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C₂×C₅²×C₁₃⋊C₉ #19154331

order	5850
isoclinism	isoclinic class of C₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₅²×C₉ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₂×C₅²×C₁₃⋊C₉
unambiguous semidirect product	(C₂×C₁₃)⋊(C₅²×C₉)
unambiguous semidirect product	(C₂×C₅×C₁₃)⋊(C₅×C₉)

Splittings

derived, Sylow	C₁₃ ⋊ C₂×C₅²×C₉
Hall	C₂×C₅²×C₁₃ ⋊ C₉
Hall	C₅²×C₁₃ ⋊ C₂×C₉
Hall	C₂×C₁₃ ⋊ C₅²×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅²	C₁₃⋊C₃
commutator, hypocenter	C₁₃	C₂×C₅²×C₉
Frattini	C₃	C₂×C₅²×C₁₃⋊C₃
Fitting, socle	C₂×C₃×C₅²×C₁₃	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₅²

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1050 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅²×Dic₁₃⋊C₉, C₅×Dic₅×C₁₃⋊C₉, C₅×Dic₆₅⋊C₉, …
maximal normal subgroup of	C₅²×Dic₁₃⋊C₉, C₅×Dic₅×C₁₃⋊C₉, C₅×Dic₆₅⋊C₉, …
maximal quotient of	C₄×C₅²×C₁₃⋊C₉, C₂²×C₅²×C₁₃⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5850, 47);