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C₁₉×Dic₂₆₁ #34090591

order	19836
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×Dic₂₆₁
unambiguous semidirect product	C₉⋊(C₁₉×Dic₂₉)

Splittings

derived, Hall	C₉×C₂₉ ⋊ C₄×C₁₉
Hall	C₉×C₁₉×C₂₉ ⋊ C₄
Hall	C₁₉×C₂₉ ⋊ Dic₉
Hall	C₉×C₁₉ ⋊ Dic₂₉
Sylow	C₂₉ ⋊ C₁₉×Dic₉
Sylow	C₉ ⋊ C₁₉×Dic₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉	D₂₆₁
commutator, hypocenter	C₉×C₂₉	C₄×C₁₉
Frattini	C₂×C₃	C₁₉×D₈₇
Fitting	C₂×C₉×C₁₉×C₂₉	C₂
socle, prime radical	C₂×C₃×C₁₉×C₂₉	D₃
cosocle	C₂×C₉×C₂₉	C₂×C₁₉
LCS	G ▷ C₉×C₂₉
UCS	C₁ ◁ C₂×C₁₉

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 19836

Conjugacy classes & character table

5016 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19836, 7);