Finite Group Databasebeta

← Prev (#31827364) Next (#31827366) →

C₉×D₁₀₀₇ #31827365

order	18126
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₁₀₀₇
unambiguous semidirect product	C₅₃⋊(C₉×D₁₉)

Splittings

Fitting, Hall	C₉×C₁₉×C₅₃ ⋊ C₂
derived, Hall	C₁₉×C₅₃ ⋊ C₂×C₉
Hall	C₉×C₅₃ ⋊ D₁₉
Hall	C₉×C₁₉ ⋊ D₅₃
Sylow	C₅₃ ⋊ C₉×D₁₉
Sylow	C₁₉ ⋊ C₉×D₅₃

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₁₀₀₇
commutator, hypocenter	C₁₉×C₅₃	C₂×C₉
Frattini	C₃	C₃×D₁₀₀₇
Fitting	C₉×C₁₉×C₅₃	C₂
socle, cosocle	C₃×C₁₉×C₅₃	C₂×C₃
prime radical	C₃×D₁₀₀₇	C₃
LCS	G ▷ C₁₉×C₅₃
UCS	C₁ ◁ C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9063

Conjugacy classes & character table

4545 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₁₉×D₅₃, D₉×D₁₀₀₇, D₁₇₁⋊D₅₃, …
maximal normal subgroup of	C₉×D₁₉×D₅₃, D₉×D₁₀₀₇, D₁₇₁⋊D₅₃, …
maximal quotient of	C₉×Dic₁₀₀₇, C₂×C₉×D₁₀₀₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18126, 5);