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C₅²×D₃×C₁₃⋊C₃ #19154366

order	5850
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅² · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅²×D₃×C₁₃⋊C₃
unambiguous semidirect product	C₃⋊(C₂×C₅²×C₁₃⋊C₃)
unambiguous semidirect product	(D₃×C₁₃)⋊(C₃×C₅²)
unambiguous semidirect product	(C₅×D₃×C₁₃)⋊(C₃×C₅)

Splittings

Fitting, socle	C₃×C₅²×C₁₃ ⋊ C₂×C₃
derived	C₃×C₁₃ ⋊ C₂×C₃×C₅²
Hall	C₃×C₅²×C₁₃⋊C₃ ⋊ C₂
Hall	C₅²×C₁₃ ⋊ C₃×D₃
Hall	C₃×C₁₃⋊C₃ ⋊ C₂×C₅²
Sylow	C₁₃ ⋊ C₃×C₅²×D₃

Subgroups

	subgroup	G/H
center, hypercenter	C₅²	D₃×C₁₃⋊C₃
commutator, hypocenter	C₃×C₁₃	C₂×C₃×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₃	C₂×C₃
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₅²

144 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

525 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅²×D₃×D₁₃⋊C₃, C₅×D₃×C₅⋊(D₁₃⋊C₃), C₅×D₃×D₅×C₁₃⋊C₃, …
maximal normal subgroup of	C₅²×D₃×D₁₃⋊C₃, C₅×D₃×C₅⋊(D₁₃⋊C₃), C₅×D₃×D₅×C₁₃⋊C₃, …
maximal quotient of	C₅²×Dic₃×C₁₃⋊C₃, C₂×C₅²×D₃×C₁₃⋊C₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5850, 82);