Finite Group Databasebeta

← Prev (#23780354) Next (#23780356) →

C₅×C₉×D₅×C₂₃ #23780355

order	10350
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₉×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₉×D₅×C₂₃
unambiguous semidirect product	C₅⋊(C₂×C₅×C₉×C₂₃)

Splittings

Fitting, Hall	C₅²×C₉×C₂₃ ⋊ C₂
derived	C₅ ⋊ C₂×C₅×C₉×C₂₃
Hall	C₅²×C₂₃ ⋊ C₂×C₉
Hall	C₅²×C₉ ⋊ C₂×C₂₃
Sylow	C₅² ⋊ C₂×C₉×C₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₉×C₂₃	D₅
commutator, hypocenter	C₅	C₂×C₅×C₉×C₂₃
Frattini	C₃	C₃×C₅×D₅×C₂₃
Fitting	C₅²×C₉×C₂₃	C₂
socle	C₃×C₅²×C₂₃	C₂×C₃
prime radical	C₃×C₅×D₅×C₂₃	C₃
cosocle	C₃×C₅	C₂×C₃×C₅×C₂₃
LCS	G ▷ C₅
UCS	C₁ ◁ C₅×C₉×C₂₃

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4140 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₉×AGL(1,𝔽₅)×C₂₃, C₅×C₉×C₂₃⋊AGL(1,𝔽₅), C₅×C₉×D₅×D₂₃, …
maximal normal subgroup of	C₅×C₉×AGL(1,𝔽₅)×C₂₃, C₅×C₉×C₂₃⋊AGL(1,𝔽₅), C₅×C₉×D₅×D₂₃, …
maximal quotient of	C₅×C₉×Dic₅×C₂₃, C₂×C₅×C₉×D₅×C₂₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10350, 29);