Finite Group Databasebeta

← Prev (#19129056) Next (#19129058) →

C₁₃×D₉×C₂₃ #19129057

order	5382
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₃×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×D₉×C₂₃
unambiguous semidirect product	C₉⋊(C₂×C₁₃×C₂₃)

Splittings

Fitting, Hall	C₉×C₁₃×C₂₃ ⋊ C₂
derived, Sylow	C₉ ⋊ C₂×C₁₃×C₂₃
Hall	C₉×C₂₃ ⋊ C₂×C₁₃
Hall	C₉×C₁₃ ⋊ C₂×C₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃×C₂₃	D₉
commutator, hypocenter	C₉	C₂×C₁₃×C₂₃
Frattini	C₃	D₃×C₁₃×C₂₃
Fitting	C₉×C₁₃×C₂₃	C₂
socle	C₃×C₁₃×C₂₃	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₁₃×C₂₃

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1794 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₁₃×D₉×C₂₃, C₁₃×C₂₃×D₄₅, C₇×C₁₃×D₉×C₂₃, …
maximal normal subgroup of	C₅×C₁₃×D₉×C₂₃, C₇×C₁₃×D₉×C₂₃
maximal quotient of	C₅×C₁₃×D₉×C₂₃, C₁₃×C₂₃×D₄₅, C₇×C₁₃×D₉×C₂₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5382, 9);