Finite Group Databasebeta

← Prev (#32912466) Next (#32912468) →

C₅×C₉×D₇×C₂₉ #32912467

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

Aliases

C₅×C₉×D₇×C₂₉

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₉×C₂₉	D₇
commutator, hypocenter	C₇	C₂×C₅×C₉×C₂₉
Frattini	C₃	C₃×C₅×D₇×C₂₉
Fitting	C₅×C₇×C₉×C₂₉	C₂
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 ◁ C₅×C₉×C₂₉

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9135

Conjugacy classes & character table

6525 conjugacy classes. The character table is too large to display.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18270, 5);