×C₁₃×C₂₅	C₂
socle	C₃×C₅×C₁₃	C₃×D₅
LCS	G ▷ C₁₃×C₂₅
UCS	C₁ ◁ C₉

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1476 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×#13049908, C₉×#13049907, C₉⋊#13049907, …
maximal normal subgroup of	C₉×#13049908, C₉×#13049907, C₉⋊#13049907, …
maximal quotient of	C₉×Dic₃₂₅, C₂×C₉×D₃₂₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5850, 8);