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C₉×C₂₉×Dic₁₉ #34090588

order	19836
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×C₂₉×Dic₁₉

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₂₉	D₁₉
commutator, hypocenter	C₁₉	C₄×C₉×C₂₉
Frattini	C₂×C₃	C₃×C₂₉×D₁₉
Fitting	C₂×C₉×C₁₉×C₂₉	C₂
socle, prime radical	C₂×C₃×C₁₉×C₂₉	C₂×C₃
cosocle	C₂×C₃×C₁₉	C₂×C₃×C₂₉
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₉×C₂₉

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 19836

Conjugacy classes & character table

5742 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19836, 4);