Finite Group Databasebeta

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C₉×C₃₇×D₂₉ #34064532

order	19314
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₃₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×C₃₇×D₂₉
unambiguous semidirect product	C₂₉⋊(C₂×C₉×C₃₇)

Splittings

Fitting, Hall	C₉×C₂₉×C₃₇ ⋊ C₂
derived, Sylow	C₂₉ ⋊ C₂×C₉×C₃₇
Hall	C₂₉×C₃₇ ⋊ C₂×C₉
Hall	C₉×C₂₉ ⋊ C₂×C₃₇

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₃₇	D₂₉
commutator, hypocenter	C₂₉	C₂×C₉×C₃₇
Frattini	C₃	C₃×C₃₇×D₂₉
Fitting	C₉×C₂₉×C₃₇	C₂
socle	C₃×C₂₉×C₃₇	C₂×C₃
prime radical	C₃×C₃₇×D₂₉	C₃
cosocle	C₃×C₂₉	C₂×C₃×C₃₇
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₉×C₃₇

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9657

Conjugacy classes & character table

5328 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×C₃₇×#1181, C₉×#16864282, C₉×D₂₉×D₃₇, …
maximal normal subgroup of	C₉×C₃₇×#1181, C₉×#16864282, C₉×D₂₉×D₃₇, …
maximal quotient of	C₉×C₃₇×Dic₂₉, C₂×C₉×C₃₇×D₂₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19314, 4);