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C₃²×C₁₉×Dic₂₉ #34090638

order	19836
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

C₃²×C₁₉×Dic₂₉

Splittings

derived, Sylow	C₂₉ ⋊ C₃²×C₄×C₁₉
Hall	C₃²×C₁₉×C₂₉ ⋊ C₄
Hall	C₁₉×C₂₉ ⋊ C₃²×C₄
Hall	C₃²×C₂₉ ⋊ C₄×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₁₉	D₂₉
commutator, hypocenter	C₂₉	C₃²×C₄×C₁₉
Frattini	C₂	C₃²×C₁₉×D₂₉
Fitting, socle, prime radical	C₂×C₃²×C₁₉×C₂₉	C₂
cosocle	C₂×C₂₉	C₂×C₃²×C₁₉
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₂×C₃²×C₁₉

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 19836

Conjugacy classes & character table

5472 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19836, 54);