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C₄₁×Dic₁₃⋊C₉ #34062859

order	19188
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₄₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₄₁×Dic₁₃⋊C₉
unambiguous semidirect product	Dic₁₃⋊(C₉×C₄₁)
unambiguous semidirect product	(C₄₁×Dic₁₃)⋊C₉

Splittings

derived, Sylow	C₁₃ ⋊ C₄×C₉×C₄₁
Hall	C₄₁×C₁₃⋊C₉ ⋊ C₄
Hall	C₄₁×Dic₁₃ ⋊ C₉
Hall	C₁₃×C₄₁ ⋊ C₄×C₉
Hall	C₁₃⋊C₉ ⋊ C₄×C₄₁
Hall	Dic₁₃ ⋊ C₉×C₄₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₄₁	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₄×C₉×C₄₁
Frattini	C₂×C₃	C₄₁×D₁₃⋊C₃
Fitting, socle, prime radical	C₂×C₃×C₁₃×C₄₁	C₂×C₃
cosocle	C₂×C₃×C₁₃	C₂×C₃×C₄₁
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₄₁

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 19188

Conjugacy classes & character table

1968 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19188, 11);