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C₅×C₉×D₂₀₃ #32912468

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

Aliases

direct product	C₅×C₉×D₂₀₃
unambiguous semidirect product	C₂₉⋊(C₅×C₉×D₇)

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₉	D₂₀₃
commutator, hypocenter	C₇×C₂₉	C₂×C₅×C₉
Frattini	C₃	C₃×C₅×D₂₀₃
Fitting	C₅×C₇×C₉×C₂₉	C₂
socle	C₃×C₅×C₇×C₂₉	C₂×C₃
prime radical	C₃×C₅×D₂₀₃	C₃
cosocle	C₃×C₇×C₂₉	C₂×C₃×C₅
LCS	G ▷ C₇×C₂₉
UCS	C₁ ◁ C₅×C₉

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9135

Conjugacy classes & character table

4635 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₉×D₇×D₂₉, C₉×D₅×D₂₀₃, C₉×D₃₅⋊D₂₉, …
maximal normal subgroup of	C₅×C₉×D₇×D₂₉, C₉×D₅×D₂₀₃, C₉×D₃₅⋊D₂₉, …
maximal quotient of	C₅×C₉×Dic₂₀₃, C₂×C₅×C₉×D₂₀₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18270, 6);