Finite Group Databasebeta

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C₅×C₂₉×D₇⋊C₉ #32912489

order	18270
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₉×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₂₉×D₇⋊C₉
unambiguous semidirect product	D₇⋊(C₅×C₉×C₂₉)
unambiguous semidirect product	(C₇⋊C₉)⋊(C₂×C₅×C₂₉)
unambiguous semidirect product	(C₅×D₇)⋊(C₉×C₂₉)
unambiguous semidirect product	(D₇×C₂₉)⋊(C₅×C₉)
unambiguous semidirect product	(C₅×D₇×C₂₉)⋊C₉

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₅×C₂₉	AGL(1,𝔽₇)
commutator, hypocenter	C₇	C₂×C₅×C₉×C₂₉
Frattini	C₃	C₅×C₂₉×AGL(1,𝔽₇)
Fitting, socle	C₃×C₅×C₇×C₂₉	C₂×C₃
prime radical	C₃×C₅×D₇×C₂₉	C₃
cosocle	C₃×C₇	C₂×C₃×C₅×C₂₉
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₅×C₂₉

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9135

Conjugacy classes & character table

3045 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×D₂₉×D₇⋊C₉, D₅×C₂₉×D₇⋊C₉, D₇⋊C₉×D₁₄₅, …
maximal normal subgroup of	C₅×D₂₉×D₇⋊C₉, D₅×C₂₉×D₇⋊C₉, D₇⋊C₉×D₁₄₅, …
maximal quotient of	C₅×C₂₉×Dic₇⋊C₉, C₂×C₅×C₂₉×D₇⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18270, 27);