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C₇×C₉×D₅×C₂₉ #32912469

order	18270
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₉×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₉×D₅×C₂₉
unambiguous semidirect product	C₅⋊(C₂×C₇×C₉×C₂₉)

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₉×C₂₉	D₅
commutator, hypocenter	C₅	C₂×C₇×C₉×C₂₉
Frattini	C₃	C₃×C₇×D₅×C₂₉
Fitting	C₅×C₇×C₉×C₂₉	C₂
socle	C₃×C₅×C₇×C₂₉	C₂×C₃
prime radical	C₃×C₇×D₅×C₂₉	C₃
cosocle	C₃×C₅	C₂×C₃×C₇×C₂₉
LCS	G ▷ C₅
UCS	C₁ ◁ C₇×C₉×C₂₉

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9135

Conjugacy classes & character table

7308 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇×C₉×AGL(1,𝔽₅)×C₂₉, C₇×C₉×#10596816, C₉×C₂₉×C₇⋊AGL(1,𝔽₅), …
maximal normal subgroup of	C₇×C₉×AGL(1,𝔽₅)×C₂₉, C₇×C₉×#10596816, C₉×C₂₉×C₇⋊AGL(1,𝔽₅), …
maximal quotient of	C₇×C₉×Dic₅×C₂₉, C₂×C₇×C₉×D₅×C₂₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18270, 7);